Publications of Robert P. Behringer    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds329760,
   Author = {Barés, J and Wang, D and Wang, D and Bertrand, T and O'Hern, CS and Behringer, RP},
   Title = {Local and global avalanches in a two-dimensional sheared
             granular medium},
   Journal = {Physical review. E},
   Volume = {96},
   Number = {5},
   Year = {2017},
   Month = {November},
   url = {http://dx.doi.org/10.1103/PhysRevE.96.052902},
   Doi = {10.1103/PhysRevE.96.052902},
   Key = {fds329760}
}

@article{fds329761,
   Author = {Bester, CS and Behringer, RP},
   Title = {Collisional model of energy dissipation in three-dimensional
             granular impact.},
   Journal = {Physical review. E},
   Volume = {95},
   Number = {3-1},
   Pages = {032906},
   Year = {2017},
   Month = {March},
   url = {http://dx.doi.org/10.1103/physreve.95.032906},
   Abstract = {We study the dynamic process occurring when a granular
             assembly is displaced by a solid impactor. The momentum
             transfer from the impactor to the target is shown to occur
             through sporadic, normal collisions of high force carrying
             grains at the intruder surface. We therefore describe the
             stopping force of the impact through a collisional-based
             model. To verify the model in impact experiments, we
             determine the forces acting on an intruder decelerating
             through a dense granular medium by using high-speed imaging
             of its trajectory. By varying the intruder shape and
             granular target, intruder-grain interactions are inferred
             from the consequent path. As a result, we connect the drag
             to the effect of intruder shape and grain density based on a
             proposed collisional model.},
   Doi = {10.1103/physreve.95.032906},
   Key = {fds329761}
}

@article{fds329765,
   Author = {Zhao, Y and Barés, J and Zheng, H and Behringer,
             R},
   Title = {Tuning strain of granular matter by basal assisted Couette
             shear},
   Journal = {EPJ Web of Conferences},
   Volume = {140},
   Pages = {03049-03049},
   Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
             JY},
   Year = {2017},
   url = {http://dx.doi.org/10.1051/epjconf/201714003049},
   Doi = {10.1051/epjconf/201714003049},
   Key = {fds329765}
}

@article{fds329766,
   Author = {Zhao, Y and Ding, J and Barés, J and Zheng, H and Dierichs, K and Menges,
             A and Behringer, R},
   Title = {Vibrational Collapse of Hexapod Packings},
   Journal = {EPJ Web of Conferences},
   Volume = {140},
   Pages = {06011-06011},
   Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
             JY},
   Year = {2017},
   url = {http://dx.doi.org/10.1051/epjconf/201714006011},
   Doi = {10.1051/epjconf/201714006011},
   Key = {fds329766}
}

@article{fds329762,
   Author = {Wang, D and Zheng, H and Behringer, RP},
   Title = {A Granular System of Ellipses under Linear
             Shear},
   Journal = {EPJ Web of Conferences},
   Volume = {140},
   Pages = {06003-06003},
   Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
             JY},
   Year = {2017},
   url = {http://dx.doi.org/10.1051/epjconf/201714006003},
   Doi = {10.1051/epjconf/201714006003},
   Key = {fds329762}
}

@article{fds329763,
   Author = {Abed Zadeh and A and Barés, J and Behringer, RP},
   Title = {Avalanches in a granular stick-slip experiment: detection
             using wavelets},
   Journal = {EPJ Web of Conferences},
   Volume = {140},
   Pages = {03038-03038},
   Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
             JY},
   Year = {2017},
   url = {http://dx.doi.org/10.1051/epjconf/201714003038},
   Doi = {10.1051/epjconf/201714003038},
   Key = {fds329763}
}

@article{fds329764,
   Author = {Zheng, H and Wang, D and Barés, J and Behringer,
             R},
   Title = {Jamming by compressing a system of granular
             crosses},
   Journal = {EPJ Web of Conferences},
   Volume = {140},
   Pages = {06014-06014},
   Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
             JY},
   Year = {2017},
   url = {http://dx.doi.org/10.1051/epjconf/201714006014},
   Doi = {10.1051/epjconf/201714006014},
   Key = {fds329764}
}

@article{fds322473,
   Author = {Behringer, RP},
   Title = {From Liquid Helium to Granular Materials},
   Journal = {Journal of Low Temperature Physics},
   Volume = {185},
   Number = {3-4},
   Pages = {230-245},
   Year = {2016},
   Month = {November},
   url = {http://dx.doi.org/10.1007/s10909-016-1660-3},
   Doi = {10.1007/s10909-016-1660-3},
   Key = {fds322473}
}

@article{fds303616,
   Author = {Cox, M and Wang, D and Barés, J and Behringer, RP},
   Title = {Self-organized magnetic particles to tune the mechanical
             behavior of a granular system},
   Journal = {EPL (Europhysics Letters)},
   Volume = {115},
   Number = {6},
   Pages = {64003-64003},
   Year = {2016},
   Month = {September},
   url = {http://arxiv.org/abs/1511.02219v1},
   Abstract = {Above a certain density a granular material jams. This
             property can be controlled by either tuning a global
             property, such as the packing fraction or by applying shear
             strain, or at the micro-scale by tuning grain shape,
             inter-particle friction or externally controlled
             organization. Here, we introduce a novel way to change a
             local granular property by adding a weak anisotropic
             magnetic interaction between particles. We measure the
             evolution of the pressure, $P$, and coordination number,
             $Z$, for a packing of 2D photo-elastic disks, subject to
             uniaxial compression. Some of the particles have embedded
             cuboidal magnets. The strength of the magnetic interactions
             between particles are too weak to have a strong direct
             effect on $P$ or $Z$ when the system is jammed. However, the
             magnetic interactions play an important role in the
             evolution of latent force networks when systems containing a
             large enough fraction of the particles with magnets are
             driven through unjammed states. In this case, a
             statistically stable network of magnetic chains
             self-organizes and overlaps with force chains, strengthening
             the granular medium. We believe this property can be used to
             reversibly control mechanical properties of granular
             materials.},
   Doi = {10.1209/0295-5075/115/64003},
   Key = {fds303616}
}

@article{fds303618,
   Author = {Clark, AH and Kondic, L and Behringer, RP},
   Title = {Steady flow dynamics during granular impact.},
   Journal = {Physical review. E},
   Volume = {93},
   Number = {5},
   Pages = {050901},
   Year = {2016},
   Month = {May},
   ISSN = {2470-0045},
   url = {http://hdl.handle.net/10161/10936 Duke open
             access},
   Abstract = {We study experimentally and computationally the dynamics of
             granular flow during impacts where intruders strike a
             collection of disks from above. In the regime where granular
             force dynamics are much more rapid than the intruder motion,
             we find that the particle flow near the intruder is
             proportional to the instantaneous intruder speed; it is
             essentially constant when normalized by that speed. The
             granular flow is nearly divergence free and remains in
             balance with the intruder, despite the latter's rapid
             deceleration. Simulations indicate that this observation is
             insensitive to grain properties, which can be explained by
             the separation of time scales between intergrain force
             dynamics and intruder dynamics. Assuming there is a
             comparable separation of time scales, we expect that our
             results are applicable to a broad class of dynamic or
             transient granular flows. Our results suggest that
             descriptions of static-in-time granular flows might be
             extended or modified to describe these dynamic flows.
             Additionally, we find that accurate grain-grain interactions
             are not necessary to correctly capture the granular flow in
             this regime.},
   Doi = {10.1103/physreve.93.050901},
   Key = {fds303618}
}

@article{fds303615,
   Author = {Zhao, Y and Liu, K and Zheng, M and Barés, J and Dierichs, K and Menges,
             A and Behringer, RP},
   Title = {Packings of 3D stars: stability and structure},
   Journal = {Granular Matter},
   Volume = {18},
   Number = {2},
   Year = {2016},
   Month = {May},
   ISSN = {1434-5021},
   url = {http://hdl.handle.net/10161/10940 Duke open
             access},
   Abstract = {We describe a series of experiments involving the creation
             of cylindrical packings of star-shaped particles, and an
             exploration of the stability of these packings. The stars
             cover a broad range of arm sizes and frictional properties.
             We carried out three different kinds of experiments, all of
             which involve columns that are prepared by raining star
             particles one-by-one into hollow cylinders. As an additional
             part of the protocol, we sometimes vibrated the column
             before removing the confining cylinder. We rate stability in
             terms of r, the ratio of the mass of particles that fall off
             a pile when it collapsed, to the total particle mass. The
             first experiment involved the intrinsic stability of the
             pile when the confining cylinder was removed. The second
             kind of experiment involved adding a uniform load to the top
             of the column, and then determining the collapse properties.
             A third experiment involved testing stability to tipping of
             the piles. We find a stability diagram relating the pile
             height, h, vs. pile diameter, delta, where the stable and
             unstable regimes are separated by a boundary that is roughly
             a power-law in h vs. delta with an exponent that is less
             than one. Increasing friction and vibration both tend to
             stabilize piles, while increasing particle size can
             destabilize the system under certain conditions.},
   Doi = {10.1007/s10035-016-0606-4},
   Key = {fds303615}
}

@article{fds303617,
   Author = {Tang, J and Behringer, RP},
   Title = {Orientation, flow, and clogging in a two-dimensional hopper:
             Ellipses vs. disks},
   Journal = {EPL (Europhysics Letters)},
   Volume = {114},
   Number = {3},
   Pages = {34002-34002},
   Year = {2016},
   Month = {May},
   ISSN = {0295-5075},
   url = {http://hdl.handle.net/10161/10941 Duke open
             access},
   Abstract = {Two-dimensional (2D) hopper flow of disks has been
             extensively studied. Here, we investigate hopper flow of
             ellipses with aspect ratio $\alpha = 2$, and we contrast
             that behavior to the flow of disks. We use a quasi-2D hopper
             containing photoelastic particles to obtain stress/force
             information. We simultaneously measure the particle motion
             and stress. We determine several properties, including
             discharge rates, jamming probabilities, and the number of
             particles in clogging arches. For both particle types, the
             size of the opening, $D$, relative to the size of particles,
             $\ell$ is an important dimensionless measure. The
             orientation of the ellipses plays an important role in flow
             rheology and clogging. The alignment of contacting ellipses
             enhances the probability of forming stable arches. This
             study offers insight for applications involving the flow of
             granular materials consisting of ellipsoidal shapes, and
             possibly other non-spherical shapes.},
   Doi = {10.1209/0295-5075/114/34002},
   Key = {fds303617}
}

@article{fds322474,
   Author = {Tordesillas, A and Pucilowski, S and Lin, Q and Peters, JF and Behringer, RP},
   Title = {Granular vortices: Identification, characterization and
             conditions for the localization of deformation},
   Journal = {Journal of the Mechanics and Physics of Solids},
   Volume = {90},
   Pages = {215-241},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.jmps.2016.02.032},
   Doi = {10.1016/j.jmps.2016.02.032},
   Key = {fds322474}
}

@article{fds303619,
   Author = {Sarkar, S and Bi, D and Zhang, J and Ren, J and Behringer, RP and Chakraborty, B},
   Title = {Shear-induced rigidity of frictional particles: Analysis of
             emergent order in stress space.},
   Journal = {Physical review. E},
   Volume = {93},
   Number = {4-1},
   Pages = {042901},
   Year = {2016},
   Month = {April},
   ISSN = {2470-0045},
   url = {http://hdl.handle.net/10161/10932 Duke open
             access},
   Abstract = {Solids are distinguished from fluids by their ability to
             resist shear. In equilibrium systems, the resistance to
             shear is associated with the emergence of broken
             translational symmetry as exhibited by a nonuniform density
             pattern that is persistent, which in turn results from
             minimizing the free energy. In this work, we focus on a
             class of systems where this paradigm is challenged. We show
             that shear-driven jamming in dry granular materials is a
             collective process controlled by the constraints of
             mechanical equilibrium. We argue that these constraints can
             lead to a persistent pattern in a dual space that encodes
             the statistics of contact forces and the topology of the
             contact network. The shear-jamming transition is marked by
             the appearance of this persistent pattern. We investigate
             the structure and behavior of patterns both in real space
             and the dual space as the system evolves through the
             rigidity transition for a range of packing fractions and in
             two different shear protocols. We show that, in the protocol
             that creates homogeneous jammed states without shear bands,
             measures of shear jamming do not depend on strain and
             packing fraction independently but obey a scaling form with
             a packing-fraction-dependent characteristic strain that goes
             to zero at the isotropic jamming point ϕ_{J}. We
             demonstrate that it is possible to define a
             protocol-independent order parameter in this dual space,
             which provides a quantitative measure of the rigidity of
             shear-jammed states.},
   Doi = {10.1103/physreve.93.042901},
   Key = {fds303619}
}

@article{fds303620,
   Author = {Bertrand, T and Behringer, RP and Chakraborty, B and O'Hern, CS and Shattuck, MD},
   Title = {Protocol dependence of the jamming transition.},
   Journal = {Physical review. E},
   Volume = {93},
   Number = {1},
   Pages = {012901},
   Year = {2016},
   Month = {January},
   ISSN = {2470-0045},
   url = {http://hdl.handle.net/10161/10616 Duke open
             access},
   Abstract = {We propose a theoretical framework for predicting the
             protocol dependence of the jamming transition for
             frictionless spherical particles that interact via repulsive
             contact forces. We study isostatic jammed disk packings
             obtained via two protocols: isotropic compression and simple
             shear. We show that for frictionless systems, all jammed
             packings can be obtained via either protocol. However, the
             probability to obtain a particular jammed packing depends on
             the packing-generation protocol. We predict the average
             shear strain required to jam initially unjammed
             isotropically compressed packings from the density of jammed
             packings, shape of their basins of attraction, and path
             traversed in configuration space. We compare our predictions
             to simulations of shear strain-induced jamming and find
             quantitative agreement. We also show that the packing
             fraction range, over which shear strain-induced jamming
             occurs, tends to zero in the large system limit for
             frictionless packings with overdamped dynamics.},
   Doi = {10.1103/physreve.93.012901},
   Key = {fds303620}
}

@article{fds292207,
   Author = {Mort, P and Michaels, JN and Behringer, RP and Campbell, CS and Kondic,
             L and Kheiripour Langroudi and M and Shattuck, M and Tang, J and Tardos,
             GI and Wassgren, C},
   Title = {Dense granular flow — A collaborative study},
   Journal = {Powder Technology},
   Volume = {284},
   Pages = {571-584},
   Year = {2015},
   Month = {November},
   ISSN = {0032-5910},
   url = {http://hdl.handle.net/10161/10935 Duke open
             access},
   Doi = {10.1016/j.powtec.2015.06.006},
   Key = {fds292207}
}

@article{fds292208,
   Author = {Dijksman, JA and Mukhopadhyay, S and Gaebler, C and Witelski, TP and Behringer, RP},
   Title = {Obtaining self-similar scalings in focusing
             flows.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {92},
   Number = {4},
   Pages = {043016},
   Year = {2015},
   Month = {October},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.92.043016},
   Abstract = {The surface structure of converging thin fluid films
             displays self-similar behavior, as was shown in the work by
             Diez et al. [Q. Appl. Math. 210, 155 (1990)]. Extracting the
             related similarity scaling exponents from either numerical
             or experimental data is nontrivial. Here we provide two such
             methods. We apply them to experimental and numerical data on
             converging fluid films driven by both surface tension and
             gravitational forcing. In the limit of pure gravitational
             driving, we recover Diez' semianalytic result, but our
             methods also allow us to explore the entire regime of mixed
             capillary and gravitational driving, up to entirely
             surface-tension-driven flows. We find scaling forms of
             smoothly varying exponents up to surprisingly small Bond
             numbers. Our experimental results are in reasonable
             agreement with our numerical simulations, which confirm
             theoretically obtained relations between the scaling
             exponents.},
   Doi = {10.1103/physreve.92.043016},
   Key = {fds292208}
}

@article{fds245414,
   Author = {Tordesillas, A and Tobin, ST and Cil, M and Alshibli, K and Behringer,
             RP},
   Title = {Network flow model of force transmission in unbonded and
             bonded granular media},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {91},
   Number = {6},
   Pages = {062204},
   Year = {2015},
   Month = {June},
   ISSN = {1539-3755},
   url = {http://hdl.handle.net/10161/10931 Duke open
             access},
   Abstract = {An established aspect of force transmission in quasistatic
             deformation of granular media is the existence of a dual
             network of strongly versus weakly loaded particles. Despite
             significant interest, the regulation of strong and weak
             forces through the contact network remains poorly
             understood. We examine this aspect of force transmission
             using data on microstructural fabric from: (I)
             three-dimensional discrete element models of grain
             agglomerates of bonded subspheres constructed from in situ
             synchrotron microtomography images of silica sand grains
             under unconfined compression and (II) two-dimensional
             assemblies of unbonded photoelastic circular disks submitted
             to biaxial compression under constant volume. We model force
             transmission as a network flow and solve the maximum
             flow-minimum cost (MFMC) problem, the solution to which
             yields a percolating subnetwork of contacts that transmits
             the "maximum flow" (i.e., the highest units of force) at
             "least cost" (i.e., the dissipated energy from such
             transmission). We find the MFMC describes a two-tier
             hierarchical architecture. At the local level, it
             encapsulates intraconnections between particles in
             individual force chains and in their conjoined 3-cycles,
             with the most common configuration having at least one force
             chain contact experiencing frustrated rotation. At the
             global level, the MFMC encapsulates interconnections between
             force chains. The MFMC can be used to predict most of the
             force chain particles without need for any information on
             contact forces, thereby suggesting the network flow
             framework may have potential broad utility in the modeling
             of force transmission in unbonded and bonded granular
             media.},
   Doi = {10.1103/PhysRevE.91.062204},
   Key = {fds245414}
}

@article{fds245419,
   Author = {Clark, AH and Petersen, AJ and Kondic, L and Behringer,
             RP},
   Title = {Nonlinear force propagation during granular
             impact.},
   Journal = {Physical Review Letters},
   Volume = {114},
   Number = {14},
   Pages = {144502},
   Year = {2015},
   Month = {April},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/physrevlett.114.144502},
   Abstract = {We experimentally study nonlinear force propagation into
             granular material during impact from an intruder, and we
             explain our observations in terms of the nonlinear
             grain-scale force relation. Using high-speed video and
             photoelastic particles, we determine the speed and spatial
             structure of the force response just after impact. We show
             that these quantities depend on a dimensionless parameter,
             M^{'}=t_{c}v_{0}/d, where v_{0} is the intruder speed at
             impact, d is the particle diameter, and t_{c} is the
             collision time for a pair of grains impacting at relative
             speed v_{0}. The experiments access a large range of M^{'}
             by using particles of three different materials. When
             M^{'}≪1, force propagation is chainlike with a speed,
             v_{f}, satisfying v_{f}∝d/t_{c}. For larger M^{'}, the
             force response becomes spatially dense and the force
             propagation speed departs from v_{f}∝d/t_{c},
             corresponding to collective stiffening of a strongly
             compressed packing of grains.},
   Doi = {10.1103/physrevlett.114.144502},
   Key = {fds245419}
}

@article{fds245415,
   Author = {Brodu, N and Dijksman, JA and Behringer, RP},
   Title = {Multiple-contact discrete-element model for simulating dense
             granular media},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {91},
   Number = {3},
   Pages = {032201},
   Year = {2015},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://hdl.handle.net/10161/10933 Duke open
             access},
   Abstract = {This article presents a new force model for performing
             quantitative simulations of dense granular materials.
             Interactions between multiple contacts (MC) on the same
             grain are explicitly taken into account. Our readily
             applicable MC-DEM method retains all the advantages of
             discrete-element method simulations and does not require the
             use of costly finite-element methods. The new model closely
             reproduces our recent experimental measurements, including
             contact force distributions in full 3D, at all compression
             levels of the packing up to the experimental maximum limit
             of 13%. Comparisons with classic simulations using the
             nondeformable spheres approach, as well as with alternative
             models for interactions between multiple contacts, are
             provided. The success of our model, compared to these
             alternatives, demonstrates that interactions between
             multiple contacts on each grain must be included for dense
             granular packings.},
   Doi = {10.1103/PhysRevE.91.032201},
   Key = {fds245415}
}

@article{fds245420,
   Author = {Brodu, N and Dijksman, JA and Behringer, RP},
   Title = {Spanning the scales of granular materials through
             microscopic force imaging.},
   Journal = {Nature Communications},
   Volume = {6},
   Pages = {6361},
   Year = {2015},
   Month = {January},
   url = {http://hdl.handle.net/10161/9502 Duke open
             access},
   Abstract = {If you walk on sand, it supports your weight. How do the
             disordered forces between particles in sand organize, to
             keep you from sinking? This simple question is surprisingly
             difficult to answer experimentally: measuring forces in
             three dimensions, between deeply buried grains, is
             challenging. Here we describe experiments in which we have
             succeeded in measuring forces inside a granular packing
             subject to controlled deformations. We connect the measured
             micro-scale forces to the macro-scale packing force response
             with an averaging, mean field calculation. This calculation
             explains how the combination of packing structure and
             contact deformations produce the observed nontrivial
             mechanical response of the packing, revealing a surprising
             microscopic particle deformation enhancement
             mechanism.},
   Doi = {10.1038/ncomms7361},
   Key = {fds245420}
}

@article{fds292647,
   Author = {Uhl, JT and Pathak, S and Schorlemmer, D and Liu, X and Swindeman, R and Brinkman, BAW and LeBlanc, M and Tsekenis, G and Friedman, N and Behringer, R and Denisov, D and Schall, P and Gu, X and Wright, WJ and Hufnagel, T and Jennings, A and Greer, JR and Liaw, PK and Becker, T and Dresen, G and Dahmen, KA},
   Title = {Universal Quake Statistics: From Compressed Nanocrystals to
             Earthquakes.},
   Journal = {Scientific Reports},
   Volume = {5},
   Pages = {16493},
   Year = {2015},
   Month = {January},
   url = {http://hdl.handle.net/10161/10956 Duke open
             access},
   Abstract = {Slowly-compressed single crystals, bulk metallic glasses
             (BMGs), rocks, granular materials, and the earth all deform
             via intermittent slips or "quakes". We find that although
             these systems span 12 decades in length scale, they all show
             the same scaling behavior for their slip size distributions
             and other statistical properties. Remarkably, the size
             distributions follow the same power law multiplied with the
             same exponential cutoff. The cutoff grows with applied force
             for materials spanning length scales from nanometers to
             kilometers. The tuneability of the cutoff with stress
             reflects "tuned critical" behavior, rather than
             self-organized criticality (SOC), which would imply
             stress-independence. A simple mean field model for
             avalanches of slipping weak spots explains the agreement
             across scales. It predicts the observed slip-size
             distributions and the observed stress-dependent cutoff
             function. The results enable extrapolations from one scale
             to another, and from one force to another, across different
             materials and structures, from nanocrystals to
             earthquakes.},
   Doi = {10.1038/srep16493},
   Key = {fds292647}
}

@article{fds303621,
   Author = {Brodu, N and Dijksman, JA and Behringer, RP},
   Title = {MC-DEM: a novel simulation scheme for modeling dense
             granular media},
   Year = {2014},
   Month = {October},
   url = {http://arxiv.org/abs/1410.6292v1},
   Abstract = {This article presents a new force model for performing
             quantitative simulations of dense granular materials.
             Interactions between multiple contacts (MC) on the same
             grain are explicitly taken into account. Our readily
             applicable method retains all the advantages of discrete
             element method (DEM) simulations and does not require the
             use of costly finite element methods. The new model closely
             reproduces our recent experimental measurements, including
             contact force distributions in full 3D, at all compression
             levels up to the experimental maximum limit of 13\%.
             Comparisons with traditional non-deformable spheres approach
             are provided, as well as with alternative models for
             interactions between multiple contacts. The success of our
             model compared to these alternatives demonstrates that
             interactions between multiple contacts on each grain must be
             included for dense granular packings.},
   Key = {fds303621}
}

@article{fds245424,
   Author = {Zheng, H and Dijksman, JA and Behringer, RP},
   Title = {Shear jamming in granular experiments without basal
             friction},
   Journal = {EPL (Europhysics Letters)},
   Volume = {107},
   Number = {3},
   Pages = {34005-34005},
   Year = {2014},
   Month = {August},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/0295-5075/107/34005},
   Doi = {10.1209/0295-5075/107/34005},
   Key = {fds245424}
}

@article{fds245422,
   Author = {Walker, DM and Tordesillas, A and Ren, J and Dijksman, JA and Behringer,
             RP},
   Title = {Uncovering temporal transitions and self-organization during
             slow aging of dense granular media in the absence of shear
             bands},
   Journal = {EPL (Europhysics Letters)},
   Volume = {107},
   Number = {1},
   Pages = {18005-18005},
   Year = {2014},
   Month = {July},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/0295-5075/107/18005},
   Doi = {10.1209/0295-5075/107/18005},
   Key = {fds245422}
}

@article{fds245423,
   Author = {Behringer, RP and Bi, D and Chakraborty, B and Clark, A and Dijksman, J and Ren, J and Zhang, J},
   Title = {Statistical properties of granular materials near
             jamming},
   Journal = {Journal of statistical mechanics (Online)},
   Volume = {2014},
   Number = {6},
   Pages = {P06004-P06004},
   Year = {2014},
   Month = {June},
   url = {http://dx.doi.org/10.1088/1742-5468/2014/06/P06004},
   Doi = {10.1088/1742-5468/2014/06/P06004},
   Key = {fds245423}
}

@article{fds245427,
   Author = {Coulais, C and Behringer, RP and Dauchot, O},
   Title = {How the ideal jamming point illuminates the world of
             granular media.},
   Journal = {Soft Matter},
   Volume = {10},
   Number = {10},
   Pages = {1519-1536},
   Year = {2014},
   Month = {March},
   ISSN = {1744-683X},
   url = {http://dx.doi.org/10.1039/c3sm51231b},
   Abstract = {The zero temperature properties of frictionless soft spheres
             near the jamming point have been extensively studied both
             numerically and theoretically; these studies provide a
             reliable base for the interpretation of experiments.
             However, recent work by Ikeda et al. showed that, in a
             parameter space of the temperature and packing fraction,
             experiments to date on colloids have been rather far from
             the theoretical scaling regime. An important question is
             then whether theoretical results concerning point-J are
             applicable to any physical/experimental system, including
             granular media, which we consider here. On the surface, such
             a-thermal, frictional systems might appear even further from
             the idealized case of thermal soft spheres. In this work we
             address this question via experiments on shaken granular
             materials near jamming. We have systematically investigated
             such systems over a number of years using hard metallic
             grains. The important feature of the present work is the use
             of much softer grains, cut from photoelastic materials,
             making it possible to determine forces at the grain scale,
             the details of the contact networks and the motion of
             individual grains. Using this new type of particle, we first
             show that the contact network exhibits remarkable dynamics.
             We find strong heterogeneities, which are maximum at the
             packing fraction ϕ*, distinct from and smaller than the
             packing fraction ϕ(†), where the average number of
             contacts per particle, z, starts to increase. In the limit
             of zero mechanical excitation, these two packing fractions
             converge at point J. We also determine dynamics on time
             scales ranging from a small fraction of the shaking cycle to
             thousands of cycles. We can then map the observed system
             behavior onto results from simulations of ideal thermal soft
             spheres. Our results indicate that the ideal jamming point
             indeed illuminates the world of granular
             media.},
   Doi = {10.1039/c3sm51231b},
   Key = {fds245427}
}

@article{fds292209,
   Author = {Walker, DM and Tordesillas, A and Small, M and Behringer, RP and Tse,
             CK},
   Title = {A complex systems analysis of stick-slip dynamics of a
             laboratory fault.},
   Journal = {Chaos},
   Volume = {24},
   Number = {1},
   Pages = {013132},
   Year = {2014},
   Month = {March},
   ISSN = {1054-1500},
   url = {http://hdl.handle.net/10161/10943 Duke open
             access},
   Abstract = {We study the stick-slip behavior of a granular bed of
             photoelastic disks sheared by a rough slider pulled along
             the surface. Time series of a proxy for granular friction
             are examined using complex systems methods to characterize
             the observed stick-slip dynamics of this laboratory fault.
             Nonlinear surrogate time series methods show that the
             stick-slip behavior appears more complex than a periodic
             dynamics description. Phase space embedding methods show
             that the dynamics can be locally captured within a four to
             six dimensional subspace. These slider time series also
             provide an experimental test for recent complex network
             methods. Phase space networks, constructed by connecting
             nearby phase space points, proved useful in capturing the
             key features of the dynamics. In particular, network
             communities could be associated to slip events and the
             ranking of small network subgraphs exhibited a heretofore
             unreported ordering.},
   Doi = {10.1063/1.4868275},
   Key = {fds292209}
}

@article{fds322475,
   Author = {Behringer, R},
   Title = {Granular materials near jamming},
   Journal = {Frontiers in Particle Science and Technology 2014: Particle
             Interactions Applied},
   Pages = {19-42},
   Year = {2014},
   Month = {January},
   ISBN = {9781510817616},
   Key = {fds322475}
}

@article{fds225614,
   Author = {Abram, H. Clark and Alec J. Petersen and R.P.
             Behringer},
   Title = {Collisional Model for Granular Impact Dynamics},
   Journal = {Phys. Rev. E},
   Volume = {89},
   Pages = {012201},
   Year = {2014},
   Key = {fds225614}
}

@article{fds225615,
   Author = {R.P. Behringer and Daping Bi and Bulbul Chakraborty and Abram Clark and Joshua Dijksman and Jie Ren and Jie Zhang},
   Title = {Statistical Properties of Granular Materials near
             Jamming},
   Journal = {J. Stat. Mech.},
   Volume = {6},
   Pages = {P06004},
   Year = {2014},
   Key = {fds225615}
}

@article{fds225618,
   Author = {Somayeh Farhadi and R.P. Behringer},
   Title = {Dynamics of Sheared Ellipses and Circular Disks: Effects of
             Particle Shape},
   Journal = {Phys. Rev. Lett.},
   Volume = {112},
   Pages = {148301},
   Year = {2014},
   Key = {fds225618}
}

@article{fds303624,
   Author = {Clark, AH and Behringer, RP},
   Title = {Jet-induced 2-D crater formation with horizontal symmetry
             breaking},
   Year = {2013},
   Month = {September},
   url = {http://arxiv.org/abs/1309.1062v1},
   Abstract = {We investigate the formation of a crater in a 2-D bed of
             granular material by a jet of impinging gas, motivated by
             the problem of a retrograde rocket landing on a planetary
             surface. The crater is characterized in terms of depth and
             shape as it evolves, as well as by the horizontal position
             of the bottom of the crater. The crater tends to grow
             logarithmically in time, a result which is common in related
             experiments. We also observe a horizontal symmetry breaking
             at certain well-defined conditions which, as we will
             demonstrate, could be of considerable practical concern for
             lunar or planetary landers. We present data on the evolution
             of these asymmetric states and attempt to give insights into
             the mechanism behind the symmetry-breaking
             bifurcation.},
   Doi = {10.1007/s10035-014-0501-9},
   Key = {fds303624}
}

@article{fds303625,
   Author = {Sarkar, S and Bi, D and Zhang, J and Behringer, RP and Chakraborty,
             B},
   Title = {Origin of Rigidity in Dry Granular Solids},
   Volume = {1111},
   Pages = {068301},
   Year = {2013},
   Month = {May},
   url = {http://arxiv.org/abs/1305.3484v2},
   Abstract = {Solids are distinguished from fluids by their ability to
             resist shear. In traditional solids, the resistance to shear
             is associated with the emergence of broken translational
             symmetry as exhibited by a non-uniform density pattern. In
             this work, we focus on the emergence of shear-rigidity in a
             class of solids where this paradigm is challenged. Dry
             granular materials have no energetically or entropically
             preferred density modulations. We show that, in contrast to
             traditional solids, the emergence of shear rigidity in these
             granular solids is a collective process, which is controlled
             solely by boundary forces, the constraints of force and
             torque balance, and the positivity of the contact forces. We
             develop a theoretical framework based on these constraints,
             which connects rigidity to broken translational symmetry in
             the space of forces, not positions of grains. We apply our
             theory to experimentally generated shear-jammed (SJ) states
             and show that these states are indeed characterized by a
             persistent, non-uniform density modulation in force space,
             which emerges at the shear-jamming transition.},
   Doi = {10.1103/PhysRevLett.111.068301},
   Key = {fds303625}
}

@article{fds303626,
   Author = {Coulais, C and Behringer, RP and Dauchot, O},
   Title = {The Jamming point street-lamp in the world of granular
             media},
   Journal = {Soft Matter},
   Volume = {10},
   Pages = {1519-1536},
   Year = {2013},
   Month = {May},
   url = {http://arxiv.org/abs/1305.0703v1},
   Abstract = {The Jamming of soft spheres at zero temperature, the
             J-point, has been extensively studied both numerically and
             theoretically and can now be considered as a safe location
             in the space of models, where a street lamp has been lit up.
             However, a recent work by Ikeda et al, 2013 reveals that, in
             the Temperature/Packing fraction parameter space,
             experiments on colloids are actually rather far away from
             the scaling regime illuminated by this lamp. Is it that the
             J-point has little to say about real system? What about
             granular media? Such a-thermal, frictional, systems are
             a-priori even further away from the idealized case of
             thermal soft spheres. In the past ten years, we have
             systematically investigated horizontally shaken grains in
             the vicinity of the Jamming transition. We discuss the above
             issue in the light of very recent experimental results.
             First, we demonstrate that the contact network exhibits a
             remarkable dynamics, with strong heterogeneities, which are
             maximum at a packing fraction phi star, distinct and smaller
             than the packing fraction phi dagger, where the average
             number of contact per particle starts to increase. The two
             cross-overs converge at point J in the zero mechanical
             excitation limit. Second, a careful analysis of the dynamics
             on time scales ranging from a minute fraction of the
             vibration cycle to several thousands of cycles allows us to
             map the behaviors of this shaken granular system onto those
             observed for thermal soft spheres and demonstrate that some
             light of the J-point street-lamp indeed reaches the granular
             universe.},
   Doi = {10.1039/C3SM51231B},
   Key = {fds303626}
}

@article{fds303627,
   Author = {Bi, D and Zhang, J and Behringer, RP and Chakraborty,
             B},
   Title = {Fluctuations in Shear-Jammed States: A Statistical Ensemble
             Approach},
   Volume = {102},
   Pages = {34002},
   Year = {2013},
   Month = {February},
   url = {http://arxiv.org/abs/1302.6891v1},
   Abstract = {Granular matter exists out of thermal equilibrium, i.e. it
             is athermal. While conventional equilibrium statistical
             mechanics is not useful for characterizing granular
             materials, the idea of constructing a statistical ensemble
             analogous to its equilibrium counterpart to describe static
             granular matter was proposed by Edwards and Oakshott more
             than two decades ago. Recent years have seen several
             implementations of this idea. One of these is the stress
             ensemble, which is based on properties of the force moment
             tensor, and applies to frictional and frictionless grains.
             We demonstrate the full utility of this statistical
             framework in shear jammed (SJ) experimental states [1,2], a
             special class of granular solids created by pure shear,
             which is a strictly non-equilbrium protocol for creating
             solids. We demonstrate that the stress ensemble provides an
             excellent quantitative description of fluctuations in
             experimental SJ states. We show that the stress fluctuations
             are controlled by a single tensorial quantity: the
             angoricity of the system, which is a direct analog of the
             thermodynamic temperature. SJ states exhibit significant
             correlations in local stresses and are thus inherently
             different from density-driven, isotropically jammed (IJ)
             states.},
   Doi = {10.1209/0295-5075/102/34002},
   Key = {fds303627}
}

@article{fds220987,
   Author = {Jie Ren and Joshua Dijksman and R. P. Behringer},
   Title = {Homoegneity and Packing Structure of a 2D shear Granular
             System},
   Journal = {Powders and Grains, 2013, AIP Conf. Proc.
             1542},
   Pages = {527},
   Year = {2013},
   Key = {fds220987}
}

@article{fds220978,
   Author = {Abrahm Clark and R. P. Behringer},
   Title = {Granular Impact Model as an Energy-Depth
             Relation},
   Journal = {Europhys. Lett.},
   Volume = {101},
   Pages = {64001},
   Year = {2013},
   Key = {fds220978}
}

@article{fds220979,
   Author = {Jie Ren and Joshua A. Dijksman and R. P. Behringer},
   Title = {Reynolds Pressure and Relaxation in a Sheared Granular
             System},
   Journal = {Phys. Rev. Lett.},
   Volume = {110},
   Pages = {018302},
   Year = {2013},
   Key = {fds220979}
}

@article{fds220985,
   Author = {Hu Zheng and Joshua A. Dijksman and R. P. Behringer},
   Title = {Novel Experimental Appartus for Granular Experiemtns on
             Basal Friction},
   Journal = {Powders and Grains, 2013, AIP Conf. Proc.
             1542},
   Pages = {465},
   Year = {2013},
   Key = {fds220985}
}

@article{fds220986,
   Author = {N. Sep’ulveda and R. P. Behringer},
   Title = {Measuring Creep and Stick-Slip Behavior in a Two-Dimensional
             Photoelastic Granular Medium},
   Journal = {Powders and Grains, 2013, AIP Conf. Proc.
             1542},
   Pages = {469},
   Year = {2013},
   Key = {fds220986}
}

@article{fds245428,
   Author = {Behringer, RP and Dijksman, J and Ren, J and Zhang, J and Majmudar, T and Chakraborty, B and Bi, D and Tordesillas, A},
   Title = {Jamming and Shear for Granular Materials},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {12-19},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811860},
   Key = {fds245428}
}

@article{fds245429,
   Author = {Ren, J and Dijksman, J and Behringer, RP},
   Title = {Homogeneity and Packing Structure of a 2D Sheared Granular
             System},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {527-530},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200127&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811984},
   Key = {fds245429}
}

@article{fds245430,
   Author = {Farhadi, S and Behringer, RP and Zhu, AZ},
   Title = {Slow Dynamics for Elliptical Particles Under Continuous
             Shear And Cyclic Compression},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {879-882},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200215&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4812072},
   Key = {fds245430}
}

@article{fds245431,
   Author = {Clark, AH and Kondic, L and Behringer, RP},
   Title = {Granular Impact Dynamics: Fluctuations at Short
             Time-Scales},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {445-448},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200106&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811963},
   Key = {fds245431}
}

@article{fds245432,
   Author = {Dijksman, JA and Zheng, H and Behringer, RP},
   Title = {Imaging Soft Sphere Packings in a Novel Triaxial Shear
             Setup},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {457-460},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200109&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811966},
   Key = {fds245432}
}

@article{fds245433,
   Author = {Sepulveda, N and Behringer, RP},
   Title = {Measuring Creep and Stick-Slip Behavior in 2-Dimensional
             Photoelastic Granular Medium},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {469-+},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200112&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811969},
   Key = {fds245433}
}

@article{fds245434,
   Author = {Zheng, H and Dijksman, JA and Behringer, RP},
   Title = {Novel Experimental Apparatus for Granular Experiments on
             Basal Friction},
   Journal = {AIP Conference Proceedings},
   Volume = {1542},
   Pages = {465-468},
   Year = {2013},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200111&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1063/1.4811968},
   Key = {fds245434}
}

@article{fds245506,
   Author = {Clark, AH and Kondic, L and Behringer, RP},
   Title = {Particle scale dynamics in granular impact.},
   Journal = {Physical Review Letters},
   Volume = {109},
   Number = {23},
   Pages = {238302},
   Year = {2012},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23368273},
   Abstract = {We perform an experimental study of granular impact, where
             intruders strike 2D beds of photoelastic disks from above.
             High-speed video captures the intruder dynamics and the
             local granular force response, allowing investigation of
             grain-scale mechanisms in this process. We observe rich
             acoustic behavior at the leading edge of the intruder,
             strongly fluctuating in space and time, and we show that
             this acoustic activity controls the intruder deceleration,
             including large force fluctuations at short time scales. The
             average intruder dynamics match previous studies using
             empirical force laws, suggesting a new microscopic picture,
             where acoustic energy is carried away and
             dissipated.},
   Doi = {10.1103/PhysRevLett.109.238302},
   Key = {fds245506}
}

@article{fds303628,
   Author = {Clark, AH and Behringer, RP},
   Title = {Granular Impact Dynamics: Acoustics and Fluctuations},
   Year = {2012},
   Month = {October},
   url = {http://arxiv.org/abs/1210.3639v1},
   Abstract = {In the corresponding fluid dynamics video, created for the
             APS DFD 2012 Gallery of Fluid Motion, we show high-speed
             videos of 2D granular impact experiments, where an intruder
             strikes a collection of bidisperse photoelastic disks from
             above. We discuss the force beneath the intruder, which is
             strongly fluctuating in space and time. These fluctuations
             correspond to acoustic pulses which propagate into the
             medium. Analysis shows that this process, in our
             experiments, is dominated by collisions with grain clusters.
             The energy from these collisions is carried into the
             granular medium along networks of grains, where is it
             dissipated.},
   Key = {fds303628}
}

@article{fds304521,
   Author = {Tordesillas, A and Walker, DM and Froyland, G and Zhang, J and Behringer, RP},
   Title = {Transition dynamics and magic-number-like behavior of
             frictional granular clusters.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {86},
   Number = {1 Pt 1},
   Pages = {011306},
   Year = {2012},
   Month = {July},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23005410},
   Abstract = {Force chains, the primary load-bearing structures in dense
             granular materials, rearrange in response to applied
             stresses and strains. These self-organized grain columns
             rely on contacts from weakly stressed grains for lateral
             support to maintain and find new stable states. However, the
             dynamics associated with the regulation of the topology of
             contacts and strong versus weak forces through such contacts
             remains unclear. This study of local self-organization of
             frictional particles in a deforming dense granular material
             exploits a transition matrix to quantify preferred
             conformations and the most likely conformational
             transitions. It reveals that favored cluster conformations
             reside in distinct stability states, reminiscent of "magic
             numbers" for molecular clusters. To support axial loads,
             force chains typically reside in more stable states of the
             stability landscape, preferring stabilizing trusslike,
             three-cycle contact triangular topologies with neighboring
             grains. The most likely conformational transitions during
             force chain failure by buckling correspond to rearrangements
             among, or loss of, contacts which break the three-cycle
             topology.},
   Doi = {10.1103/PhysRevE.86.011306},
   Key = {fds304521}
}

@article{fds303631,
   Author = {Coulais, C and Behringer, RP and Dauchot, O},
   Title = {Contacts Dynamics Reveals Widom Lines for
             Jamming},
   Journal = {EPL},
   Volume = {100},
   Pages = {44005},
   Year = {2012},
   Month = {February},
   url = {http://arxiv.org/abs/1202.5687v3},
   Abstract = {We experimentally study the vicinity of the Jamming
             transition by investigating the statics and the dynamics of
             the contact network of an horizontally shaken bi-disperse
             packing of photo-elastic discs. Compressing the packing very
             slowly, while maintaining a mechanical excitation, yields a
             granular glass, namely a frozen structure of vibrating
             grains. In this glass phase, we observe a remarkable
             dynamics of the contact network, which exhibits strong
             dynamical heterogeneities. Such heterogeneities are maximum
             at a packing fraction $\phi^*$, \emph{distinct} and smaller
             than the jamming packing fraction $\phi_J$, which is
             indicated by the abrupt variation of the average number of
             contact per particle. We demonstrate that the two
             cross-overs, one for the maximum dynamical heterogeneity,
             and the other for static jamming, converge at point J in the
             zero mechanical excitation limit, a behavior reminiscent of
             the Widom lines in the supercritical phase of a second order
             critical point. Our findings are discussed in the light of
             recent numerical and theoretical studies of thermal soft
             spheres.},
   Doi = {10.1209/0295-5075/100/44005},
   Key = {fds303631}
}

@article{fds245492,
   Author = {Coulais, C and Behringer, RP and Dauchot, O},
   Title = {Dynamics of the contacts reveals Widom lines for
             jamming},
   Journal = {EPL (Europhysics Letters)},
   Volume = {100},
   Number = {4},
   Year = {2012},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/0295-5075/100/44005},
   Abstract = {We experimentally study the vicinity of the jamming
             transition by investigating the statics and the dynamics of
             the contact network of a horizontally shaken bi-disperse
             packing of photo-elastic discs. Compressing the packing very
             slowly, while maintaining a mechanical excitation, yields a
             granular glass, namely a frozen structure of vibrating
             grains. In this glass phase, we observe a remarkable
             dynamics of the contact network, which exhibits strong
             dynamical heterogeneities. Such heterogeneities are maximum
             at a packing fraction φ*, distinct and smaller than the
             structural packing fraction φ†, which is indicated by an
             abrupt variation of the average number of contacts per
             particle. We demonstrate that the two crossovers, one for
             the maximum dynamical heterogeneity, and the other for
             static jamming, converge at point J in the zero
             mechanical-excitation limit, a behavior reminiscent of the
             Widom lines in the supercritical phase of a second-order
             critical point. Our findings are discussed in the light of
             recent numerical and theoretical studies of thermal soft
             spheres. © Copyright EPLA, 2012.},
   Doi = {10.1209/0295-5075/100/44005},
   Key = {fds245492}
}

@article{fds245493,
   Author = {Tordesillas, A and Walker, DM and Froyland, G and Zhang, J and Behringer, RP},
   Title = {Transition dynamics and magic-number-like behavior of
             frictional granular clusters},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {86},
   Number = {1},
   Pages = {011306},
   Year = {2012},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23005410},
   Abstract = {Force chains, the primary load-bearing structures in dense
             granular materials, rearrange in response to applied
             stresses and strains. These self-organized grain columns
             rely on contacts from weakly stressed grains for lateral
             support to maintain and find new stable states. However, the
             dynamics associated with the regulation of the topology of
             contacts and strong versus weak forces through such contacts
             remains unclear. This study of local self-organization of
             frictional particles in a deforming dense granular material
             exploits a transition matrix to quantify preferred
             conformations and the most likely conformational
             transitions. It reveals that favored cluster conformations
             reside in distinct stability states, reminiscent of "magic
             numbers" for molecular clusters. To support axial loads,
             force chains typically reside in more stable states of the
             stability landscape, preferring stabilizing trusslike,
             three-cycle contact triangular topologies with neighboring
             grains. The most likely conformational transitions during
             force chain failure by buckling correspond to rearrangements
             among, or loss of, contacts which break the three-cycle
             topology. © 2012 American Physical Society.},
   Doi = {10.1103/PhysRevE.86.011306},
   Key = {fds245493}
}

@article{fds245505,
   Author = {Kondic, L and Goullet, A and O'Hern, CS and Kramar, M and Mischaikow, K and Behringer, RP},
   Title = {Topology of force networks in compressed granular
             media},
   Journal = {EPL (Europhysics Letters)},
   Volume = {97},
   Number = {5},
   Pages = {54001},
   Year = {2012},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/0295-5075/97/54001},
   Abstract = {Using numerical simulations, we investigate the evolution of
             the structure of force networks in slowly compressed model
             granular materials in two spatial dimensions. We quantify
             the global properties of the force networks using the zeroth
             Betti number B0, which is a topological invariant. We find
             that B0 can distinguish among force networks in systems with
             frictionless vs. frictional disks and varying size
             distributions. In particular, we show that 1) the force
             networks in systems composed of frictionless, monodisperse
             disks differ significantly from those in systems with
             frictional, polydisperse disks and we isolate the effect
             (friction, polydispersity) leading to the differences; 2)
             the structural properties of force networks change as the
             system passes through the jamming transition; and 3) the
             force network continues to evolve as the system is
             compressed above jamming, e.g., the size of connected
             clusters with forces larger than a given threshold decreases
             significantly with increasing packing fraction. ©
             Europhysics Letters Association, 2012.},
   Doi = {10.1209/0295-5075/97/54001},
   Key = {fds245505}
}

@article{fds245509,
   Author = {Behringer, RP and Bi, D and Zhang, J and Chakraborty,
             B},
   Title = {Sheared Granular Materials near Jamming},
   Journal = {Proceedings of the 8th European Solid Mechanics
             Society},
   Year = {2012},
   Key = {fds245509}
}

@article{fds245510,
   Author = {Tordesillas, A and Walker, DM and Froyland, G and Zhang, J and Behringer, RP},
   Title = {Transition Dynamics of Frictional Granular
             Clusters},
   Journal = {Phys, Rev, E},
   Volume = {86},
   Number = {1 Pt 1},
   Pages = {011306},
   Year = {2012},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23005410},
   Abstract = {Force chains, the primary load-bearing structures in dense
             granular materials, rearrange in response to applied
             stresses and strains. These self-organized grain columns
             rely on contacts from weakly stressed grains for lateral
             support to maintain and find new stable states. However, the
             dynamics associated with the regulation of the topology of
             contacts and strong versus weak forces through such contacts
             remains unclear. This study of local self-organization of
             frictional particles in a deforming dense granular material
             exploits a transition matrix to quantify preferred
             conformations and the most likely conformational
             transitions. It reveals that favored cluster conformations
             reside in distinct stability states, reminiscent of "magic
             numbers" for molecular clusters. To support axial loads,
             force chains typically reside in more stable states of the
             stability landscape, preferring stabilizing trusslike,
             three-cycle contact triangular topologies with neighboring
             grains. The most likely conformational transitions during
             force chain failure by buckling correspond to rearrangements
             among, or loss of, contacts which break the three-cycle
             topology.},
   Doi = {10.1103/PhysRevE.86.011306},
   Key = {fds245510}
}

@article{fds245511,
   Author = {Kondic, L and Fang, X and Losert, W and O'Hern, CS and Behringer,
             RP},
   Title = {Microstructure evolution during impact on granular
             matter},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {85},
   Number = {1},
   Year = {2012},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/PhysRevE.85.011305},
   Abstract = {We study the impact of an intruder on a dense granular
             material. The process of impact and interaction between the
             intruder and the granular particles is modeled using
             discrete element simulations in two spatial dimensions. In
             the first part of the paper we discuss how the intruder's
             dynamics depends on (1) the intruder's properties, including
             its size, shape and composition, (2) the properties of the
             grains, including friction, polydispersity, structural
             order, and elasticity, and (3) the properties of the system,
             including its size and gravitational field. It is found that
             polydispersity and related structural order, and frictional
             properties of the granular particles, play a crucial role in
             determining impact dynamics. In the second part of the paper
             we consider the response of the granular system itself. We
             discuss the force networks that develop, including their
             topological evolution. The influence of friction and
             structural order on force propagation, including the
             transition from hyperbolic-like to elastic-like behavior is
             discussed, as well as the affine and nonaffine components of
             the grain dynamics. Several broad observations include the
             following: tangential forces between granular particles are
             found to play a crucial role in determining impact dynamics;
             both force networks and particle dynamics are correlated
             with the dynamics of the intruder itself. © 2012 American
             Physical Society.},
   Doi = {10.1103/PhysRevE.85.011305},
   Key = {fds245511}
}

@article{fds245512,
   Author = {Clark, AH and Mort, P and Behringer, RP},
   Title = {Coarse graining for an impeller-driven mixer
             system},
   Journal = {Granular Matter},
   Volume = {14},
   Number = {2},
   Pages = {283-288},
   Year = {2012},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-011-0306-z},
   Abstract = {We apply a coarse graining approach developed by Isaac
             Goldhirsch to data acquired from a model of an
             impeller-driven mixer system. The experiment uses a
             bidisperse system of photoelastic particles in a quasi-2D
             system to determine local mass and momentum densities,
             velocities, granular temperatures, size concentration, and
             pressure. Raw data consist of high speed video images
             obtained with polarizers (to obtain particle-scale force
             data) and without polarizers (to obtain particle positions).
             We coarse grain the experimental data using a Gaussian
             coarse graining function, φ, of variable width, w. ©
             Springer-Verlag 2012.},
   Doi = {10.1007/s10035-011-0306-z},
   Key = {fds245512}
}

@article{fds245516,
   Author = {Bi, D and Zhang, J and Chakraborty, B and Behringer,
             RP},
   Title = {Jamming by shear.},
   Journal = {Nature},
   Volume = {480},
   Number = {7377},
   Pages = {355-358},
   Year = {2011},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22170683},
   Abstract = {A broad class of disordered materials including foams,
             glassy molecular systems, colloids and granular materials
             can form jammed states. A jammed system can resist small
             stresses without deforming irreversibly, whereas unjammed
             systems flow under any applied stresses. The broad
             applicability of the Liu-Nagel jamming concept has attracted
             intensive theoretical and modelling interest but has
             prompted less experimental effort. In the Liu-Nagel
             framework, jammed states of athermal systems exist only
             above a certain critical density. Although numerical
             simulations for particles that do not experience friction
             broadly support this idea, the nature of the jamming
             transition for frictional grains is less clear. Here we show
             that jamming of frictional, disk-shaped grains can be
             induced by the application of shear stress at densities
             lower than the critical value, at which isotropic
             (shear-free) jamming occurs. These jammed states have a much
             richer phenomenology than the isotropic jammed states: for
             small applied shear stresses, the states are fragile, with a
             strong force network that percolates only in one direction.
             A minimum shear stress is needed to create robust,
             shear-jammed states with a strong force network percolating
             in all directions. The transitions from unjammed to fragile
             states and from fragile to shear-jammed states are
             controlled by the fraction of force-bearing grains. The
             fractions at which these transitions occur are statistically
             independent of the density. Jammed states with densities
             lower than the critical value have an anisotropic fabric
             (contact network). The minimum anisotropy of shear-jammed
             states vanishes as the density approaches the critical value
             from below, in a manner reminiscent of an order-disorder
             transition.},
   Doi = {10.1038/nature10667},
   Key = {fds245516}
}

@article{fds245500,
   Author = {Ren, J and Dijksman, JA and Behringer, RP},
   Title = {Linear shear in a model granular system.},
   Journal = {Chaos},
   Volume = {21},
   Number = {4},
   Pages = {041105},
   Year = {2011},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22225335},
   Abstract = {winner video entry APS-GSNP Gallery of Images, March
             2011},
   Doi = {10.1063/1.3664407},
   Key = {fds245500}
}

@article{fds245501,
   Author = {Tang, J and Behringer, RP},
   Title = {How granular materials jam in a hopper.},
   Journal = {Chaos},
   Volume = {21},
   Number = {4},
   Pages = {041107},
   Year = {2011},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22225337},
   Doi = {10.1063/1.3669495},
   Key = {fds245501}
}

@article{fds245515,
   Author = {Mukhopadhyay, S and Murisic, N and Behringer, RP and Kondic,
             L},
   Title = {Evolution of droplets of perfectly wetting liquid under the
             influence of thermocapillary forces.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {83},
   Number = {4 Pt 2},
   Pages = {046302},
   Year = {2011},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21599290},
   Abstract = {We consider the evolution of sessile droplets of a
             nonvolatile perfectly wetting liquid on differentially
             radially heated solid substrates. The heating induces
             thermocapillary Marangoni forces that affect the contact
             line dynamics. Our experiments involving a particular
             heating pattern reveal that the Marangoni effect suppresses
             the spreading of a drop, typical for perfectly wetting
             liquids. The result is a rather slow receding motion and a
             distinctive thinning of the liquid layer in the region close
             to the contact line. Our theoretical model, based on the
             lubrication approximation and incorporating the Marangoni
             effect, recovers the main features observed in the
             experiments, and in addition predicts novel features that
             are still to be observed.},
   Doi = {10.1103/PhysRevE.83.046302},
   Key = {fds245515}
}

@article{fds245513,
   Author = {Tordesillas, A and Lin, Q and Zhang, J and Behringer, RP and Shi,
             J},
   Title = {Stability of self-organized mesoscopic structures in dense
             granular materials},
   Journal = {Journal of the Mechanics and Physics of Solids},
   Volume = {59},
   Number = {2},
   Pages = {265-296},
   Year = {2011},
   ISSN = {0022-5096},
   url = {http://dx.doi.org/10.1016/j.jmps.2010.10.007},
   Abstract = {We examine emergent, self-organized particle cluster
             conformations in quasistatically deforming dense granular
             materials from the perspective of structural stability. A
             structural mechanics approach is employed, first, to devise
             a new stability measure for such conformations in
             equilibrium and, second, to use this measure to explore the
             evolving stability of jammed states of specific cluster
             conformations, i.e. particles forming force chains and
             minimal contact cycles. Knowledge gained on (a) the spatial
             and temporal evolution of stability of individual jammed
             conformations and (b) their relative stability levels, offer
             valuable clues on the rheology and, in particular,
             self-assembly of granular materials. This study is
             undertaken using data from assemblies of nonuniformly sized
             circular particles undergoing 2D deformation in two biaxial
             compression tests: a discrete element simulation of
             monotonic loading under constant confining pressure, and
             cyclic loading of a photoelastic disk assembly under
             constant volume. Our results suggest that the process of
             self-assembly in these systems is realized at multiple
             length scales, and that jammed force chains and minimal
             cycles form the basic building blocks of this process. In
             particular, 3-cycles are stabilizing agents that act as
             granular trusses to the load-bearing force chain columns.
             This co-evolutionary synergy between force chains and
             3-cycles proved common to the different materials under
             different loading conditions. Indeed, the remarkable
             similarities in the evolution of stability, prevalence and
             persistence of minimal cycles and force chains in these
             systems suggest that these structures and their co-evolution
             together form a generic feature of dense granular systems
             under quasistatic loading. © 2010 2010 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.jmps.2010.10.007},
   Key = {fds245513}
}

@article{fds245514,
   Author = {Walker, DM and Tordesillas, A and Thornton, C and Behringer, RP and Zhang, J and Peters, JF},
   Title = {Percolating contact subnetworks on the edge of
             isostaticity},
   Journal = {Granular Matter},
   Volume = {13},
   Number = {3},
   Pages = {233-240},
   Year = {2011},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-011-0250-y},
   Abstract = {We search for a percolating, strong subnetwork of contacts
             in a quasi-statically deforming, frictional granular
             material. Of specific interest in this study is that
             subnetwork which contributes to the majority of the total
             deviator stress and is, or is on the edge of being,
             isostatic. We argue that a subnetwork derived from the
             minimal spanning trees of a graph - optimized to include as
             many elastic contacts as possible and which bear normal
             contact forces above a given threshold delivers such a
             network. Moreover adding the strong 3-force-cycles to the
             spanning tree introduces a level of redundancy required to
             achieve a network that is almost if not isostatic. Results
             are shown for assemblies of non-uniformly sized circular
             particles under biaxial compression, in two-dimensions: a
             discrete element (DEM) simulation of monotonic loading under
             constant confining pressure, and cyclic loading of
             photoelastic disks under constant volume. © 2011
             Springer-Verlag.},
   Doi = {10.1007/s10035-011-0250-y},
   Key = {fds245514}
}

@article{fds245517,
   Author = {Zhang, J and Oron, A and Behringer, RP},
   Title = {Novel pattern forming states for Marangoni convection in
             volatile binary liquids},
   Journal = {Physics of Fluids},
   Volume = {23},
   Number = {7},
   Pages = {072102},
   Year = {2011},
   ISSN = {1070-6631},
   url = {http://dx.doi.org/10.1063/1.3609287},
   Abstract = {We describe experiments on Marangoni convection in thin
             evaporating liquid films. The films are binary mixtures of
             ethanol and water exposed to the ambient room air during all
             experimental runs. These experiments exhibit a variety of
             different, often novel, patterns, depending on the
             concentration (weight fraction) c of ethanol. Among these
             are mobile circular convective patterns, which have not been
             previously observed, to our knowledge. The convective
             patterns evolve due to the evaporation of both the solvent
             and the solute, and their size increases substantially with
             the initial concentration c. The patterns reported here
             differ from those found in binary mixtures of NaCl and
             water, where only water evaporates. © 2011 American
             Institute of Physics.},
   Doi = {10.1063/1.3609287},
   Key = {fds245517}
}

@article{fds245518,
   Author = {Krim, J and Yu, P and Behringer, RP},
   Title = {Stick-Slip and the Transition to Steady Sliding in a 2D
             Granular Medium and a Fixed Particle Lattice},
   Journal = {pure and applied geophysics},
   Volume = {168},
   Number = {12},
   Pages = {2259-2275},
   Year = {2011},
   ISSN = {0033-4553},
   url = {http://dx.doi.org/10.1007/s00024-011-0364-5},
   Abstract = {We report an experimental study of the stick-slip to steady
             sliding behavior of a solid object pulled, via a spring,
             across 2D granular substrates of photoelastic disks that are
             either fixed in a solid lattice (granular solid) or
             unconstrained, forming a granular bed. We observe a
             progression of friction regimes with increasing sliding
             speed, including single-slip, double-slip, and mixed
             stick-slip regimes, steady sliding, and inertial
             oscillations. For the case of the granular bed, we report a
             detailed analysis of frictional behavior for the low speed
             stick-slip regime, including spring and elastic energy
             dependencies during the stick and slip portions of the
             motion. For the case of the granular solid, we explore
             friction in the presence and absence of externally applied
             vibrations, and compare it with sliding on a granular bed,
             which is intrinsically disordered. We observe that external
             vibration reduces transition values for both the single-slip
             to double-slip transition and the stick-slip to steady
             sliding transition. Moreover, we observe that the effect of
             packing disorder on granular friction seems similar to the
             effect of vibration-induced disorder, a result that, to our
             knowledge, has not been reported previously in the
             experimental literature. © 2011 Springer Basel
             AG.},
   Doi = {10.1007/s00024-011-0364-5},
   Key = {fds245518}
}

@article{fds304526,
   Author = {Tordesillas, A and Lin, Q and Zhang, J and Behringer, RP and Shi,
             J},
   Title = {Structural stability and jamming of self-organized cluster
             conformations in dense granular materials},
   Journal = {Journal of the Mechanics and Physics of Solids},
   Volume = {59},
   Number = {2},
   Pages = {265-296},
   Year = {2011},
   ISSN = {0022-5096},
   url = {http://dx.doi.org/10.1016/j.jmps.2010.10.007},
   Abstract = {We examine emergent, self-organized particle cluster
             conformations in quasistatically deforming dense granular
             materials from the perspective of structural stability. A
             structural mechanics approach is employed, first, to devise
             a new stability measure for such conformations in
             equilibrium and, second, to use this measure to explore the
             evolving stability of jammed states of specific cluster
             conformations, i.e. particles forming force chains and
             minimal contact cycles. Knowledge gained on (a) the spatial
             and temporal evolution of stability of individual jammed
             conformations and (b) their relative stability levels, offer
             valuable clues on the rheology and, in particular,
             self-assembly of granular materials. This study is
             undertaken using data from assemblies of nonuniformly sized
             circular particles undergoing 2D deformation in two biaxial
             compression tests: a discrete element simulation of
             monotonic loading under constant confining pressure, and
             cyclic loading of a photoelastic disk assembly under
             constant volume. Our results suggest that the process of
             self-assembly in these systems is realized at multiple
             length scales, and that jammed force chains and minimal
             cycles form the basic building blocks of this process. In
             particular, 3-cycles are stabilizing agents that act as
             granular trusses to the load-bearing force chain columns.
             This co-evolutionary synergy between force chains and
             3-cycles proved common to the different materials under
             different loading conditions. Indeed, the remarkable
             similarities in the evolution of stability, prevalence and
             persistence of minimal cycles and force chains in these
             systems suggest that these structures and their co-evolution
             together form a generic feature of dense granular systems
             under quasistatic loading. © 2010 2010 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.jmps.2010.10.007},
   Key = {fds304526}
}

@article{fds184671,
   Author = {J. Wambaugh and R. R. Hartley and R. P. Behringer},
   Title = {Force networks and elasticity in granular
             silos},
   Journal = {Euro. Phys. Journal E},
   Volume = {32},
   Pages = {135-145},
   Year = {2010},
   Key = {fds184671}
}

@article{fds245519,
   Author = {Zhang, J and Majmudar, TS and Sperl, M and Behringer,
             RP},
   Title = {Jamming for a 2D granular material},
   Journal = {Soft Matter},
   Volume = {6},
   Number = {13},
   Pages = {2982-2991},
   Year = {2010},
   ISSN = {1744-683X},
   url = {http://hdl.handle.net/10161/4125 Duke open
             access},
   Abstract = {This paper focuses on the nature of jamming, as seen in
             two-dimensional frictional granular systems consisting of
             photoelastic particles. The photoelastic technique is unique
             at this time, in its capability to provide detailed
             particle-scale information on forces and kinematic
             quantities such as particle displacements and rotations.
             These experiments first explore isotropic stress states near
             point J through measurements of the mean contact number per
             particle, Z, and the pressure, P as functions of the packing
             fraction, . In this case, the experiments show some but not
             all aspects of jamming, as expected on the basis of
             simulations and models that typically assume conservative,
             hence frictionless, forces between particles. Specifically,
             there is a rapid growth in Z, at a reasonable which we
             identify with as c. It is possible to fit Z and P, to power
             law expressions in - c above c, and to obtain exponents that
             are in agreement with simulations and models. However, the
             experiments differ from theory on several points, as
             typified by the rounding that is observed in Z and P near c.
             The application of shear to these same 2D granular systems
             leads to phenomena that are qualitatively different from the
             standard picture of jamming. In particular, there is a range
             of packing fractions below c, where the application of shear
             strain at constant leads to jammed stress-anisotropic
             states, i.e. they have a non-zero shear stress, τ. The
             application of shear strain to an initially isotropically
             compressed (hence jammed) state, does not lead to an
             unjammed state per se. Rather, shear strain at constant
             first leads to an increase of both τ and P. Additional
             strain leads to a succession of jammed states interspersed
             with relatively localized failures of the force network
             leading to other stress-anisotropic states that are jammed
             at typically somewhat lower stress. The locus of jammed
             states requires a state space that involves not only and τ,
             but also P. P, τ, and Z are all hysteretic functions of
             shear strain for fixed . However, we find that both P and τ
             are roughly linear functions of Z for strains large enough
             to jam the system. This implies that these shear-jammed
             states satisfy a Coulomb like-relation, τ = μP. © 2010
             The Royal Society of Chemistry.},
   Doi = {10.1039/c000147c},
   Key = {fds245519}
}

@article{fds245520,
   Author = {Zhang, J and Majmudar, TS and Tordesillas, A and Behringer,
             RP},
   Title = {Statistical properties of a 2D granular material subjected
             to cyclic shear},
   Journal = {Granular Matter},
   Volume = {12},
   Number = {2},
   Pages = {159-172},
   Year = {2010},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-010-0170-2},
   Abstract = {This work focuses on the evolution of structure and stress
             for an experimental system of 2D photoelastic particles that
             is subjected to multiple cycles of pure shear. Throughout
             this process, we determine the contact network and the
             contact forces using particle tracking and photoelastic
             techniques. These data yield the fabric and stress tensors
             and the distributions of contact forces in the normal and
             tangential directions. We then find that there is, to a
             reasonable approximation, a functional relation between the
             system pressure, P, and the mean contact number, Z. This
             relationship applies to the shear stress τ , except for the
             strains in the immediate vicinity of the contact network
             reversal. By contrast, quantities such as P ,τ and Z are
             strongly hysteretic functions of the strain, e. We find that
             the distributions of normal and tangential forces, when
             expressed in terms of the appropriate means, are essentially
             independent of strain. We close by analyzing a subset of
             shear data in terms of strong and weak force networks. ©
             Springer-Verlag 2010.},
   Doi = {10.1007/s10035-010-0170-2},
   Key = {fds245520}
}

@article{fds245521,
   Author = {Zhang, J and Behringer, RP and Goldhirsch, I},
   Title = {Coarse-Graining of a Physical Granular System},
   Journal = {Progress of Theoretical Physics},
   Volume = {184},
   Number = {SUPPL. 184},
   Pages = {16-30},
   Year = {2010},
   ISSN = {0033-068X},
   Abstract = {Results, including displacement, strain and stress fields,
             obtained by applying a resolution-controlled coarse-graining
             method to an experiment, comprised of a bidisperse system of
             photoelastic disks under pure shear, are presented. The
             paper reviews the experimental methods as well as the
             philosophical and technical bases of the coarse-graining
             methods employed in this study. Some fields reveal the
             emergence of a shear band while others do not. Correlations
             of the displacement fluctuations are shown to decay on a
             very small scale, of the order of a few particle diameters,
             even close to jamming. An unexpectedly simple relation
             between the particle rotation angles and the rotation field
             is reported. Implications of these and other findings are
             discussed.},
   Key = {fds245521}
}

@article{fds318408,
   Author = {Zhang, J and Behringer, RP and Goldhirsch, I},
   Title = {Coarse-graining of a physical granular system},
   Journal = {Progress of Theoretical Physics Supplement},
   Number = {184},
   Pages = {16-30},
   Year = {2010},
   Abstract = {Results, including displacement, strain and stress fields,
             obtained by applying a resolution-controlled coarse-graining
             method to an experiment, comprised of a bidisperse system of
             photoelastic disks under pure shear, are presented. The
             paper reviews the experimental methods as well as the
             philosophical and technical bases of the coarse-graining
             methods employed in this study. Some fields reveal the
             emergence of a shear band while others do not. Correlations
             of the displacement fluctuations are shown to decay on a
             very small scale, of the order of a few particle diameters,
             even close to jamming. An unexpectedly simple relation
             between the particle rotation angles and the rotation field
             is reported. Implications of these and other findings are
             discussed.},
   Key = {fds318408}
}

@article{fds245523,
   Author = {Mukhopadhyay, S and Behringer, RP},
   Title = {Wetting dynamics of thin liquid films and drops under
             Marangoni and centrifugal forces.},
   Journal = {Journal of Physics: Condensed Matter},
   Volume = {21},
   Number = {46},
   Pages = {464123},
   Year = {2009},
   Month = {November},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21715887},
   Abstract = {This paper presents an experimental study on thin liquid
             drops and films under the combined action of centrifugal
             forces due to rotation and radial Marangoni forces due to a
             corresponding temperature gradient. We shall examine
             thinning of a given liquid layer both with and without
             rotation and also consider the onset of the fingering
             instability in a completely wetting liquid drop. In many of
             the experiments described here, we use an interferometric
             technique which provides key information on height profiles.
             For thick rotating films in the absence of a temperature
             gradient, when an initially thick layer of fluid is spun to
             angular velocities where the classical Newtonian solution is
             negative, the fluid never dewets for the case of a
             completely wetting fluid, but leaves a microscopic uniform
             wet layer in the center. Similar experiments with a radially
             inward temperature gradient reveal the evolution of a radial
             height profile given by h(r) = A(t)r(α), where A(t) decays
             logarithmically with time, and [Formula: see text]. In the
             case where there is no rotation, small centrally placed
             drops show novel retraction behavior under a sufficiently
             strong temperature gradient. Using the same interferometric
             arrangement, we observed the onset of the fingering
             instability of small drops placed at the center of the
             rotating substrate in the absence of a temperature gradient.
             At the onset of the instability, the height profile for
             small drops is more complex than previously
             assumed.},
   Doi = {10.1088/0953-8984/21/46/464123},
   Key = {fds245523}
}

@article{fds303632,
   Author = {Lois, G and Zhang, J and Majmudar, TS and Henkes, S and Chakraborty, B and O'Hern, CS and Behringer, RP},
   Title = {Entropic origin of stress correlations in granular
             materials},
   Journal = {Phys. Rev. E},
   Volume = {80},
   Pages = {060303},
   Year = {2009},
   Month = {May},
   url = {http://arxiv.org/abs/0906.0056v1},
   Abstract = {We study the response of granular materials to external
             stress using experiment, simulation, and theory. We derive
             an entropic, Ginzburg-Landau functional that enforces
             mechanical stability and positivity of contact forces. In
             this framework, the elastic moduli depend only on the
             applied stress. A combination of this feature and the
             positivity constraint leads to stress correlations whose
             shape and magnitude are extremely sensitive to the applied
             stress. The predictions from the theory describe the stress
             correlations for both simulations and experiments
             semiquantitatively.},
   Key = {fds303632}
}

@article{fds166682,
   Author = {J. Zhang and J. Ren and S. Farhadi and R.P. Behringer and T. S. Majmudar and A. Tordesillas},
   Title = {Dense 2D Granular Material Subject to Cyclic Pure
             Shear},
   Journal = {Powders and Grains 2009},
   Pages = {553--556},
   Year = {2009},
   Key = {fds166682}
}

@collection{fds166675,
   Author = {B. Chakraborty and R.P. Behringer},
   Title = {Jamming in granular matter},
   Booktitle = {Encyclopedia of Complexity and System Science},
   Publisher = {Springer},
   Year = {2009},
   Key = {fds166675}
}

@article{fds245437,
   Author = {Tordesillas, A and Behringer, RP},
   Title = {Are we there yet? Following the energy trail in cohesionless
             granular solids},
   Journal = {MECHANICS OF NATURAL SOLIDS},
   Pages = {47-+},
   Year = {2009},
   ISBN = {978-3-642-03577-7},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000273629400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/978-3-642-03578-4_3},
   Key = {fds245437}
}

@article{fds245480,
   Author = {Tang, J and Sagdiphour, S and Behringer, RP},
   Title = {Jamming and flow in 2D hoppers},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {515-518},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179975},
   Abstract = {We consider jamming that occurs for the flow of dry granular
             materials from a hopper as the outlet size, D, is reduced
             relative to the particle size, d. We propose and test a
             model based on the simple idea that the probability of
             jamming on a short time, dt, is a constant, t. This leads to
             the prediction that the probability of surviving until time
             t without jamming is an exponentially decaying function,
             Ps(t) =exp(-t / t ). The important physical question is what
             determinest? Experiments to date have confirmed the
             exponential character of the survival probability. Work in
             progress characterizes t(D,d), fluctuations and their
             possible relation to the jamming process. © 2009 American
             Institute of Physics.},
   Doi = {10.1063/1.3179975},
   Key = {fds245480}
}

@article{fds245481,
   Author = {Kondic, L and Fang, X and Dybenko, OM and Behringer,
             RP},
   Title = {Energy transport through dense granular matter},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {293-296},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179916},
   Abstract = {In order to probe the process of energy propagation through
             dense granular systems, we carry out discrete element
             simulations of the system response to excitations where we
             control the driving frequency and wavelength independently.
             The soft-disk simulations are carried out in two spatial
             dimensions, and include the effects of energy loss due to
             inelasticity of collisions, frictional damping, rotations,
             and polydispersity. Our ability to control independently
             spatial and temporal properties of the imposed perturbations
             allows us to extract significant new information. In
             particular, Fourier analysis of the system response shows
             that properties of the propagating signal strongly depend on
             the spatial scales introduced by the perturbation itself.
             Then, we consider a sheared granular system and discuss how
             shearing influences the nature of the propagating signal.
             The simulations are carried out using realistic system sizes
             and material properties, allowing for direct experimental
             verification of the obtained results. © 2009 American
             Institute of Physics.},
   Doi = {10.1063/1.3179916},
   Key = {fds245481}
}

@article{fds245482,
   Author = {Dutt, M and Behringer, RP},
   Title = {A particle-substrate numerical model for a quasi-2D driven
             dissipative granular gas},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {1112-1115},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179841},
   Abstract = {A complete understanding of the microscopic dynamics of a
             monolayer of identical spheres moving on a substrate must
             encompass the effects of collisions and the substrate on the
             particles. We begin from first principles by considering
             collections of spherical frictional particles that roll and
             slip on a flat horizontally vibrated substrate. We present a
             numerical model which accounts for the substrate motion,
             collisional and surface frictional dissipation and their
             influence on particle dynamics for a quasi 2-dimensional
             dilute granular gas. In such systems, the ratio of the
             substrate acceleration to the particlesubstrate static
             frictional force (Kondic, Phys Rev. E (1999)) dominates the
             individual particle dynamics and the collision dynamics.
             This model is an extension of a previous numerical model
             which accounted for the influence of the collisional and
             substrate dissipation on a quasi two-dimensional cooling
             granular gas (Dutt Behringer, Phys. Rev. E (2004)). We
             willpresent results from our numerical experiments which
             highlight the progression of dynamical variables and
             fluctuation velocity distributions as a function of the
             initial conditions and the driving acceleration. © 2009
             American Institute of Physics.},
   Doi = {10.1063/1.3179841},
   Key = {fds245482}
}

@article{fds245483,
   Author = {Hartley, RR and Behringer, RP and Henkes, S and Bi, D and Chakraborty,
             B},
   Title = {Logarithmic strengthening of granular materials with shear
             rate},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {1089-1092},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179834},
   Abstract = {Experiments on sheared granular materials show that the
             stresses grow as the first power of the log of the shear
             rate, γ. We suggest that this may be evidence of the stress
             ensemble recently proposed by Henkes, O'Hern, and
             Chakraborty. The picture that we propose is that under
             steady shearing, the local force network builds up over
             time, and then fails when the force on the network exceeds a
             characteristic value. In analogy to soft glassy rheology, we
             assume that this is an activated process, but now, with the
             Boltzmann factor replaced by the stress ensemble analogue.
             We assume that the probability that a local part of the
             network fails is proportional to exp[(σ- σm)/σo], where s
             is the local stress, sm is a failure threshold, and σo is
             related to the generalized temperature, α, of Henkes and
             Chakraborty. It is then possible to show that these
             assumptions lead to logarithmic increases in the stress as a
             function of γ. This contrasts with the SGR result that the
             stress grows as the square root of l og(γ). © 2009
             American Institute of Physics.},
   Doi = {10.1063/1.3179834},
   Key = {fds245483}
}

@article{fds245484,
   Author = {Utter, B and Behringer, RP},
   Title = {Multiscale motion in the shear band of granular couette
             flow},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {339-342},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179928},
   Abstract = {We probe the nature of slow flow in the shear band of a 2D
             granular Couette experiment. The experiment consists of an
             inner shearing wheel, an outer circular boundary, and
             particles which occupy the space between these two. The mean
             flow is strictly azimuthal, maximal at the shearing wheel,
             and decaying roughly exponentially with distance from wheel.
             In addition to the mean flow and its implied shear, there is
             also inherently stochastic non-affine motion that is
             associated with diffusion of the particles and not
             describable in terms of a smooth deformation. We represent
             the motion of particles in such small local regions over a
             short time by the sum of three parts: a mean flow,
             characterized by the exponential velocity profile; a smooth
             affine deformation; and a non-affine component. The key
             observation from this analysis is that each of these
             components has comparable magnitude. Displacements from
             mean, affine, and non-affine motion are all described within
             an O(1) scale factor by the same function of distance from
             the shearing wheel. The same function also describes the
             diffusivities determined from variance-vs.-time traces. The
             non-affine displacements are distributed according to a
             guassian-like function, except that the exponent is closer
             to 3/2 rather than 2. © 2009 American Institute of
             Physics.},
   Doi = {10.1063/1.3179928},
   Key = {fds245484}
}

@article{fds245485,
   Author = {Zhang, J and Behringer, RP and Majmudar, TS and Sperl,
             M},
   Title = {Experiments on force fluctuations and the jamming
             transition},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {527-530},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179979},
   Abstract = {Using photoelastic experimental techniques, we probe the
             nature of jamming in dense 2D granular systems. This
             approach allows a complete characterization of the system,
             including contact forces, and particle motion. Key findings
             for systems of disks include: force distributions that are
             sensitive to the stress state of the system (e.g. isotropic
             or not), The distributions have a roughly exponential tail
             following pure shear, but transition to a more gaussian-like
             distribution for isotropic compression. Near jamming, we
             find that the contact number per particle, Z, rises sharply
             as a function of packing fraction, f, at jamming, and then
             continues to rise above critical with an exponent that is
             consistent with 1/2. The pressure also rises as a function
             of f above jamming with an exponent slightly larger than
             1.0, which is consistent with predictions. We also find that
             under cyclic shear, a dense granular material undergoes a
             different type of jamming transition, and we present initial
             results showing that P is a function of Z above this
             transition. © 2009 American Institute of
             Physics.},
   Doi = {10.1063/1.3179979},
   Key = {fds245485}
}

@article{fds245486,
   Author = {Kondic, L and Dybenko, OM and Behringer, RP},
   Title = {Probing dense granular materials by space-time dependent
             perturbations},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {79},
   Number = {4},
   Year = {2009},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/PhysRevE.79.041304},
   Abstract = {The manner in which signals propagate through dense granular
             systems in both space and time is not well understood. In
             order to probe this process, we carry out discrete element
             simulations of the system response to excitations where we
             control the driving frequency and wavelength independently.
             Fourier analysis shows that properties of the signal depend
             strongly on the space-time scales of the perturbation. The
             features of the response provide a test bed for models that
             predict statistical and continuum space-time properties. We
             illustrate this connection between microscale physics and
             macroscale behavior by comparing the system response to a
             simple elastic model with damping. © 2009 The American
             Physical Society.},
   Doi = {10.1103/PhysRevE.79.041304},
   Key = {fds245486}
}

@article{fds245487,
   Author = {Zhang, J and Ren, J and Farhadi, S and Behringer, RP and Majmudar, TS and Tordesillas, A},
   Title = {A dense 2D granular material subject to cyclic pure
             shear},
   Journal = {AIP Conference Proceedings},
   Volume = {1145},
   Pages = {553-556},
   Year = {2009},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.3179985},
   Abstract = {This work focuses on the evolution of fabric and stress
             tensors for an assembly of dense 2D photoelastic particles
             subjected to cyclic pure shear. The fabric and stress
             tensors are computed from the contact network and contact
             forces using particle tracking and photoelastic techniques.
             The system pressure, P, shear stress, t, and the mean
             contact number, Z fluctuate during the shear process. Their
             fluctuations are strongly correlated. We find, to a
             reasonable approximation, a functional relation between P, t
             and Z. By tracking the average contact number Z, we also
             find that there are jammed states at a packing fraction f =
             0.758 below fc = 0.84 for the isotropic jamming transition
             in two dimensions. © 2009 American Institute of
             Physics.},
   Doi = {10.1063/1.3179985},
   Key = {fds245487}
}

@article{fds245489,
   Author = {Lois, G and Zhang, J and Majmudar, TS and Henkes, S and Chakraborty, B and O'Hern, CS and Behringer, RP},
   Title = {Stress correlations in granular materials: An entropic
             formulation},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {80},
   Number = {6},
   Year = {2009},
   ISSN = {1539-3755},
   url = {http://hdl.handle.net/10161/4281 Duke open
             access},
   Abstract = {We study the response of dry granular materials to external
             stress using experiment, simulation, and theory. We derive a
             Ginzburg-Landau functional that enforces mechanical
             stability and positivity of contact forces. In this
             framework, the elastic moduli depend only on the applied
             stress. A combination of this feature and the positivity
             constraint leads to stress correlations whose shape and
             magnitude are extremely sensitive to the nature of the
             applied stress. The predictions from the theory describe the
             stress correlations for both simulations and experiments
             semiquantitatively. © 2009 The American Physical
             Society.},
   Doi = {10.1103/PhysRevE.80.060303},
   Key = {fds245489}
}

@article{fds245522,
   Author = {Krim, J and Behringer, RP},
   Title = {Friction, force chains, and falling fruit},
   Journal = {Physics today},
   Volume = {62},
   Number = {9},
   Pages = {66-67},
   Year = {2009},
   ISSN = {0031-9228},
   url = {http://dx.doi.org/10.1063/1.3226776},
   Doi = {10.1063/1.3226776},
   Key = {fds245522}
}

@article{fds245524,
   Author = {Kondic, L and Dybenko, OM and Behringer, RP},
   Title = {Signal Propagation Through Dense Granular SystemsProbing
             dense granular materials by space-time dependent
             perturbations},
   Journal = {Phys. Rev. E},
   Volume = {79},
   Pages = {041304},
   Year = {2009},
   Key = {fds245524}
}

@article{fds245527,
   Author = {Sanfratello, L and Fukushima, E and Behringer,
             RP},
   Title = {Using MR elastography to image the 3D force chain structure
             of a quasi-static granular assembly},
   Journal = {Granular Matter},
   Volume = {11},
   Number = {1},
   Pages = {1-6},
   Year = {2009},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-008-0112-4},
   Abstract = {We have developed a magnetic resonance elastography (MRE)
             technique to experimentally investigate the force chain
             structure within a densely packed 3D granular assembly. MRE
             is an MRI technique whereby small periodic displacements
             within an elastic material are measured. We verified our MRE
             technique using a gel phantom and then extended the method
             to image the force carrying chain structure within a 3D
             granular assembly of particles under an initial pre-stressed
             condition, on top of which is superimposed a small-amplitude
             vibration. We find that significant coherent displacements
             form along force chains, where spin phase accumulates
             preferentially, allowing visualization. This work represents
             the first time that the internal force chain structure of a
             dry assembly of granular solids has been fully acquired in
             three dimensions. © 2008 Springer-Verlag.},
   Doi = {10.1007/s10035-008-0112-4},
   Key = {fds245527}
}

@article{fds245528,
   Author = {Tordesillas, A and Zhang, J and Behringer, R},
   Title = {Buckling force chains in dense granular assemblies: Physical
             and numerical experiments},
   Journal = {Geomechanics & Geoengineering: An International
             Journal},
   Volume = {4},
   Number = {1},
   Pages = {3-16},
   Year = {2009},
   ISSN = {1748-6025},
   url = {http://dx.doi.org/10.1080/17486020902767347},
   Abstract = {This paper focuses on the columnar particle structures known
             as force chains, and their failure via buckling. The local
             kinematics and frictional dissipation of this failure
             mechanism are examined quantitatively for dense,
             cohesionless granular assemblies, under quasistatic and
             strain-controlled compression. Data are taken from a
             physical experiment and a discrete element simulation of
             bidisperse assemblies of circular particles undergoing shear
             banding. Particular attention is paid to the deformation and
             dissipation within a class of particle clusters, each
             composed of a buckled force chain segment and its laterally
             supporting neighbours. These particle clusters are found to
             be confined to the shear band. We establish measures of
             their local micropolar deformation, including nonaffine
             deformation, and the evolution of these quantities with
             strain. Temporally and spatially, the kinematics of this
             class of particles exhibits trends consistent with the
             particle motions that form the major contributors to
             deformation on the mesoscopic and macroscopic scales. The
             predominant mode of contact failure in a force chain
             undergoing buckling, and in the contacts with and within its
             laterally supporting neighbours, is frictional rolling.
             Rolling friction thus serves as one of, if not the main
             control valve for the energy flow from the force chain to
             its surrounding medium.},
   Doi = {10.1080/17486020902767347},
   Key = {fds245528}
}

@article{fds303630,
   Author = {Behringer, RP and Bi, D and Chakraborty, B and Henkes, S and Hartley,
             RR},
   Title = {Why do granular materials stiffen with shear rate? Test of
             novel stress-based statistics.},
   Journal = {Physical Review Letters},
   Volume = {101},
   Number = {26},
   Pages = {268301},
   Year = {2008},
   Month = {December},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19437678},
   Abstract = {Recent experiments exhibit a rate dependence for granular
             shear such that the stress grows linearly in the logarithm
             of the shear rate, gamma. Assuming a generalized activated
             process mechanism, we show that these observations are
             consistent with a recent proposal for a stress-based
             statistical ensemble. By contrast, predictions for rate
             dependence using conventional energy-based statistical
             mechanics to describe activated processes, predicts a rate
             dependence of (ln(gamma))(1/2).},
   Doi = {10.1103/PhysRevLett.101.268301},
   Key = {fds303630}
}

@article{fds245529,
   Author = {Utter, B and Behringer, RP},
   Title = {Experimental measures of affine and nonaffine deformation in
             granular shear.},
   Journal = {Physical Review Letters},
   Volume = {100},
   Number = {20},
   Pages = {208302},
   Year = {2008},
   Month = {May},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18518583},
   Abstract = {Through 2D granular Couette flow experiments, we probe
             failure and deformation of disordered solids under shear.
             Shear produces a mean azimuthal flow, smooth affine
             deformations, and irreversible so-called nonaffine particle
             displacements. We find that these processes are all of
             comparable magnitude and depend on the local shear rate. We
             compute the parameter of Falk and Langer characterizing
             nonaffine motion, Dmin2, and find that it is reasonably well
             described in terms of collections of single particles making
             locally nearly isotropic random steps, delta ri.
             Distributions for single particle nonaffine displacements,
             delta ri, satisfy P1(delta ri) proportional,
             variantexp[-|delta ri/Delta r|alpha] (alpha < or
             approximately 2).},
   Doi = {10.1103/PhysRevLett.100.208302},
   Key = {fds245529}
}

@article{fds245477,
   Author = {Matas, J-P and Uehara, J and Behringer, RP},
   Title = {Gas-driven subharmonic waves in a vibrated two-phase
             granular material.},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {25},
   Number = {4},
   Pages = {431-438},
   Year = {2008},
   Month = {April},
   ISSN = {1292-8941},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18421417},
   Abstract = {Vibrated powders exhibit striking phenomena: subharmonic
             waves, oscillons, convection, heaping, and even bubbling. We
             demonstrate novel rectangular profile subharmonic waves for
             vibrated granular material, that occur uniquely in the
             two-phase case of grains, and a fluid, such as air. These
             waves differ substantially from those for the gas-free case,
             exhibit different dispersion relations, and occur for
             specific shaking parameters and air pressure, understandable
             with gas-particle flow models. These waves occur when the
             gas diffusively penetrates the granular layer in a time
             comparable to the shaker period. As the pressure is lowered
             towards P =0, the granular-gas system exhibits a Knudsen
             regime. This instability provides an opportunity to
             quantitatively test models of two-phase flow.},
   Doi = {10.1140/epje/i2007-10310-5},
   Key = {fds245477}
}

@article{fds245530,
   Author = {Behringer, RP and Daniels, KE and Majmudar, TS and Sperl,
             M},
   Title = {Fluctuations, correlations and transitions in granular
             materials: statistical mechanics for a non-conventional
             system.},
   Journal = {Philosophical Transactions A},
   Volume = {366},
   Number = {1865},
   Pages = {493-504},
   Year = {2008},
   Month = {February},
   ISSN = {1364-503X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17698474},
   Abstract = {In this work, we first review some general properties of
             dense granular materials. We are particularly concerned with
             a statistical description of these materials, and it is in
             this light that we briefly describe results from four
             representative studies. These are: experiment 1: determining
             local force statistics, vector forces, force distributions
             and correlations for static granular systems; experiment 2:
             characterizing the jamming transition, for a static
             two-dimensional system; experiment 3: characterizing plastic
             failure in dense granular materials; and experiment 4: a
             dynamical transition where the material 'freezes' in the
             presence of apparent heating for a sheared and shaken
             system.},
   Doi = {10.1098/rsta.2007.2106},
   Key = {fds245530}
}

@article{fds152445,
   Author = {L. Kondic and C. O'Hern and R.P. Behringer},
   Title = {Dense Granular systems: From Theory to Applications},
   Journal = {SIAM News},
   Volume = {40},
   Pages = {13-15},
   Year = {2008},
   Key = {fds152445}
}

@article{fds245478,
   Author = {Behringer, RP and Herrmann, HJ and Luding, S},
   Title = {Granular Matter: Editorial},
   Journal = {Granular Matter},
   Volume = {10},
   Number = {5},
   Pages = {351-},
   Year = {2008},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-008-0110-6},
   Doi = {10.1007/s10035-008-0110-6},
   Key = {fds245478}
}

@article{fds245525,
   Author = {Behringer, RP and Chakraborty, B and Henkes, S},
   Title = {Why Do Granular Materials Stiffen at Faster Shear Rates? A
             Test of Novel Stress-Based Statsitical Mechanics},
   Journal = {Phys. Rev. Lett.},
   Volume = {101},
   Number = {26},
   Pages = {268301},
   Year = {2008},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19437678},
   Abstract = {Recent experiments exhibit a rate dependence for granular
             shear such that the stress grows linearly in the logarithm
             of the shear rate, gamma. Assuming a generalized activated
             process mechanism, we show that these observations are
             consistent with a recent proposal for a stress-based
             statistical ensemble. By contrast, predictions for rate
             dependence using conventional energy-based statistical
             mechanics to describe activated processes, predicts a rate
             dependence of (ln(gamma))(1/2).},
   Doi = {10.1103/PhysRevLett.101.268301},
   Key = {fds245525}
}

@article{fds245526,
   Author = {Zhang, J and Majmudar, T and Behringer, R},
   Title = {Force chains in a two-dimensional granular pure shear
             experiment},
   Journal = {Chaos},
   Volume = {18},
   Number = {4},
   Pages = {041107-1},
   Year = {2008},
   ISSN = {1054-1500},
   url = {http://dx.doi.org/10.1063/1.2997139},
   Doi = {10.1063/1.2997139},
   Key = {fds245526}
}

@article{fds245531,
   Author = {Matas, J-P and Behringer, RP},
   Title = {Square subharmonic waves in a vibrated two-phase granular
             material},
   Journal = {Europhys. J. E},
   Volume = {25},
   Pages = {431-438},
   Year = {2008},
   Key = {fds245531}
}

@article{fds245538,
   Author = {Wambaugh, JF and Behringer, RP and Matthews, JV and Gremaud,
             PA},
   Title = {Response to perturbations for granular flow in a
             hopper.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {76},
   Number = {5 Pt 1},
   Pages = {051303},
   Year = {2007},
   Month = {November},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18233648},
   Abstract = {We experimentally investigate the response to perturbations
             of circular symmetry for dense granular flow inside a
             three-dimensional right-conical hopper. These experiments
             consist of particle tracking velocimetry for the flow at the
             outer boundary of the hopper. We are able to test commonly
             used constitutive relations and observe granular flow
             phenomena that we can model numerically. Unperturbed conical
             hopper flow has been described as a radial velocity field
             with no azimuthal component. Guided by numerical models
             based upon continuum descriptions, we find experimental
             evidence for secondary, azimuthal circulation in response to
             perturbation of the symmetry with respect to gravity by
             tilting. For small perturbations we can discriminate between
             constitutive relations, based upon the agreement between the
             numerical predictions they produce and our experimental
             results. We find that the secondary circulation can be
             suppressed as wall friction is varied, also in agreement
             with numerical predictions. For large tilt angles we observe
             the abrupt onset of circulation for parameters where
             circulation was previously suppressed. Finally, we observe
             that for large tilt angles the fluctuations in velocity
             grow, independent of the onset of circulation.},
   Doi = {10.1103/PhysRevE.76.051303},
   Key = {fds245538}
}

@article{fds245539,
   Author = {Daniels, KE and Mukhopadhyay, S and Houseworth, PJ and Behringer,
             RP},
   Title = {Instabilities in droplets spreading on gels.},
   Journal = {Physical Review Letters},
   Volume = {99},
   Number = {12},
   Pages = {124501},
   Year = {2007},
   Month = {September},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17930507},
   Abstract = {We report a novel surface-tension driven instability
             observed for droplets spreading on a compliant substrate.
             When a droplet is released on the surface of an agar gel, it
             forms arms or cracks when the ratio of surface-tension
             gradient to gel strength is sufficiently large. We explore a
             range of gel strengths and droplet surface tensions and find
             that the onset of the instability and the number of arms
             depend on the ratio of surface tension to gel strength.
             However, the arm length grows with an apparently universal
             law L proportional t(3/4).},
   Doi = {10.1103/PhysRevLett.99.124501},
   Key = {fds245539}
}

@article{fds245542,
   Author = {Majmudar, TS and Sperl, M and Luding, S and Behringer,
             RP},
   Title = {Jamming transition in granular systems.},
   Journal = {Physical Review Letters},
   Volume = {98},
   Number = {5},
   Pages = {058001},
   Year = {2007},
   Month = {February},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17358902},
   Abstract = {Recent simulations have predicted that near jamming for
             collections of spherical particles, there will be a
             discontinuous increase in the mean contact number Z at a
             critical volume fraction phi(c). Above phi(c), Z and the
             pressure P are predicted to increase as power laws in
             phi-phi(c). In experiments using photoelastic disks we
             corroborate a rapid increase in Z at phi(c) and power-law
             behavior above phi(c) for Z and P. Specifically we find a
             power-law increase as a function of phi-phi(c) for Z-Z(c)
             with an exponent beta around 0.5, and for P with an exponent
             psi around 1.1. These exponents are in good agreement with
             simulations. We also find reasonable agreement with a recent
             mean-field theory for frictionless particles.},
   Doi = {10.1103/PhysRevLett.98.058001},
   Key = {fds245542}
}

@article{fds245532,
   Author = {Dutt, M and Behringer, RP},
   Title = {Effects of surface friction on a two-dimensional granular
             system: numerical model of a granular collider
             experiment.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {75},
   Number = {2 Pt 1},
   Pages = {021305},
   Year = {2007},
   Month = {February},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17358335},
   Abstract = {We present numerical results from a simulation of a granular
             collider experiment [B. Painter, M. Dutt, and R. P.
             Behringer, Physica D 175, 43 (2003)] using a numerical model
             which accounts for substrate frictional effects [M. Dutt and
             R. P. Behringer, Phys. Rev. E 70, 061304 (2004)]. We find
             the gradual birth and growth of a central cluster for the
             final state of the particles that depends on the system
             size, the substrate frictional dissipation, and the initial
             average kinetic energy. For systems where a central cluster
             is observed in the final state, the autocorrelation function
             C(r) of the interparticle spacing satisfies a Gaussian
             functional form C(r)=Ae-(r/sigma)2. We also find that the
             fluctuation speed distributions adhere to a
             Maxwell-Boltzmann distribution for times in the vicinity of
             collapse. Our results strongly indicate that the principal
             mechanism responsible for the energy and momentum
             dissipation is the particle-substrate kinetic friction. Our
             findings reiterate the importance of considering the effects
             of substrate friction in particle-substrate systems, as
             shown by the agreement between our numerical results with
             experimental findings of Painter, Dutt, and
             Behringer.},
   Doi = {10.1103/PhysRevE.75.021305},
   Key = {fds245532}
}

@proceedings{fds139224,
   Author = {R.P. Behringer},
   Title = {Jamming, Plasticity, and Diffusion in Dense Granular
             Materials},
   Booktitle = {Proceedings in Applied Mathematics and Mechanics},
   Year = {2007},
   Key = {fds139224}
}

@proceedings{fds139225,
   Author = {L. Kondic and R.P. Behringer},
   Title = {Signal Propagation through Dense Granular
             Systems},
   Booktitle = {Proceedings in Applied Mathematics and Mechanics},
   Year = {2007},
   Key = {fds139225}
}

@incollection{fds139760,
   Author = {R.P. Behringer},
   Title = {Fluctuations in Granular Materials},
   Volume = {8},
   Series = {Lecture Notes in Complex Systems},
   Pages = {187-215},
   Booktitle = {Granular and Complex Materials},
   Publisher = {World Scientific},
   Address = {Singapore},
   Editor = {T. Aste and T. De Matteo and A. Tordesillas},
   Year = {2007},
   Key = {fds139760}
}

@article{fds245475,
   Author = {Zhang, J and Behringer, RP and Oron, A},
   Title = {Marangoni convection in binary mixtures},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {76},
   Number = {1},
   Year = {2007},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/PhysRevE.76.016306},
   Abstract = {Marangoni instabilities in binary mixtures in the presence
             of the Soret effect and evaporation are different from those
             in pure liquids. In contrast to a large amount of
             experimental work on Marangoni convection in pure liquids,
             such experiments in binary mixtures are not available in the
             literature, to our knowledge. Using binary mixtures of
             NaCl/water in an open system, evaporation of water molecules
             at the liquid-vapor interface is inevitable. We have
             systematically investigated the pattern formation for a set
             of substrate temperatures and solute concentrations in an
             open system. The flow patterns evolve with time, driven by
             surface-tension fluctuations due to evaporation and the
             Soret effect, while the air-liquid interface does not
             deform. A shadow-graph method is used to follow the pattern
             formation in time. The patterns are mainly composed of
             polygons and rolls. The mean pattern size first decreases
             slightly, and then gradually increases during the evolution.
             Evaporation affects the pattern formation mainly at the
             early stages and the local evaporation rate tends to become
             spatially uniform at the film surface. The Soret effect
             becomes important at the later stages and affects the
             mixture for a large mean solute concentration where the
             Soret number is significantly above zero. The strength of
             convection increases with the initial solute concentration
             and the substrate temperature. Our findings differ from the
             theoretical predictions in which evaporation is neglected.
             © 2007 The American Physical Society.},
   Doi = {10.1103/PhysRevE.76.016306},
   Key = {fds245475}
}

@article{fds245476,
   Author = {Behringer, RP and Wilkinson, A and Metzger, PT},
   Title = {Grenular Matter: Editorial},
   Journal = {Granular Matter},
   Volume = {9},
   Number = {5},
   Pages = {293-294},
   Year = {2007},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-007-0048-0},
   Doi = {10.1007/s10035-007-0048-0},
   Key = {fds245476}
}

@article{fds245537,
   Author = {Kondic, L and O'Hern, C and Behringer, RP},
   Title = {Dense Granular Systems: From Theory to Applications},
   Journal = {SIAM News},
   Volume = {40},
   Pages = {13-15},
   Year = {2007},
   Key = {fds245537}
}

@article{fds245540,
   Author = {Zhang, J and Behringer, RP and Oron, A},
   Title = {Maragoni convection in binary mixtures},
   Journal = {Phys. Rev. E},
   Volume = {76},
   Pages = {106307},
   Year = {2007},
   Key = {fds245540}
}

@article{fds52398,
   Author = {R.P. Behringer and K.E. Daniels and T. S. Majmudar and M.
             Sperl},
   Title = {Fluctuations, Correlations, and Transitions in Granular
             Materials: Statistical Mechanics for a Non-Conventional
             System},
   Series = {9th Experimental Chaos Conference, Sao Jose dos Campos,
             Brazil, 2006},
   Booktitle = {Proceedings (refereed) of the 9th Experimental Chaos
             Conference},
   Year = {2006},
   Month = {June},
   Key = {fds52398}
}

@proceedings{fds245474,
   Author = {Mort, P and McKenzie, K and Wambaugh, J and Behringer,
             R},
   Title = {Granular flow through an orifice - effect of granule size
             and shape distributions},
   Journal = {AIChE Annual Meeting, Conference Proceedings},
   Booktitle = {World Congress on Particle Technology},
   Year = {2006},
   Abstract = {This paper investigates jamming probabilities of vertical
             granular flow through an orifice, specifically the effects
             of granule size distribution, granule shape and the normal
             stress above the orifice. Both wedge-shape and cylindrical
             hopper flows are considered. The jamming probability can be
             taken as a measure of differentiation between relatively
             free-flowing granules.},
   Key = {fds245474}
}

@article{fds245543,
   Author = {Daniels, KE and Behringer, RP},
   Title = {Characterization of a freezing/melting transition in a
             vibrated and sheared granular medium},
   Journal = {Journal of statistical mechanics (Online)},
   Volume = {1},
   Number = {7},
   Pages = {357-360},
   Year = {2006},
   ISSN = {1742-5468},
   url = {http://dx.doi.org/10.1088/1742-5468/2006/07/P07018},
   Abstract = {We describe experiments on monodisperse spherical particles
             in an annular cell geometry, vibrated from below and sheared
             from above. This system shows a freezing/melting transition
             such that under sufficient vibration a crystallized state is
             observed, which can be melted by sufficient shear. We
             characterize the hysteretic transition between these two
             states, and observe features reminiscent of both a jamming
             transition and critical phenomena. © 2006 IOP Publishing
             Ltd and SISSA.},
   Doi = {10.1088/1742-5468/2006/07/P07018},
   Key = {fds245543}
}

@article{fds245533,
   Author = {Daniels, KE and Mukhopadhyay, S and Behringer,
             RP},
   Title = {Starbursts and wispy drops: surfactants spreading on
             gels.},
   Journal = {Chaos},
   Volume = {15},
   Number = {4},
   Pages = {041107},
   Year = {2005},
   Month = {December},
   ISSN = {1054-1500},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16396583},
   Doi = {10.1063/1.2139968},
   Key = {fds245533}
}

@article{fds245534,
   Author = {Yu, P and Behringer, RP},
   Title = {Granular friction: a slider experiment.},
   Journal = {Chaos},
   Volume = {15},
   Number = {4},
   Pages = {041102},
   Year = {2005},
   Month = {December},
   ISSN = {1054-1500},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16396578},
   Doi = {10.1063/1.2130689},
   Key = {fds245534}
}

@article{fds245545,
   Author = {Majmudar, TS and Behringer, RP},
   Title = {Contact force measurements and stress-induced anisotropy in
             granular materials.},
   Journal = {Nature},
   Volume = {435},
   Number = {7045},
   Pages = {1079-1082},
   Year = {2005},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15973358},
   Abstract = {Interparticle forces in granular media form an inhomogeneous
             distribution of filamentary force chains. Understanding such
             forces and their spatial correlations, specifically in
             response to forces at the system boundaries, represents a
             fundamental goal of granular mechanics. The problem is of
             relevance to civil engineering, geophysics and physics,
             being important for the understanding of jamming,
             shear-induced yielding and mechanical response. Here we
             report measurements of the normal and tangential grain-scale
             forces inside a two-dimensional system of photoelastic disks
             that are subject to pure shear and isotropic compression.
             Various statistical measures show the underlying differences
             between these two stress states. These differences appear in
             the distributions of normal forces (which are more rounded
             for compression than shear), although not in the
             distributions of tangential forces (which are exponential in
             both cases). Sheared systems show anisotropy in the
             distributions of both the contact network and the contact
             forces. Anisotropy also occurs in the spatial correlations
             of forces, which provide a quantitative replacement for the
             idea of force chains. Sheared systems have long-range
             correlations in the direction of force chains, whereas
             isotropically compressed systems have short-range
             correlations regardless of the direction.},
   Doi = {10.1038/nature03805},
   Key = {fds245545}
}

@article{fds245550,
   Author = {Atman, APF and Brunet, P and Geng, J and Reydellet, G and Claudin, P and Behringer, RP and Clément, E},
   Title = {From the stress response function (back) to the sand pile
             "dip".},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {17},
   Number = {1},
   Pages = {93-100},
   Year = {2005},
   Month = {May},
   ISSN = {1292-8941},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15864732},
   Abstract = {We relate the pressure "dip" observed at the bottom of a
             sand pile prepared by successive avalanches to the stress
             profile obtained on sheared granular layers in response to a
             localized vertical overload. We show that, within a simple
             anisotropic elastic analysis, the skewness and the tilt of
             the response profile caused by shearing provide a
             qualitative agreement with the sand pile dip effect. We
             conclude that the texture anisotropy produced by the
             avalanches is in essence similar to that induced by a simple
             shearing --albeit tilted by the angle of repose of the pile.
             This work also shows that this response function technique
             could be very well adapted to probe the texture of static
             granular packing.},
   Doi = {10.1140/epje/i2005-10002-2},
   Key = {fds245550}
}

@article{fds245547,
   Author = {Daniels, KE and Behringer, RP},
   Title = {Hysteresis and competition between disorder and
             crystallization in sheared and vibrated granular
             flow.},
   Journal = {Physical Review Letters},
   Volume = {94},
   Number = {16},
   Pages = {168001},
   Year = {2005},
   Month = {April},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15904265},
   Abstract = {Experiments on spherical particles in a 3D annular shear
             cell vibrated from below and sheared from above show a
             hysteretic freezing or melting transition. Under sufficient
             vibration a crystallized state is observed, which can be
             melted by sufficient shear. The critical line for this
             transition coincides with equal kinetic energies for
             vibration and shear. The force distribution is double peaked
             in the crystalline state and single peaked with an
             approximately exponential tail in the disordered state.
             Continuous relations between pressure and volume (with
             dP/dV>0) exist for a continuum of partially and/or
             intermittently melted states over a range of
             parameters.},
   Doi = {10.1103/PhysRevLett.94.168001},
   Key = {fds245547}
}

@article{fds43799,
   Author = {M. Dutt and R.P. Behringer},
   Title = {The Granular Collider: Introduction to a Particle-Substrate
             Model and the Numerical Experiment},
   Pages = {1253-1256},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Key = {fds43799}
}

@article{fds139521,
   Author = {M. Bowen and A. Bertozzi and R.P. Behringer Bowen and Jeanman Sur and Andrea L. Bertozzi and R.P. Behringer},
   Title = {Nonlinear dynamics of two-dimensional undercompressive
             shocks},
   Journal = {Physica D},
   Volume = {209},
   Pages = {36-48},
   Year = {2005},
   Key = {fds139521}
}

@article{fds139522,
   Author = {A. Atman and P. Brunet and J. Geng and G. Reydellet and G. Combe and P.
             Claudin, R.P. Behringer and E. Clement},
   Title = {Sensitivity of the stress response function to
             packing},
   Journal = {Jour.Phys.:Cond.Matt. special issue on Granular
             Media},
   Volume = {17},
   Pages = {S2391-S2403},
   Year = {2005},
   Key = {fds139522}
}

@article{fds245435,
   Author = {Herrmann, HJ and Gudehus, G and Luding, S and Sommer, K and Parsons, M and McNamara, S and García-Rojo, R and Adams, MJ and Allersma, HGB and Ancey, C and Bardet, JP and Behringer, RP and Bideau, D and Bolton, M and Bouvard, D and Cambou, B and Chang, CS and Darve, F and Evesque, P and Ghadiri, M and Goddard, J and Gourves, R and Gudehus, G and Herrmann,
             HJ and Hidaka, J and Jaeger, HM and Jenkins, JT and Khakhar, DV and Kishino, Y and Lanier, J and Luding, S and Luong, MP and Matsuoka, H and Mehta, A and Muehlhaus, H and Nakagawa, M and Nova, R and Oda, M and Oger,
             L and Ottino, JM and Rasmussen, K and Satake, M et
             al.},
   Title = {Preface},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {1},
   Pages = {XXI-XXII},
   Year = {2005},
   Key = {fds245435}
}

@proceedings{fds245436,
   Author = {Behringer, RP and Clement, E and Geng, J and Hartley, R and Howell, D and Reydellet, G and Utter, B},
   Title = {Statistical properties of dense granular
             matter},
   Journal = {TRAFFIC AND GRANULAR FLOW '03},
   Pages = {431-444},
   Booktitle = {Proceedings of Traffic and Granular Flow,
             Delft},
   Year = {2005},
   ISBN = {3-540-25814-0},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000232132800044&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/3-540-28091-X_44},
   Key = {fds245436}
}

@article{fds245464,
   Author = {Wambaugh, JF and Behringer, RP},
   Title = {Asymmetry-induced circulation in granular hopper
             flows},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {2},
   Pages = {915-918},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Abstract = {The Jenike radial solutions have long been used to describe
             granular hopper flow by modeling particle paths as radial
             lines converging upon the vertex of a hopper. A
             finite-element simulation, based upon the Jenike solutions,
             has recently been developed and predicts that if the
             symmetry of the hopper is perturbed, a swirling,
             secondary-circulation flow arises in addition to the radial
             flow out of the hopper. (Gremaud et al. 2003) Additionally,
             increasing the roughness of the hopper walls is predicted to
             change the direction of this secondary-circulation and
             suppress its magnitude. Our experimental study tests for
             secondary-circulation in a hopper tilted to various angles,
             by tracking tracer grains within the flowing sand through
             windows in the side of the test hopper. Results indicate
             that perturbing the hopper by tilting with respect to
             gravity does indeed cause secondary-circulation. We do not,
             however, observe that varying the roughness of the hopper
             walls affects the secondary- circulation. © 2005 Taylor
             &amp; Francis Group.},
   Key = {fds245464}
}

@article{fds245465,
   Author = {Geng, J and Behringer, RP},
   Title = {Slow drag in two-dimensional granular media},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {71},
   Number = {1},
   Year = {2005},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/PhysRevE.71.011302},
   Abstract = {We study the drag force experienced by an object slowly
             moving at constant velocity through a two-dimensional
             granular material consisting of bidisperse disks. The drag
             force is dominated by force chain structures in the bulk of
             the system, thus showing strong fluctuations. We consider
             the effect of three important control parameters for the
             system: the packing fraction, the drag velocity and the size
             of the tracer particle. We find that the mean drag force
             increases as a power law (exponent of 1.5) in the reduced
             packing fraction, (γ-γ c)/γ c as γ passes through a
             critical packing fraction, γ c. By comparison, the mean
             drag grows slowly (basically logarithmic) with the drag
             velocity, showing a weak rate dependence. We also find that
             the mean drag force depends nonlinearly on the diameter, a
             of the tracer particle when a is comparable to the
             surrounding particles' size. However, the system
             nevertheless exhibits strong statistical invariance in the
             sense that many physical quantities collapse onto a single
             curve under appropriate scaling: force distributions P(f)
             collapse with appropriate scaling by the mean force, the
             power spectra P(ω) collapse when scaled by the drag
             velocity, and the avalanche size and duration distributions
             collapse when scaled by the mean avalanche size and
             duration. We also show that the system can be understood
             using simple failure models, which reproduce many
             experimental observations. These observations include the
             following: a power law variation of the spectrum with
             frequency characterized by an exponent α=-2, exponential
             distributions for both the avalanche size and duration, and
             an exponential fall-off at large forces for the force
             distributions. These experimental data and simulations
             indicate that fluctuations in the drag force seem to be
             associated with the force chain formation and breaking in
             the system. Moreover, our simulations suggest that the
             logarithmic increase of the mean drag force with rate can be
             accounted for if slow relaxation of the force chain networks
             is included. © 2005 The American Physical
             Society.},
   Doi = {10.1103/PhysRevE.71.011302},
   Key = {fds245465}
}

@article{fds245466,
   Author = {Wilkinson, RA and Behringer, RP and Jenkins, JT and Louge,
             MY},
   Title = {Granular materials and the risks they pose for success on
             the moon and mars},
   Journal = {AIP Conference Proceedings},
   Volume = {746},
   Pages = {1216-1223},
   Booktitle = {Proceedings, STAIF},
   Year = {2005},
   ISSN = {0094-243X},
   url = {http://dx.doi.org/10.1063/1.1867248},
   Abstract = {Working with soil, sand, powders, ores, cement and sintered
             bricks, excavating, grading construction sites, driving
             off-road, transporting granules in chutes and pipes, sifting
             gravel, separating solids from gases, and using hoppers are
             so routine that it seems straightforward to do it on the
             Moon and Mars as we do it on Earth. This paper brings to the
             fore how little these processes are understood and the
             millennia-long trial-and-error practices that lead to
             today's massive over-design, high failure rate, and
             extensive incremental scaling up of industrial processes
             because of the inadequate predictive tools for design. We
             present a number of pragmatic scenarios where granular
             materials play a role, the risks involved, and what
             understanding is needed to greatly reduce the risks. © 2005
             American Institute of Physics.},
   Doi = {10.1063/1.1867248},
   Key = {fds245466}
}

@article{fds245467,
   Author = {Majmudar, TS and Behringer, RP},
   Title = {Contact forces and stress induced anisotropy},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {1},
   Pages = {65-68},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Abstract = {We present experiments measuring vector contact forces in a
             two-dimensional (2D) granular system consisting of
             bi-disperse, photoelastic disks. Using a bi-axial test
             apparatus, we study the response of the system to isotropic
             compression, uniaxial compression and pure shear. We obtain
             normal and tangential force distributions for each case and
             find that different loading conditions give rise to
             different force chain structures and different normal force
             distributions. © 2005 Taylor &amp; Francis
             Group.},
   Key = {fds245467}
}

@article{fds245468,
   Author = {Behringer, RP and Dutt, M},
   Title = {A granular collider: Particle-substrate model and a
             numerical experiment},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {2},
   Pages = {1253-1256},
   Year = {2005},
   Abstract = {We consider collections of spherical frictional particles
             that roll and slip on a flat substrate. Experiments
             performed by Painter et al. (Phys. Rev E (2000)) on two
             particle collisions emphasized the importance of the role
             played by substrate friction, in particular kinetic
             friction, on the particle dynamics after collision on a
             substrate. We present a numerical model which accounts for
             collisional and surface frictional dissipation and their
             influence on particle dynamics for a quasi 2-dimensional
             cooling granular material. We apply this model to a
             simulation of a granular collider experiment (Painter et
             al., Physica D (2003)), in which collections of particles
             collided as they moved radially inward on a substrate. We
             find the gradual birth and growth of a central cluster for
             the final state of the particles, dependent upon the number
             of particles, kinetic frictional dissipation and average
             initial kinetic energy. For systems where a central cluster
             is observed in the final state, the autocorrelation function
             C(r) of the inter-particle spacing fits the Gaussian
             functional form seen in experiments. We also compute the
             fluctuation speed distributions which adheres to a
             Maxwell-Boltzmann distribution for early times, but evolves
             to a strongly non-Gaussian form as the process evolves. The
             slipping phase of the motion of the particles is responsible
             for the high rate of energy dissipation. For example, by
             decreasing the effect of kinetic friction to unrealistically
             low values or by discounting the effects of substrate
             friction, most of the particles escape the system. © 2005
             Taylor &amp; Francis Group.},
   Key = {fds245468}
}

@article{fds245469,
   Author = {Geng, J and Behringer, RP},
   Title = {Diffusion, mobility and failure for a stirred granular
             system},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {2},
   Pages = {933-937},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Abstract = {We describe experimentsto determine diffusivity and
             mobilityin a stirred densegranular system. We find that the
             diffusion is well described as simple Brownian. We find that
             the force to push a tracer through a surrounding sea of
             particles is almost independent of pushing speed, modulo a
             slow logarithmic increase. We model the pushing experiments,
             borrowing from a spring-failure model proposed by Khang et
             al. The agreement between experiment and model is
             substantial. © 2005 Taylor &amp; Francis
             Group.},
   Key = {fds245469}
}

@article{fds245470,
   Author = {Kondic, L and Behringer, RP},
   Title = {Elastic energy, fluctuations and temperature for granular
             materials},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {1},
   Pages = {397-400},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Abstract = {In our recent work (Europhys. Lett. 67,205 (2004)) we have
             shown that in granular systems characterized by large volume
             fractions, the elastic energy dominates the kinetic energy,
             and energy fluctuations are primarily elastic in nature. As
             a logical consequence of this observation, we have started
             exploring possible generalizations of the concept of
             granular temperature to dense, jammed systems where kinetic
             granular temperature is not expected to be relevant, at
             least from the energetic point of view. Therefore, we have
             introduced generalized granular temperature, which turns out
             to be roughly consistent with a temperature based on the
             equilibrium statistical mechanics. In this paper, we discuss
             the influence of various system properties on this new
             generalized granular temperature. These properties include
             the shearing rate, as well as the material properties such
             as stiffness, elasticity and friction. © 2005 Taylor &amp;
             Francis Group.},
   Key = {fds245470}
}

@article{fds245471,
   Author = {Utter, BC and Behringer, RP},
   Title = {Diffusion, transients and non-affine deformations for
             granular Couette shear flow},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {1},
   Pages = {197-201},
   Booktitle = {Powders and Grains, 2005},
   Publisher = {Balkema},
   Editor = {R. Garcia-Rojo, and H. J. Herrmann},
   Year = {2005},
   Abstract = {Measurements of diffusivity provide important insights
             intothe nature of the dynamical processes involved in the
             slow shear of dense granular materials. We report
             experiments that determine the diffusivities for a
             two-dimensional Couette shear system. In these measurements,
             we track the positions and orientations of particles (disks)
             undergoing steady shear. The shear is generated by a
             rotating inner wheel, which creates a roughly exponential
             mean azimuthal velocity. The variances associated with
             particle displacements are initially linear with time, which
             allows us to extract diffusivities. For later times, the
             variances exhibit nonlinearity, which we understand in terms
             of Taylor dispersion associated with the nonlinear velocity
             profile and boundary effects. The diffusivities are
             proportional to the local shear rate. We also determine the
             underlying force structures using the fact that the
             particles are photoelastic. A preferred direction for the
             force chains leads to a rotation of the principal directions
             of the diffusion tensor away from radial and azimuthal.
             These structures also come into play if the shearing
             direction is reversed. Lastly, we apply an idea suggested by
             Falk and Langer to characterize the non-affine motion of
             particles in terms of D 2, the minimum variance from an
             affine flow field. D 2 and the diffusivities are identical
             within scale factors (and experimental errors). © 2005
             Taylor &amp; Francis Group.},
   Key = {fds245471}
}

@article{fds245544,
   Author = {Behringer, RP},
   Title = {A grain of a good idea},
   Journal = {Nature},
   Volume = {437},
   Pages = {1069},
   Year = {2005},
   Key = {fds245544}
}

@article{fds245548,
   Author = {Atman, APF and Brunet, P and Geng, J and Reydellet, G and Combe, G and Claudin, P and Behringer, RP and Clément, E},
   Title = {Sensitivity of the stress response function to packing
             preparation},
   Journal = {Journal of Physics Condensed Matter},
   Volume = {17},
   Number = {24},
   Pages = {S2391-S2403},
   Year = {2005},
   url = {http://dx.doi.org/10.1088/0953-8984/17/24/002},
   Abstract = {A granular assembly composed of a collection of identical
             grains may pack under different microscopic configurations
             with microscopic features that are sensitive to the
             preparation history. A given configuration may also change
             in response to external actions such as compression and
             shearing. We show, using a mechanical response function
             method developed experimentally and numerically, that the
             macroscopic stress profiles are strongly dependent on these
             preparation procedures. These results were obtained for both
             two and three dimensions. The method reveals that, under a
             given preparation history, the macroscopic symmetries of the
             granular material is affected, and in most cases significant
             departures from isotropy should be observed. This suggests a
             new path towards a non-intrusive test of granular material
             constitutive properties. © 2005 IOP Publishing
             Ltd.},
   Doi = {10.1088/0953-8984/17/24/002},
   Key = {fds245548}
}

@article{fds245549,
   Author = {Behringer, RP and Shearer, M},
   Title = {Preface to the Special Issue "Nonlinear Dynamics of Thin
             Films and Fluid Interfaces},
   Journal = {Physica D},
   Volume = {209},
   Number = {1-4 SPEC. ISS.},
   Pages = {vii-viii},
   Year = {2005},
   url = {http://dx.doi.org/10.1016/j.physd.2005.08.003},
   Doi = {10.1016/j.physd.2005.08.003},
   Key = {fds245549}
}

@article{fds245551,
   Author = {Bowen, M and Sur, J and Bertozzi, AL and Behringer,
             RP},
   Title = {Nonlinear dynamics of two-dimensional undercompressive
             shocks},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {209},
   Number = {1-4 SPEC. ISS.},
   Pages = {36-48},
   Year = {2005},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/10.1016/j.physd.2005.06.011},
   Abstract = {We consider the problem of a thin film driven by a thermal
             gradient with an opposing gravitational force. Under
             appropriate conditions, an advancing film front develops a
             leading undercompressive shock followed by a trailing
             compressive shock. Here, we investigate the nonlinear
             dynamics of these shock structures that describe a
             surprisingly stable advancing front. We compare
             two-dimensional simulations with linear stability theory,
             shock theory, and experimental results. The
             theory/experiment considers the propagation of information
             through the undercompressive shock towards the trailing
             compressive shock. We show that a local perturbation
             interacting with the undercompressive shock leads to
             nonlocal effects at the compressive shock. © 2005 Elsevier
             B.V. All rights reserved.},
   Doi = {10.1016/j.physd.2005.06.011},
   Key = {fds245551}
}

@article{fds304525,
   Author = {Behringer, RP and Shearer, M},
   Title = {Physica D: Nonlinear Phenomena: Preface},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {209},
   Number = {1-4 SPEC. ISS.},
   Pages = {vii-viii},
   Year = {2005},
   url = {http://dx.doi.org/10.1016/j.physd.2005.08.003},
   Doi = {10.1016/j.physd.2005.08.003},
   Key = {fds304525}
}

@article{fds318409,
   Author = {Daniels, KE and Behringer, RP},
   Title = {Characterization of a freezing/melting transition in a
             vibrated and sheared granular medium},
   Journal = {Powders and Grains 2005 - Proceedings of the 5th
             International Conference on Micromechanics of Granular
             Media},
   Volume = {1},
   Pages = {357-360},
   Year = {2005},
   Abstract = {We describe experiments on monodisperse spherical particles
             in an annular cell geometry, vibrated from below and sheared
             from above. This system shows a freezing/melting transition
             such that under sufficient vibration a crystallized state is
             observed, which can be melted by sufficient shear. We
             characterize the hysteretic transition between these two
             states, and observe features reminiscent of both a jamming
             transition and critical phenomena. © 2005 Taylor &amp;
             Francis Group.},
   Key = {fds318409}
}

@article{fds303629,
   Author = {Sur, J and Witelski, TP and Behringer, RP},
   Title = {Steady-profile fingering flows in Marangoni driven thin
             films.},
   Journal = {Physical Review Letters},
   Volume = {93},
   Number = {24},
   Pages = {247803},
   Year = {2004},
   Month = {December},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15697861},
   Abstract = {We present experimental and computational results indicating
             the existence of finite-amplitude fingering solutions in a
             flow of a thin film of a viscous fluid driven by thermally
             induced Marangoni stresses. Using carefully controlled
             experiments, spatially periodic perturbations to the contact
             line of an initially uniform thin film flow are shown to
             lead to the development of steady-profile two-dimensional
             traveling wave fingers. Using an infrared laser and scanning
             mirror, we impose thermal perturbations with a known
             wavelength to an initially uniform advancing fluid front. As
             the front advances in the experiment, we observe convergence
             to fingers with the initially prescribed wavelength.
             Experiments and numerical computations show that this family
             of solutions arises from a subcritical bifurcation.},
   Doi = {10.1103/PhysRevLett.93.247803},
   Key = {fds303629}
}

@article{fds245643,
   Author = {Geng, J and Behringer, RP},
   Title = {Diffusion and mobility in a stirred dense granular
             material.},
   Journal = {Physical Review Letters},
   Volume = {93},
   Number = {23},
   Pages = {238002},
   Year = {2004},
   Month = {December},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15601205},
   Abstract = {We describe a probe of diffusivity (D) and mobility (B) for
             a dense 2D granular system. We introduce random motion by
             stirring, and characterize D by particle tracking. To
             measure B we measure the force needed to push a particle
             through the medium at fixed velocity, v, using three sizes
             of tracer particle. We find simple Brownian diffusion, but B
             depends strongly on v because the force needed to push a
             tracer through a sample is nearly independent of v. Data for
             D/B depend on the tracer particle size.},
   Doi = {10.1103/PhysRevLett.93.238002},
   Key = {fds245643}
}

@article{fds245546,
   Author = {Dutt, M and Behringer, RP},
   Title = {Effects of surface friction on a two-dimensional granular
             system: cooling bound system.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {70},
   Number = {6 Pt 1},
   Pages = {061304},
   Year = {2004},
   Month = {December},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15697352},
   Abstract = {Experiments performed by Phys. Rev. E 62, 2380 (2000)] on
             two-particle collisions and dynamics emphasized the
             importance of the role played by substrate friction, in
             particular kinetic friction, on the particle dynamics after
             collisions on a substrate. We present a numerical model
             which accounts for collisional and surface frictional
             dissipation and their influence on particle dynamics for a
             quasi-two-dimensional cooling initially dilute granular
             material. This model makes the simplifying assumption that
             the collision dynamics is determined solely by the incoming
             velocity and angular velocities of the colliding particles.
             We apply this model to a numerical simulation of a monolayer
             of monodisperse particles moving on a substrate, enclosed
             between inelastic walls. We find that surface friction-in
             particular, kinetic friction-plays a dominant role in
             determining the dynamics of quasi-two-dimensional
             multiparticle systems where the particles are in continuous
             contact with a substrate. Results from simulations performed
             for different system sizes indicate that surface friction
             and the inelastic walls lead to clustering of the particles
             in and near the vicinity of the walls. We find that the rate
             of decrease of average total kinetic energy is the highest
             when the majority of the particles have just collided and
             are experiencing kinetic frictional forces and torques. We
             also find from our calculations that, on average,
             particle-wall collisions lead to more dissipation than
             particle-particle collisions for a single particle for fixed
             restitutional parameters.},
   Doi = {10.1103/PhysRevE.70.061304},
   Key = {fds245546}
}

@article{fds245638,
   Author = {Daniels, KE and Coppock, JE and Behringer, RP},
   Title = {Dynamics of meteor impacts.},
   Journal = {Chaos},
   Volume = {14},
   Number = {4},
   Pages = {S4},
   Year = {2004},
   Month = {December},
   ISSN = {1054-1500},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15568901},
   Doi = {10.1063/1.1821711},
   Key = {fds245638}
}

@article{fds245639,
   Author = {Utter, B and Behringer, RP},
   Title = {Transients in sheared granular matter.},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {14},
   Number = {4},
   Pages = {373-380},
   Year = {2004},
   Month = {August},
   ISSN = {1292-8941},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15338433},
   Abstract = {As dense granular materials are sheared, a shear band and an
             anisotropic force network form. The approach to steady-state
             behavior depends on the history of the packing and the
             existing force and contact network. We present experiments
             on shearing of dense granular matter in a 2D Couette
             geometry in which we probe the history and evolution of
             shear bands by measuring particle trajectories and stresses
             during transients. We find that when shearing is stopped and
             restarted in the same direction, steady-state behavior is
             immediately reached, in agreement with the typical
             assumption that the system is quasistatic. Although some
             relaxation of the force network is observed when shearing is
             stopped, quasistatic behavior is maintained because the
             contact network remains essentially unchanged. When the
             direction of shear is reversed, a transient occurs in which
             stresses initially decrease, changes in the force network
             reach further into the bulk, and particles far from the
             wheel become more mobile. This occurs because the force
             network is fragile to changes transverse to the force
             network established under previous shear; particles must
             rearrange before becoming jammed again, thereby providing
             resistance to shear in the reversed direction. The strong
             force network is re-established after displacing the
             shearing surface approximately equal 3d, where d is the mean
             grain diameter. Steady-state velocity profiles are reached
             after a shear of < or approximately equal 30 d. Particles
             immediately outside of the shear band move on average less
             than 1 diameter before becoming jammed again. We also
             examine particle rotation during this transient and find
             that mean particle spin decreases during the transient,
             which is related to the fact that grains are not interlocked
             as strongly.},
   Doi = {10.1140/epje/i2004-10022-4},
   Key = {fds245639}
}

@article{fds303634,
   Author = {Geng, J and Behringer, RP},
   Title = {Slow Drag in 2D Granular Media},
   Volume = {71},
   Pages = {011302},
   Year = {2004},
   Month = {June},
   url = {http://arxiv.org/abs/cond-mat/0406327v1},
   Abstract = {We study the drag force experienced by an object slowly
             moving at constant velocity through a 2D granular material
             consisting of bidisperse disks. The drag force is dominated
             by force chain structures in the bulk of the system, thus
             showing strong fluctuations. We consider the effect of three
             important control parameters for the system: the packing
             fraction, the drag velocity and the size of the tracer
             particle. We find that the mean drag force increases as a
             power-law (exponent of 1.5) in the reduced packing fraction,
             $(\gamma - \gamma_c)/\gamma_c$, as $\gamma$ passes through a
             critical packing fraction, $\gamma_c$. By comparison, the
             mean drag grows slowly (basically logarithmic) with the drag
             velocity, showing a weak rate-dependence. However, the
             system nevertheless exhibits strong statistical invariance
             in the sense that many physical quantities collapse onto a
             single curve under appropriate scaling. We also show that
             the system can be understood using simple failure models,
             which reproduce many experimental observations. These
             experimental data and simulations indicate that fluctuations
             in the drag force seem to be associated with the force chain
             formation and breaking in the system. Moreover, our
             simulations suggest that the logarithmic increase of the
             mean drag force with rate can be accounted for if slow
             relaxation of the force chain networks is
             included.},
   Key = {fds303634}
}

@article{fds245642,
   Author = {Utter, B and Behringer, RP},
   Title = {Self-diffusion in dense granular shear flows.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {69},
   Number = {3 Pt 1},
   Pages = {031308},
   Year = {2004},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15089287},
   Abstract = {Diffusivity is a key quantity in describing velocity
             fluctuations in granular materials. These fluctuations are
             the basis of many thermodynamic and hydrodynamic models
             which aim to provide a statistical description of granular
             systems. We present experimental results on diffusivity in
             dense, granular shear flows in a two-dimensional Couette
             geometry. We find that self-diffusivities D are proportional
             to the local shear rate gamma; with diffusivities along the
             direction of the mean flow approximately twice as large as
             those in the perpendicular direction. The magnitude of the
             diffusivity is D approximately gamma;a(2), where a is the
             particle radius. However, the gradient in shear rate,
             coupling to the mean flow, and strong drag at the moving
             boundary lead to particle displacements that can appear
             subdiffusive or superdiffusive. In particular, diffusion
             appears to be superdiffusive along the mean flow direction
             due to Taylor dispersion effects and subdiffusive along the
             perpendicular direction due to the gradient in shear rate.
             The anisotropic force network leads to an additional
             anisotropy in the diffusivity that is a property of dense
             systems and has no obvious analog in rapid flows.
             Specifically, the diffusivity is suppressed along the
             direction of the strong force network. A simple random walk
             simulation reproduces the key features of the data, such as
             the apparent superdiffusive and subdiffusive behavior
             arising from the mean velocity field, confirming the
             underlying diffusive motion. The additional anisotropy is
             not observed in the simulation since the strong force
             network is not included. Examples of correlated motion, such
             as transient vortices, and Lévy flights are also observed.
             Although correlated motion creates velocity fields which are
             qualitatively different from collisional Brownian motion and
             can introduce nondiffusive effects, on average the system
             appears simply diffusive.},
   Doi = {10.1103/PhysRevE.69.031308},
   Key = {fds245642}
}

@article{fds29637,
   Author = {R.P. Behringer and M. Carey and M. Steen and L.
             Howle},
   Title = {Onset of Convection for a Miscible Fluid in a Porous
             Medium},
   Series = {Warsaw, Poland},
   Booktitle = {Proceedings of the 21st International Congress of
             Theoretical and Applied Mechanics},
   Year = {2004},
   Key = {fds29637}
}

@article{fds43790,
   Author = {L. Kondic and R.P. Behringer},
   Title = {Extended Granular Temperature},
   Pages = {12-12399},
   Booktitle = {Proceedings of te 21st International Congress of Theoretical
             and Applied Mechanics},
   Year = {2004},
   Key = {fds43790}
}

@article{fds43792,
   Author = {R.P. Behringer and M. Carey and M. Steen and L.
             Howle},
   Title = {Onset of Convectin for a Miscible Fluid in a Porous
             Medium},
   Pages = {26-10746},
   Booktitle = {Proceedings of te 21st International Congress of Theoretical
             and Applied Mechanics},
   Year = {2004},
   Key = {fds43792}
}

@article{fds245640,
   Author = {Sur, J and Witelski, TP and Behringer, RP},
   Title = {Steady Fingering Flows in Marangoni Driven
             Film},
   Journal = {Phys. Rev. Lett.},
   Volume = {93},
   Number = {24},
   Pages = {247803},
   Year = {2004},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15697861},
   Abstract = {We present experimental and computational results indicating
             the existence of finite-amplitude fingering solutions in a
             flow of a thin film of a viscous fluid driven by thermally
             induced Marangoni stresses. Using carefully controlled
             experiments, spatially periodic perturbations to the contact
             line of an initially uniform thin film flow are shown to
             lead to the development of steady-profile two-dimensional
             traveling wave fingers. Using an infrared laser and scanning
             mirror, we impose thermal perturbations with a known
             wavelength to an initially uniform advancing fluid front. As
             the front advances in the experiment, we observe convergence
             to fingers with the initially prescribed wavelength.
             Experiments and numerical computations show that this family
             of solutions arises from a subcritical bifurcation.},
   Doi = {10.1103/PhysRevLett.93.247803},
   Key = {fds245640}
}

@article{fds245641,
   Author = {Kondic, L and Behringer, RP},
   Title = {Elastic energy, fluctuations and temperature for granular
             materials},
   Journal = {Europhysics Letters},
   Volume = {67},
   Number = {2},
   Pages = {205-211},
   Year = {2004},
   url = {http://dx.doi.org/10.1209/epl/i2004-10061-5},
   Abstract = {We probe, using a model system, elastic and kinetic energies
             for sheared granular materials. For large enough P/Ey
             (pressure/Young's modulus) and P/v2 (P/kinetic energy
             density) elastic dominates kinetic energy, and energy
             fluctuations become primarily elastic in nature. This regime
             has likely been reached in recent experiments. We consider a
             generalization of the granular temperature, Tg, with both
             kinetic and elastic terms and that changes smoothly from one
             regime to the other. This Tg is roughly consistent with a
             temperature adapted from equilibrium statistical
             mechanics.},
   Doi = {10.1209/epl/i2004-10061-5},
   Key = {fds245641}
}

@article{fds245644,
   Author = {Sur, J and Bertozzi, AL and Behringer, RP},
   Title = {Reverse undercompressive shock structures in driven thin
             film flow.},
   Journal = {Physical Review Letters},
   Volume = {90},
   Number = {12},
   Pages = {126105},
   Year = {2003},
   Month = {March},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12688890},
   Abstract = {We show experimental and computational evidence of a new
             structure: an undercompressive and reverse undercompressive
             shock for draining films driven by a surface tension
             gradient against gravity. The reverse undercompressive shock
             is unstable to transverse perturbations while the leading
             undercompressive shock is stable. Depending on the pinch-off
             film thickness, as controlled by the meniscus, either a
             trailing rarefaction wave or a compressive shock separates
             from the reverse undercompressive shock.},
   Doi = {10.1103/PhysRevLett.90.126105},
   Key = {fds245644}
}

@article{fds17070,
   Author = {Marc Laetzel and Stefan Luding and H.J. Herrmann and D.W. Howell and R.P. Behringer},
   Title = {Eur. Phys. J. E},
   Volume = {11},
   Pages = {325-333},
   Year = {2003},
   Key = {fds17070}
}

@article{fds17071,
   Author = {R. R Hartley and R.P. Behringer},
   Title = {Logarithmic rate dependence of force networks in sheared
             granular materials},
   Journal = {Nature},
   Volume = {421},
   Pages = {928-930},
   Year = {2003},
   Key = {fds17071}
}

@article{fds245535,
   Author = {R.P. Behringer and Painter, B and Dutt, M and Behringer, RP},
   Title = {Energy dissipation and clustering for a cooling granular
             material on a substrate},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {175},
   Number = {1-2},
   Pages = {43-68},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0167-2789(02)00566-3},
   Abstract = {We experimentally study the dynamics of a cooling
             two-dimensional granular system of steel spheres moving
             radially inward on an aluminum substrate. We find that the
             cooling process in this system differs significantly from
             model calculations that include realistic restitutional
             losses and rolling (hence, weak) friction. A likely
             explanation for the experimental observations is the fact
             that particles typically slide on the substrate for some
             time after each collision, losing energy rapidly. Using
             results from an MD simulation as a reference point, we
             consider detailed experimental results for the cooling of
             systems of spheres on a substrate as a function of the
             system size, N. For systems with more than N=300 particles,
             we find that final spatial configurations consist primarily
             of dense central clusters, and that the velocity
             distributions, which have an exponential character, are only
             weakly dependent on system size. Thus, there is a critical
             system size above which a majority of particles come to rest
             in a densely packed lattice. We also find evidence of a
             spatial ordering size scale in the cooled state that is much
             smaller than the system size. Velocity distributions in the
             cooling system are nearly Maxwell-Boltzmann (MB)-like at
             early times, but show significant differences from a MB
             distribution after particles have undergone a moderate
             number of collisions. © 2002 Published by Elsevier
             B.V.},
   Doi = {10.1016/S0167-2789(02)00566-3},
   Key = {fds245535}
}

@article{fds245616,
   Author = {Kondic, L and Hartley, RR and Tennakoon, SGK and Painter, B and Behringer, RP},
   Title = {Segregation by friction},
   Journal = {Europhysics Letters},
   Volume = {61},
   Number = {6},
   Pages = {742-748},
   Year = {2003},
   url = {http://dx.doi.org/10.1209/epl/i2003-00291-y},
   Abstract = {Granular materials are known to separate by size under a
             variety of circumstances. Experiments presented here and
             elucidated by modeling and MD simulation document a new
             segregation mechanism, namely segregation by friction. The
             experiments are carried out by placing steel spheres on a
             horizontal plane enclosed by rectangular sidewalls, and
             subjecting them to horizontal shaking. Half the spheres are
             highly smooth; the remainder are identical to the first
             half, except that their surfaces have been roughened by
             chemical etching, giving them higher coefficients of
             friction. Segregation due to this difference in friction
             occurs, particularly when the grains have a relatively long
             mean free path. In the presence of an appropriately chosen
             small "hill" in the middle of the container, the grains can
             be made to completely segregate by friction
             type.},
   Doi = {10.1209/epl/i2003-00291-y},
   Key = {fds245616}
}

@article{fds245645,
   Author = {Geng, J and Behringer, RP and Reydellet, G and Clement,
             E},
   Title = {Green's Function Measurements in2D Granualr
             Materials},
   Journal = {Physica D},
   Volume = {182},
   Number = {3-4},
   Pages = {274-303},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0167-2789(03)00137-4},
   Abstract = {We describe experiments that probe the response to a point
             force of 2D granular systems under a variety of conditions.
             Using photoelastic particles to determine forces at the
             grain scale, we obtain ensembles of responses for the
             following particle types, packing geometries and conditions:
             monodisperse ordered hexagonal packings of disks, bidisperse
             packings of disks with different amounts of disorder, disks
             packed in a regular rectangular lattice with different
             frictional properties, packings of pentagonal particles,
             systems with forces applied at an arbitrary angle at the
             surface, and systems prepared with shear deformation, hence
             with texture or anisotropy. We experimentally show that
             disorder, packing structure, friction and texture
             significantly affect the average force response in granular
             systems. For packings with weak disorder, the mean forces
             propagate primarily along lattice directions. The width of
             the response along these preferred directions grows with
             depth, increasingly so as the disorder of the system grows.
             Also, as the disorder increases, the two propagation
             directions of the mean force merge into a single direction.
             The response function for the mean force in the most
             strongly disordered system is quantitatively consistent with
             an elastic description for forces applied nearly normally to
             a surface, but this description is not as good for
             non-normal applied forces. These observations are consistent
             with recent predictions of Bouchaud et al. [Eur. Phys. J. E
             4 (2001) 451] and Socolar et al. [Eur. Phys. J. E 7 (2002)
             353] and with the anisotropic elasticity models of
             Goldenberg and Goldhirsch [Phys. Rev. Lett. 89 (2002)
             084302]. At this time, it is not possible to distinguish
             between these two models. The data do not support a
             diffusive picture, as in the q-model, and they are in
             conflict with data by Da Silva and Rajchenbach [Nature 406
             (2000) 708] that indicate a parabolic response for a system
             consisting of cuboidal blocks. We also explore the spatial
             properties of force chains in an anisotropic textured system
             created by a nearly uniform shear. This system is
             characterized by stress chains that are strongly oriented
             along an angle of 45°, corresponding to the compressive
             direction of the shear deformation. In this case, the
             spatial correlation function for force has a range of only
             one particle size in the direction transverse to the chains,
             and varies as a power law in the direction of the chains,
             with an exponent of -0.81. The response to forces is the
             strongest along the direction of the force chains, as
             expected. Forces applied in other directions are effectively
             refocused towards the strong force chain direction. ©
             2003 Elsevier Science B.V. All rights reserved.},
   Doi = {10.1016/S0167-2789(03)00137-4},
   Key = {fds245645}
}

@article{fds304524,
   Author = {Geng, J and Reydellet, G and Clément, E and Behringer,
             RP},
   Title = {Green's function measurements of force transmission in 2D
             granular materials},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {182},
   Number = {3-4},
   Pages = {274-303},
   Year = {2003},
   url = {http://dx.doi.org/10.1016/S0167-2789(03)00137-4},
   Abstract = {We describe experiments that probe the response to a point
             force of 2D granular systems under a variety of conditions.
             Using photoelastic particles to determine forces at the
             grain scale, we obtain ensembles of responses for the
             following particle types, packing geometries and conditions:
             monodisperse ordered hexagonal packings of disks, bidisperse
             packings of disks with different amounts of disorder, disks
             packed in a regular rectangular lattice with different
             frictional properties, packings of pentagonal particles,
             systems with forces applied at an arbitrary angle at the
             surface, and systems prepared with shear deformation, hence
             with texture or anisotropy. We experimentally show that
             disorder, packing structure, friction and texture
             significantly affect the average force response in granular
             systems. For packings with weak disorder, the mean forces
             propagate primarily along lattice directions. The width of
             the response along these preferred directions grows with
             depth, increasingly so as the disorder of the system grows.
             Also, as the disorder increases, the two propagation
             directions of the mean force merge into a single direction.
             The response function for the mean force in the most
             strongly disordered system is quantitatively consistent with
             an elastic description for forces applied nearly normally to
             a surface, but this description is not as good for
             non-normal applied forces. These observations are consistent
             with recent predictions of Bouchaud et al. [Eur. Phys. J. E
             4 (2001) 451] and Socolar et al. [Eur. Phys. J. E 7 (2002)
             353] and with the anisotropic elasticity models of
             Goldenberg and Goldhirsch [Phys. Rev. Lett. 89 (2002)
             084302]. At this time, it is not possible to distinguish
             between these two models. The data do not support a
             diffusive picture, as in the q-model, and they are in
             conflict with data by Da Silva and Rajchenbach [Nature 406
             (2000) 708] that indicate a parabolic response for a system
             consisting of cuboidal blocks. We also explore the spatial
             properties of force chains in an anisotropic textured system
             created by a nearly uniform shear. This system is
             characterized by stress chains that are strongly oriented
             along an angle of 45°, corresponding to the compressive
             direction of the shear deformation. In this case, the
             spatial correlation function for force has a range of only
             one particle size in the direction transverse to the chains,
             and varies as a power law in the direction of the chains,
             with an exponent of -0.81. The response to forces is the
             strongest along the direction of the force chains, as
             expected. Forces applied in other directions are effectively
             refocused towards the strong force chain direction. © 2003
             Elsevier Science B.V. All rights reserved.},
   Doi = {10.1016/S0167-2789(03)00137-4},
   Key = {fds304524}
}

@article{fds17075,
   Author = {Jeanman Sur and A.L. Bertozzi and R.P. Behringer},
   Title = {Reverse Undercompressive Shock Structures in Driven Thin
             Film Flow},
   Journal = {Phys. Rev. Lett.},
   Volume = {90},
   Pages = {126105},
   Year = {2002},
   Month = {December},
   Key = {fds17075}
}

@article{fds17078,
   Author = {L. Kondic and S. G. K. Tennakoon and B. Painter and R. Hartley and R.P. Behringer},
   Title = {A frictional Analoguye of the Brazil Nut
             Effect},
   Year = {2002},
   Month = {December},
   Key = {fds17078}
}

@article{fds245633,
   Author = {Painter, B and Dutt, M and Behringer, RP},
   Title = {Energy dissipation and clustering for a cooling granular
             material on a substrate},
   Journal = {Physica D},
   Volume = {2979},
   Pages = {1-26},
   Year = {2002},
   Month = {December},
   Key = {fds245633}
}

@article{fds245630,
   Author = {Metcalfe, G and Tennakoon, SGK and Kondic, L and Schaeffer, DG and Behringer, RP},
   Title = {Granular friction, Coulomb failure, and the fluid-solid
             transition for horizontally shaken granular
             materials.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {65},
   Number = {3 Pt 1},
   Pages = {031302},
   Year = {2002},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11909041},
   Abstract = {We present the results of an extensive series of
             experiments, molecular dynamics simulations, and models that
             address horizontal shaking of a layer of granular material.
             The goal of this work was to better understand the
             transition between the "fluid" and "solid" states of
             granular materials. In the experiments, the
             material-consisting of glass spheres, smooth and rough
             sand-was contained in a container of rectangular cross
             section, and subjected to horizontal shaking of the form x=A
             sin(omega(t)). The base of the container was porous, so that
             it was possible to reduce the effective weight of the sample
             by means of a vertical gas flow. The acceleration of the
             shaking could be precisely controlled by means of an
             accelerometer mounted onboard the shaker, plus feedback
             control and lockin detection. The relevant control parameter
             for this system was the dimensionless acceleration,
             Gamma=Aomega(2)/g, where g was the acceleration of gravity.
             As Gamma was varied, the layer underwent a backward
             bifurcation between a solidlike state that was stationary in
             the frame of the shaker and a fluidlike state that typically
             consisted of a sloshing layer of maximum depth H riding on
             top of a solid layer. That is, with increasing Gamma, the
             solid state made a transition to the fluid state at
             Gamma(cu) and once the system was in the fluid state, a
             decrease in Gamma left the system in the fluidized state
             until Gamma reached Gamma(cd)<Gamma(cu). In the fluidized
             state, the flow consisted of back and forth sloshing at the
             shaker frequency, plus a slower convective flow along the
             shaking direction and additionally in the horizontal
             direction transverse to the shaking direction. Molecular
             dynamics simulations show that the last of these flows is
             associated with shear and dilation at the vertical
             sidewalls. For Gamma<Gamma(cu) and in the solid state, there
             was a "gas" of free particles sliding on the surface of the
             material. These constituted much less than one layer's worth
             of particles in all cases. If these "sliders" were
             suppressed by placing a thin strip of plastic on the
             surface, the hysteresis was removed, and the transition to
             fluidization occurred at a slightly lower value than
             Gamma(cd) for the free surface case. The hysteresis was also
             suppressed if a vertical gas flow from the base was
             sufficient to support roughly 40% of the weight of the
             sample. Both the transition to the fluid state from the
             solid and the reverse transition from the fluid to the solid
             were characterized by similar divergent time scales. If
             Gamma was increased above Gamma(cu) by a fractional amount
             epsilon=(Gamma-Gamma(cu))/Gamma(cu), where epsilon was
             small, there was a characteristic time tau=Aepsilon(-beta)
             for the transition from solid to fluid to occur, where beta
             is 1.00+/-0.06. Similarly, if Gamma was decreased below
             Gamma(cd) in the fluidized state by an amount
             epsilon=(Gamma-Gamma(cd))/Gamma(cd), there was also a
             transient time tau=Bepsilon(-beta), where beta is again
             indistinguishable from 1.00. In addition, the amplitudes A
             and B are essentially identical. By placing a small
             "impurity" on top of the layer, consisting of a heavier
             particle, we found that the exponent beta varied as the
             impurity mass squared and changed by a factor of 3. A simple
             Coulomb friction model with friction coefficients
             mu(k)<mu(s) for the fluid and solid states predicts a
             reversible rather than hysteretic transition to the fluid
             state, similar to what we observe with the addition of the
             small overload from a plastic strip. In an improved model,
             we provide a relaxational mechanism that allows the friction
             coefficient to change continuously between the low and high
             values. This model produces the hysteresis seen in
             experiments.},
   Doi = {10.1103/PhysRevE.65.031302},
   Key = {fds245630}
}

@article{fds304520,
   Author = {Behringer, B},
   Title = {Granular materials: Taking the temperature},
   Journal = {Nature},
   Volume = {415},
   Number = {6872},
   Pages = {594-595},
   Year = {2002},
   Month = {February},
   url = {http://dx.doi.org/10.1038/415594a},
   Abstract = {The 'temperature' of a granular material depends on its
             entropy, but is hard to measure in the laboratory. So a
             theory that ties temperature to grain mobility and diffusion
             is welcome.},
   Doi = {10.1038/415594a},
   Key = {fds304520}
}

@article{fds245635,
   Author = {Behringer, RP},
   Title = {Taking the Temperature},
   Journal = {Nature},
   Volume = {415},
   Number = {6872},
   Pages = {594-595},
   Year = {2002},
   Month = {February},
   Abstract = {The 'temperature' of a granular material depends on its
             entropy, but is hard to measure in the laboratory. So a
             theory that ties temperature to grain mobility and diffusion
             is welcome.},
   Key = {fds245635}
}

@article{fds245634,
   Author = {Behringer, RP and Doorn, EV and Hartley, RR and Pak,
             HK},
   Title = {Making a rough place "plane": Why heaping of vertically
             shaken sand must stop at low pressure},
   Journal = {Granular Matter},
   Volume = {4},
   Number = {1},
   Pages = {9-15},
   Year = {2002},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-001-0098-7},
   Abstract = {The heaping of a granular material subject to vertical
             vibration vanishes abruptly as the pressure of the
             surrounding gas, P, is lowered below a critial value ̃10
             Torr, depending on particle diameter etc. We show that the
             vanishing of the heap is consistent with two different
             effects. One of these is the onset of a Knudsen regime where
             the mean free path of a gas molecule becomes comparable to
             or larger than the typical distance to a grain. The usual
             Darcian gas flow models fail in this regime, and a Knudsen
             replacement predicts a vanishing of gas effects as P → 0.
             The other is that at low enough pressures, there is not
             enough gas to sustain flow under the usual linearized flow
             scenario. A detailed description of this regime is beyond
             the present analysis. © Springer-Verlag
             2002.},
   Doi = {10.1007/s10035-001-0098-7},
   Key = {fds245634}
}

@article{fds3965,
   Author = {Guy Metcalfe and S.G.K. Tennakoon and L. Kondic and D.G. Schaeffer and R.P. Behringer},
   Title = {Solid-Liquid transitions of horizontally shaken drygranular
             materials},
   Journal = {Powders and Grains 2001},
   Volume = {4},
   Pages = {513-516},
   Year = {2001},
   Month = {December},
   Key = {fds3965}
}

@article{fds245426,
   Author = {Behringer, RP},
   Title = {Fluctuations and phase transitions in granular
             materials},
   Journal = {2001 Conference and Exhibit on International Space Station
             Utilization},
   Year = {2001},
   Month = {December},
   Abstract = {We describe background science for proposed experiments on
             granular materials. These materials present a rich set of
             phenmonena and a host of unanswered questions. Earth's
             gravity is a significant impediment to new knowledge. Here,
             I review some of the important questions. At the conclusion
             of the presentation, I will indicate the direction for new
             experiments in reduced g. © 2001 by the American Institute
             of Aeronautics and Astronautics, Inc.},
   Key = {fds245426}
}

@article{fds245627,
   Author = {Geng, J and Longhi, E and Behringer, RP and Howell,
             DW},
   Title = {Memory in two-dimensional heap experiments.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {64},
   Number = {6 Pt 1},
   Pages = {060301},
   Year = {2001},
   Month = {December},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11736161},
   Abstract = {The measurement of force distributions in sandpiles provides
             a useful way to test concepts and models of the way forces
             propagate within noncohesive granular materials. Recent
             theory [J.-P. Bouchaud, M.E. Cates, and P. Claudin, J. Phys.
             I 5, 639 (1995); M. E. Cates, J. P. Wittmer, J.-P. Bouchaud,
             and P. Claudin, Phil. Trans. Roy. Soc. 356, 2535 (1998)] by
             Bouchaud et al. implies that the internal structure of a
             heap (and therefore the force pathway) is a strong function
             of the construction history. In general, it is difficult to
             obtain information that could test this idea from
             three-dimensional granular experiments except at boundaries.
             However, two-dimensional systems, such as those used here,
             can yield information on forces and particle arrangements in
             the interior of a sample. We obtain position and force
             information through the use of photoelastic particles. These
             experiments show that the history of the heap formation has
             a dramatic effect on the arrangement of particles (texture)
             and a weaker but clear effect on the forces within the
             sample. Specifically, heaps prepared by pouring from a point
             source show strong anisotropy in the contact angle
             distribution. Depending on additional details, they show a
             stress dip near the center. Heaps formed from a broad source
             show relatively little contact angle anisotropy and no
             indication of a stress dip.},
   Doi = {10.1103/PhysRevE.64.060301},
   Key = {fds245627}
}

@article{fds245632,
   Author = {Behringer, RP and Clement, E and Geng, J and Howell, D and Kondic,
             L},
   Title = {Science in the Sandbox: Fluctuations, Friction
             and},
   Journal = {Lecture Notes in Physics},
   Volume = {567},
   Pages = {351-391},
   Year = {2001},
   Month = {December},
   Key = {fds245632}
}

@article{fds3957,
   Author = {R.P. Behringer},
   Title = {Fluctuations and Phase Transitions in GranularMaterials},
   Journal = {AIAA Conference on International Space Station
             Utilization},
   Year = {2001},
   Month = {October},
   Key = {fds3957}
}

@article{fds245628,
   Author = {Behringer, RP and Geng, J and Howell, D and Longhi, E and Reydellet, G and Vanel, L and Clement, E},
   Title = {Fluctuations in granular materials},
   Journal = {Powders and Grains},
   Volume = {4},
   Pages = {347-354},
   Year = {2001},
   Month = {June},
   Key = {fds245628}
}

@article{fds245460,
   Author = {Behringer, RP},
   Title = {Books},
   Journal = {Physics today},
   Volume = {54},
   Number = {4},
   Pages = {63-},
   Year = {2001},
   ISSN = {0031-9228},
   Key = {fds245460}
}

@article{fds245629,
   Author = {Geng, J and Howell, D and Longhi, E and Behringer, RP and Reydellet, G and Vanel, L and Clément, E and Luding, S},
   Title = {Footprints in sand: The response of a granular material to
             local perturbations},
   Journal = {Physical Review Letters},
   Volume = {87},
   Number = {3},
   Pages = {355061-355064},
   Year = {2001},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11461569},
   Abstract = {The forced response of granular packings to point forces was
             experimentally measured and compared to recent models for
             force propogation in a granular material. 2D granular arrays
             made of photoelastic particles were used for the modeling.
             Spatial ordering of the particles was found to be a key
             factor in the force response. The propogative component of
             ordered packings was found to dimnish with the degree of
             disorder.},
   Doi = {10.1103/PhysRevLett.87.035506},
   Key = {fds245629}
}

@article{fds3971,
   Author = {E. Clement and G. Reydellet. L. Vanel and D.W. Howell and J. Geng
             andR.P. Behringer},
   Title = {Experiments on stress propagation in granular},
   Journal = {XIIIth International Congress on Rheolog},
   Pages = {24-26},
   Year = {2000},
   Month = {December},
   Key = {fds3971}
}

@article{fds245626,
   Author = {Painter, B and Behringer, RP},
   Title = {Dynamics of two-particle},
   Journal = {Phys. Rev. E},
   Volume = {62},
   Number = {2 B},
   Pages = {2380},
   Year = {2000},
   Month = {December},
   ISSN = {1063-651X},
   Abstract = {A study was carried out to examine in detail some important
             aspects of the dynamics of two-particle collisions that
             occur on a surface. For this purpose, 2.38 mm diameter steel
             balls were moved on a flat aluminum surface. The motion of
             the particles, as well as the surface effects were
             determined through measurements.},
   Key = {fds245626}
}

@article{fds245631,
   Author = {Behringer, RP and Kondic, L and Metcalfe, G and Schaeffer, D and Tennakoon, GK},
   Title = {Friction and Flow in Granular Materials},
   Journal = {Mat. Res. Soc. Proc.},
   Volume = {627},
   Pages = {BB5.4.1},
   Year = {2000},
   Month = {December},
   Abstract = {We probe the transitions between solid-like and fluid-like
             granular states in the presence of shaking in the horizontal
             and vertical directions. These transitions are fundamental
             to other aspects of granular flow such as avalanche flow, in
             which there is a free surface. Key control parameters
             include accelerations in the vertical and horizontal
             directions, Γ, = A,ω2,/g, for shaking of the form s,
             = A, cos(ωl + φ,), i = h, v. Here, g is the
             acceleration of gravity. Also important is the relative
             phase between the two modes of shaking. We focus on low to
             moderate dimensionless accelerations, 0 &gt; Γv.h &gt;
             1.6. We consider first the case Γv = 0, i.e. pure
             horizontal shaking. In this case, there is a hysteretic
             transition between solid and fluid states, where the fluid
             state consists of a sloshing layer of material of height ti
             plus additional transverse flow. The hysteresis is lifted in
             the presence of a modest amount of fluidization by gas flow,
             or if a slight overburden is provided. We also identify a
             time scale, Ï„, for the transition between the phases
             that diverges inversely as the distance ε =
             (Γh-Γhc)/Γhc, from the appropriate transition
             points, i.e. as τ α ε-1. We identify a new
             convective mechanism, associated with horizontal shearing at
             the walls, as the mechanism that drives the transverse
             convective flow. For combined horizontal and vertical
             shaking, there exist a related set of novel dynamics and
             stability properties. These include the spontaneous
             formation of a static heap and a transition to flow, similar
             to the flow state under horizontal shaking, when the
             vertical acceleration Γv &gt; Ι. A simple friction
             model provides a good description of the steady states and a
             reasonably good description of the transition to flow.
             Horizontal and vertical shaking frequencies that differ by a
             small amount can lead to a novel switching state, as the
             relative phase, φh - φv, shifts over
             time.},
   Key = {fds245631}
}

@article{fds245624,
   Author = {Painter, B and Behringer, RP},
   Title = {Substrate interactions, effects of symmetry breaking, and
             convection in a 2D horizontally shaken granular
             system},
   Journal = {Physical Review Letters},
   Volume = {85},
   Number = {16},
   Pages = {3396-3399},
   Year = {2000},
   Month = {October},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11030905},
   Abstract = {We describe experiments on a horizontally shaken [x =
             Asin(omegat)] single layer of hard spheres rolling on a
             nearly horizontal surface. We identify a novel
             substrate-mediated convective flow which occurs when the
             system is tilted slightly so that the weak gravitational
             force, g-->(eff), acting on the particles is not parallel to
             the driving direction. As the shaking amplitude is
             increased, the system progresses through four regimes:
             solid-flat, solid-inclined, convective, and disordered. The
             control parameter is the driving velocity, Aomega, rather
             than the usual Aomega(2) of vertically shaken 3D systems. At
             the onset of convection, the critical velocity is V(c)
             approximately sqrt[2g(eff)d].},
   Doi = {10.1103/PhysRevLett.85.3396},
   Key = {fds245624}
}

@article{fds304522,
   Author = {Painter, B and Behringer, RP},
   Title = {Dynamics of two-particle granular collisions on a
             surface},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {62},
   Number = {2 B},
   Pages = {2380-2387},
   Year = {2000},
   ISSN = {1063-651X},
   Abstract = {A study was carried out to examine in detail some important
             aspects of the dynamics of two-particle collisions that
             occur on a surface. For this purpose, 2.38 mm diameter steel
             balls were moved on a flat aluminum surface. The motion of
             the particles, as well as the surface effects were
             determined through measurements.},
   Key = {fds304522}
}

@article{fds304523,
   Author = {Behringer, RP and Kondic, L and Metcalfe, G and Schaeffer, D and Tennakoon, SGK},
   Title = {Friction and flow in granular materials},
   Journal = {Materials Research Society Symposium - Proceedings},
   Volume = {627},
   Pages = {BB541-BB5411},
   Year = {2000},
   Abstract = {We probe the transitions between solid-like and fluid-like
             granular states in the presence of shaking in the horizontal
             and vertical directions. These transitions are fundamental
             to other aspects of granular flow such as avalanche flow, in
             which there is a free surface. Key control parameters
             include accelerations in the vertical and horizontal
             directions, Γ, = A,ω2,/g, for shaking of the form s, = A,
             cos(ωl + φ,), i = h, v. Here, g is the acceleration of
             gravity. Also important is the relative phase between the
             two modes of shaking. We focus on low to moderate
             dimensionless accelerations, 0 &gt; Γv.h &gt; 1.6. We
             consider first the case Γv = 0, i.e. pure horizontal
             shaking. In this case, there is a hysteretic transition
             between solid and fluid states, where the fluid state
             consists of a sloshing layer of material of height ti plus
             additional transverse flow. The hysteresis is lifted in the
             presence of a modest amount of fluidization by gas flow, or
             if a slight overburden is provided. We also identify a time
             scale, τ, for the transition between the phases that
             diverges inversely as the distance ε = (Γh-Γhc)/Γhc,
             from the appropriate transition points, i.e. as τ α ε-1.
             We identify a new convective mechanism, associated with
             horizontal shearing at the walls, as the mechanism that
             drives the transverse convective flow. For combined
             horizontal and vertical shaking, there exist a related set
             of novel dynamics and stability properties. These include
             the spontaneous formation of a static heap and a transition
             to flow, similar to the flow state under horizontal shaking,
             when the vertical acceleration Γv &gt; Ι. A simple
             friction model provides a good description of the steady
             states and a reasonably good description of the transition
             to flow. Horizontal and vertical shaking frequencies that
             differ by a small amount can lead to a novel switching
             state, as the relative phase, φh - φv, shifts over
             time.},
   Key = {fds304523}
}

@article{fds3980,
   Author = {R.P. Behringer and H. Jaeger and S. Nagel},
   Title = {Introduction to the Focus Issue on Granular
             Materials},
   Journal = {Chaos},
   Volume = {9},
   Pages = {509-510},
   Year = {1999},
   Month = {December},
   Key = {fds3980}
}

@article{fds245619,
   Author = {Behringer, RP and Howell, D},
   Title = {Fluctuations in Granular Flows},
   Journal = {Chaos},
   Volume = {9},
   Pages = {559-572},
   Year = {1999},
   Month = {December},
   Key = {fds245619}
}

@article{fds245620,
   Author = {Tennakoon, SGK and Kondic, L and Behringer, RP},
   Title = {Onset of Flow in a Horizontally Vibrated Granular Bed:
             Convection by},
   Journal = {Europhys. Lett.},
   Volume = {45},
   Pages = {470-475},
   Year = {1999},
   Month = {December},
   Key = {fds245620}
}

@article{fds245622,
   Author = {Veje, C and Howell, D and Behringer, RP},
   Title = {Kinematics of a 2D Granular Couette Experiment at the
             Transition to},
   Journal = {Phys. Rev. E},
   Volume = {59},
   Pages = {739-745},
   Year = {1999},
   Month = {December},
   Key = {fds245622}
}

@article{fds245623,
   Author = {Vanel, L and Howell, D and Clark, D and Behringer, RP and Clement,
             E},
   Title = {Memories in Sand: Experimental tests of construction history
             on stress},
   Journal = {Phys. Rev. E},
   Number = {60},
   Pages = {R5040},
   Year = {1999},
   Month = {December},
   Key = {fds245623}
}

@booklet{Olafsen99,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {AC thermal conductivity measurements in dilute mixtures of
             He-3 in superfluid He-4},
   Journal = {Journal of Low Temperature Physics},
   Volume = {117},
   Number = {1-2},
   Pages = {53-65},
   Year = {1999},
   Month = {October},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000082955500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1023/A:1021809821766},
   Key = {Olafsen99}
}

@booklet{Behringer99,
   Author = {R.P. Behringer and D. Howell and L. Kondic and S. Tennakoon and C.
             Veje},
   Title = {Predictability and granular materials},
   Journal = {Physica D},
   Volume = {133},
   Number = {1-4},
   Pages = {1 -- 17},
   Year = {1999},
   Month = {September},
   Key = {Behringer99}
}

@booklet{Howell99,
   Author = {Howell, DW and Behringer, RP and Veje, CT},
   Title = {Fluctuations in granular media.},
   Journal = {Chaos},
   Volume = {9},
   Number = {3},
   Pages = {559-572},
   Year = {1999},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12779852},
   Abstract = {Dense slowly evolving or static granular materials exhibit
             strong force fluctuations even though the spatial disorder
             of the grains is relatively weak. Typically, forces are
             carried preferentially along a network of "force chains."
             These consist of linearly aligned grains with
             larger-than-average force. A growing body of work has
             explored the nature of these fluctuations. We first briefly
             review recent work concerning stress fluctuations. We then
             focus on a series of experiments in both two- and
             three-dimension [(2D) and (3D)] to characterize force
             fluctuations in slowly sheared systems. Both sets of
             experiments show strong temporal fluctuations in the local
             stress/force; the length scales of these fluctuations extend
             up to 10(2) grains. In 2D, we use photoelastic disks that
             permit visualization of the internal force structure. From
             this we can make comparisons to recent models and
             calculations that predict the distributions of forces.
             Typically, these models indicate that the distributions
             should fall off exponentially at large force. We find in the
             experiments that the force distributions change
             systematically as we change the mean packing fraction,
             gamma. For gamma's typical of dense packings of
             nondeformable grains, we see distributions that are
             consistent with an exponential decrease at large forces. For
             both lower and higher gamma, the observed force
             distributions appear to differ from this prediction, with a
             more Gaussian distribution at larger gamma and perhaps a
             power law at lower gamma. For high gamma, the distributions
             differ from this prediction because the grains begin to
             deform, allowing more grains to carry the applied force, and
             causing the distributions to have a local maximum at nonzero
             force. It is less clear why the distributions differ from
             the models at lower gamma. An exploration in gamma has led
             to the discovery of an interesting continuous or "critical"
             transition (the strengthening/softening transition) in which
             the mean stress is the order parameter, and the mean packing
             fraction, gamma, must be adjusted to a value gamma(c) to
             reach the "critical point." We also follow the motion of
             individual disks and obtain detailed statistical information
             on the kinematics, including velocities and particle
             rotations or spin. Distributions for the azimuthal velocity,
             V(theta), and spin, S, of the particles are nearly rate
             invariant, which is consistent with conventional wisdom.
             Near gamma(c), the grain motion becomes intermittent causing
             the mean velocity of grains to slow down. Also, the length
             of stress chains grows as gamma-->gamma(c). The 3D
             experiments show statistical rate invariance for the stress
             in the sense that when the power spectra and spectral
             frequencies of the stress time series are appropriately
             scaled by the shear rate, Omega, all spectra collapse onto a
             single curve for given particle and sample sizes. The
             frequency dependence of the spectra can be characterized by
             two different power laws, P proportional, variant
             omega(-alpha), in the high and low frequency regimes: alpha
             approximately 2 at high omega; alpha<2 at low omega. The
             force distributions computed from the 3D stress time series
             are at least qualitatively consistent with exponential
             fall-off at large stresses. (c) 1999 American Institute of
             Physics.},
   Doi = {10.1063/1.166430},
   Key = {Howell99}
}

@booklet{Howell99a,
   Author = {D. Howell and R.P. Behringer and C. Veje},
   Title = {Stress fluctuations in a 2D granular Couette experiment: A
             continuous transition},
   Journal = {Phys. Rev. Lett.},
   Volume = {82},
   Number = {26},
   Pages = {5241 -- 5244},
   Year = {1999},
   Month = {June},
   Key = {Howell99a}
}

@article{fds245541,
   Author = {Hammes, GG},
   Title = {Editorial},
   Journal = {Biochemistry},
   Volume = {38},
   Number = {1},
   Pages = {1},
   Year = {1999},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9890876},
   Doi = {10.1021/bi9900018},
   Key = {fds245541}
}

@article{fds245454,
   Author = {Kondic, L and Tennakoon, SGK and Painter, B and Behringer,
             R},
   Title = {Friction based segregation of 2D granular
             assembly},
   Journal = {Materials Research Society Symposium - Proceedings},
   Volume = {543},
   Pages = {357-362},
   Year = {1999},
   ISSN = {0272-9172},
   Abstract = {We present theoretical, computational (molecular dynamics),
             and experimental results describing the dynamical properties
             of a set of monodisperse, spherical particles confined to a
             two dimensional surface. An interaction model, which
             includes the interaction between the particles via
             collisions as well as the interaction with the substrate,
             shows that the properties of this granular system are
             influenced significantly by the latter. In particular, we
             analyze in detail the effects of slipping and rolling
             friction, which are usually overlooked. Theoretically, we
             explore the possibility of formulating a continuum,
             hydrodynamic-like theory applicable to this system. Further,
             we apply our model to the particular problem of a system of
             two kinds of particles with different frictional properties.
             Our experiments have found that friction-based segregation
             of particles moving on a horizontally shaken substrate can
             be achieved. Computational results give further insight into
             this novel segregation mechanism and confirm that careful
             and realistic modeling is needed in order to understand this
             effect.},
   Key = {fds245454}
}

@booklet{Veje99,
   Author = {Veje, CT and Howell, DW and Behringer, RP},
   Title = {Kinematics of a two-dimensional granular Couette experiment
             at the transition to shearing},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {59},
   Number = {1},
   Pages = {739-745},
   Year = {1999},
   Abstract = {We describe experiments on a two-dimensional granular
             Couette system consisting of photoelastic disks undergoing
             slow shearing. The disks rest on a smooth surface and are
             confined between an inner wheel and an outer ring. Only
             shearing from the inner wheel is considered here. We obtain
             velocity, particle rotation rate (spin), and density
             distributions for the system by tracking positions and
             orientations of individual particles. At a characteristic
             packing fraction, γc ≃ 0.77, the wheel just engages the
             particles. In a narrow range of γ, 0.77≤γ≤0.80 the
             system changes from just able to shear to densely packed.
             The transition at γc has a number of hallmarks of a
             critical transition, including critical slowing down, and an
             order parameter. For instance, the mean stress grows from 0
             as γ increases above γc, and hence plays the role of an
             order parameter. Also, the mean particle velocity vanishes
             at the transition point, implying slowing down at γc. Above
             γc, the mean azimuthal velocity decreases roughly
             exponentially with distance from the inner shearing wheel,
             and the local packing fraction shows roughly comparable
             exponential decay from a highly dilated region next to the
             wheel to a denser but frozen packing further away.
             Approximate but not perfect shear rate invariance occurs;
             variations from perfect rate invariance appear to be related
             to small long-time rearrangements of the disks. The
             characteristic width of the induced "shear band" near the
             wheel varies most rapidly with distance from the wheel for
             γ≃γc, and is relatively insensitive to the packing
             fraction for the larger γ's studied here. The mean particle
             spin oscillates near the wheel, and falls rapidly to zero
             away from the shearing surface. The distributions for the
             tangential velocity and particle spins are wide and show a
             complex shape, particularly for the disk layer nearest to
             the shearing surface. The two-variable distribution function
             for tangential velocity and spin reveals a separation of the
             kinematics into a slipping state and a nonslipping state
             consisting of a combination of rolling and translation.
             ©1999 The American Physical Society.},
   Key = {Veje99}
}

@booklet{Tennakoon99,
   Author = {Tennakoon, SGK and Kondic, L and Behringer, RP},
   Title = {Onset of flow in a horizontally vibrated granular bed:
             Convection by horizontal shearing},
   Journal = {EPL (Europhysics Letters)},
   Volume = {45},
   Number = {4},
   Pages = {470-475},
   Year = {1999},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/epl/i1999-00190-3},
   Abstract = {We present experimental observations of the onset of flow
             for horizontally vibrated 3D granular systems. For
             accelerations Γ above Γ*, the top layers of granular
             material flow, leading to convection with motion both
             parallel and transverse to the shaking; the lower part of
             the layer moves with the shaker in solid body motion. With
             increasing Γ, more of the layer becomes liquefied. The
             initial bifurcation is backward, but a small amount of
             fluidization by gas flow lifts the hysteresis. A new
             convective mechanism, which we explore both experimentally
             and computationally, associated with horizontal shearing at
             the walls, is identified as the mechanism driving the
             transverse convective flow.},
   Doi = {10.1209/epl/i1999-00190-3},
   Key = {Tennakoon99}
}

@booklet{Vanel99,
   Author = {Vanel, L and Howell, D and Clark, D and Behringer, RP and Clément,
             E},
   Title = {Memories in sand: Experimental tests of construction history
             on stress distributions under sandpiles},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {60},
   Number = {5 A},
   Pages = {R5040-R5043},
   Year = {1999},
   ISSN = {1063-651X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000083870700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {We report experiments on piles of cohesionless granular
             materials showing the effect of construction history on
             static stress distributions. Stresses under piles are
             monitored by sensitive capacitive techniques. The piles are
             formed either by pouring granular material from a funnel
             with a small outlet (localized source), or from a large
             sieve (homogeneous rain). Localized sources yield stress
             profiles with a clear stress dip near the center of the
             pile; the homogeneous rain profiles have no stress dip. We
             show that the stress profiles scale linearly with the pile
             height. Experiments on wedge-shaped piles show similar but
             weaker effects.},
   Doi = {10.1103/PhysRevE.60.R5040},
   Key = {Vanel99}
}

@article{fds245621,
   Author = {Howell, D and Behringer, RP and Veje, C},
   Title = {Stress fluctuations in a 2D granular Couette experiment: A
             continuous transition},
   Journal = {Physical Review Letters},
   Volume = {82},
   Number = {26 I},
   Pages = {5241-5244},
   Year = {1999},
   Abstract = {Experiments on a slowly sheared 2D granular material show a
             continuous transition as the packing fraction γ passes
             through γc ≃ 0.776. The mean stress, σ̄, plays the role
             of an order parameter. As γ → γc from above, (1) the
             compressibility becomes large, (2) a slowing down of the
             mean velocity occurs, (3) the force distributions change,
             and (4) the network of stress chains changes from
             intermittent long radial chains near γc to a tangled dense
             network for larger γ. © 1999 The American Physical
             Society.},
   Key = {fds245621}
}

@article{fds245625,
   Author = {Behringer, RP and Howell, D and Kondic, L and Tennakoon, S and Veje,
             C},
   Title = {Predictability and granular materials},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {133},
   Number = {1-4},
   Pages = {1-17},
   Year = {1999},
   Abstract = {Granular materials present a number of challenges to
             predictability. The classical description of a dense
             granular material is based on Coulomb friction. For a static
             array of grains, the Coulomb friction forces are typically
             underdetermined. If we are to make useful statements about
             such arrays, we must develop new approaches, including the
             development of statistical descriptions. Granular materials
             also show large fluctuations in the local forces. These
             fluctuations are quite sensitive to small perturbations in
             the packing geometry of the grains. In the past, they have
             typically been ignored. However, recent experiments and
             models are beginning to shed new light on their
             characteristics. This article briefly reviews some of this
             new work, and in particular presents experimental results
             characterizing fluctuations and the role of friction in
             granular materials. © 1999 Elsevier Science
             B.V.},
   Key = {fds245625}
}

@article{fds287564,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {AC Thermal Conductivity Measurements in Dilute Mixtures of
             3He in Superfluid 4He},
   Journal = {Journal of Low Temperature Physics},
   Volume = {117},
   Number = {1-2},
   Pages = {53-65},
   Year = {1999},
   Abstract = {In Part III of a three-part study, we report measurements of
             the thermal response, ΔT(ω), of 3He-superfluid-4He
             mixtures to an ac heat flux, Q(t) = Q0eiωt. These data are
             for dilute concentrations, X, and they show the presence of
             three separate thermal resistances. One of these is the
             bulk-fluid resistance predicted by Khalatnikov and
             associated with the effective conductivity, Keff. Results
             for this component of the resistance are in quantitative
             agreement with the Khalatnikov predictions. With parallel
             work by Murphy and Meyer, these experiments resolve a
             long-standing conflict between theory and experiment. One of
             the remaining resistances is the ordinary boundary
             resistance Rb. The third resistance, R0, is independent of
             the fluid layer height, d. This resistance is presumably the
             same as that seen in earlier dc measurements. Both the
             temperature and concentration dependences of this anomalous
             resistance differ from that of either Rfluid or Rb. It has
             been ascribed recently by Murphy and Meyer to effects
             associated with the narrow gaps usually present in cryogenic
             thermal conductivity experiments. We use an ad hoc model as
             a convenient way to parameterize the extra thermal
             resistance. The present studies have been carried out with
             an apparatus which permits us to vary d continuously and in
             situ from zero to 3 mm. This feature and the ac technique
             are important for separating the various components of the
             thermal resistance. In two preceeding studies, we considered
             related aspects of the ac thermal response of liquid helium.
             Part I addresses the response of normal liquid helium. Part
             II, provides the theoretical backdrop for the present
             experimental study.},
   Key = {fds287564}
}

@article{fds4021,
   Author = {B. Painter},
   Title = {Collisions and Fluctuations for Granular
             Materials},
   Series = {NATO ASi Series},
   Booktitle = {Physics of Dry Granular Media},
   Publisher = {Kouwer},
   Editor = {H. J. Herrmann and J.-P. Hovi and and},
   Year = {1998},
   Month = {December},
   Key = {fds4021}
}

@article{fds4022,
   Author = {C. Veje and R.P. Behringer and S. Schoellmann and S. Luding and H.
             Hermann},
   Title = {Fluctuations and Flow for a 2D Granular Medium},
   Series = {Nato Asi Series, Vol 350},
   Booktitle = {Physics of Dry Granular Media},
   Publisher = {Kluwer},
   Editor = {H. J. Herrmann and J.-P. Hovi and and},
   Year = {1998},
   Month = {December},
   Key = {fds4022}
}

@article{fds4024,
   Author = {R.P. Behringer},
   Title = {Granular Dynamics: Shearing, Shaking, and
             Mixing},
   Booktitle = {Proc. of the 4th Experimental Choas Conferenc},
   Editor = {M. Z. Ding and W. Ditto and L. Pecora and M. Spano and S.
             Vohra},
   Year = {1998},
   Month = {December},
   Key = {fds4024}
}

@article{fds4028,
   Author = {R.P. Behringer},
   Title = {Pattern Formation in an Inhomogeneous Environment},
   Series = {Lecture Notes in Physics},
   Booktitle = {Evolution of Spontaneous Structures in},
   Editor = {Friedrich H. Busse and Stefan},
   Year = {1998},
   Month = {December},
   Key = {fds4028}
}

@article{fds4030,
   Author = {R.P. Behringer and Guy},
   Title = {3He-Superfluid-4He: A Novel System for Studying},
   Booktitle = {Flow at Ultra-High Reynolds Numbers: A Status},
   Publisher = {Springer},
   Editor = {R.J. Donnelly and K.R. Sreenivasan},
   Year = {1998},
   Month = {December},
   Key = {fds4030}
}

@article{fds4023,
   Author = {S. Tennakoon and E. van Doorn H. K. Pak and R.P.
             Behringer},
   Title = {Dynamics of Shaken Granular Materials},
   Series = {NATO ASI Series, Vol 350},
   Booktitle = {Physics of Dry Granular},
   Editor = {H. J. Herrmann and J.-P. Hovi and S. Luding},
   Year = {1998},
   Month = {December},
   Key = {fds4023}
}

@booklet{Painter98,
   Author = {B.D. Painter and R.P. Behringer},
   Title = {Effects of spatial disorder on the transition to Taylor
             vortex flow},
   Journal = {Europhys. Lett.},
   Volume = {44},
   Number = {5},
   Pages = {599 -- 605},
   Year = {1998},
   Month = {December},
   Key = {Painter98}
}

@article{fds245618,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {Dynamic Measurements of Thermal Transport Coefficients and
             Boundary},
   Journal = {J. Low Temp. Phys},
   Volume = {111},
   Pages = {863-877},
   Year = {1998},
   Month = {December},
   Key = {fds245618}
}

@article{fds4026,
   Author = {R.P. Behringer and Daniel Howell and Lou},
   Title = {Gravity and Granular Materials},
   Booktitle = {NASA},
   Year = {1998},
   Month = {August},
   Key = {fds4026}
}

@article{fds245455,
   Author = {Zimmermann, W and Painter, B and Behringer, R},
   Title = {Pattern formation in an inhomogeneous environment},
   Journal = {European Physical Journal B},
   Volume = {5},
   Number = {3},
   Pages = {757-770},
   Year = {1998},
   Abstract = {A major step in understanding pattern formation has been
             achieved by studying idealized systems. However, in nature
             inhomogeneous systems are much more abundant than their
             idealized homogeneous counterparts. Here we report about
             experimental results on pattern formation in two
             inhomogeneous systems, thermal convection in porous media
             and Taylor-vortex flow between a rough and a smooth
             cylinder. Several aspects of heterogeneity effects in
             pattern formation are theoretically investigated for model
             equations and analytical descriptions are given for a few
             phenomena.},
   Key = {fds245455}
}

@booklet{Tennakoon98,
   Author = {Tennakoon, SGK and Behringer, RP},
   Title = {Vertical and horizontal vibration of granular materials:
             Coulomb friction and a novel switching state},
   Journal = {Physical Review Letters},
   Volume = {81},
   Number = {4},
   Pages = {794-797},
   Year = {1998},
   Abstract = {Experiments for simultaneous horizontal (h) and vertical (v)
             vibration of granular materials show novel flow dynamics. We
             focus on moderate dimensionless accelerations 0 &lt; Γh.v
             &lt; 1.6. Phenomena include the spontaneous formation of a
             static heap at Γhs (Γv,) when Γv &lt; 1, convective flow
             for Γhe &gt; Γhs, and a novel switching state for
             frequencies ωv ≠ ωh. A simple friction model provides an
             approximate, but not exact, description of the steady states
             and the transition to convection.},
   Key = {Tennakoon98}
}

@booklet{Olafsen98,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {Dynamic Measurements of Thermal Transport Coefficients and
             Boundary Resistance. II. Model for 3He-Superfluid
             4He Mixtures},
   Journal = {Journal of Low Temperature Physics},
   Volume = {111},
   Number = {5-6},
   Pages = {863-877},
   Year = {1998},
   Abstract = {This is the second of a three-part study of the ac response
             of liquid helium. We derive the temperature response
             function, ΔT(ω), of a 3He-superfluid 4He mixture from the
             equations of superfluid hydrodynamics in the presence of two
             interfacial boundary resistances, Rb. Specifically, we
             consider the response ΔT(ω), across a fluid layer of
             thickness, d, to an ac heat flux, Q(t) = Qoexp(iωt).
             ΔT(ω) depends on the effective thermal conductivity,
             κeff, Griffin's diffusion coefficient, Γo (i.e. the
             thermal diffusivity of 3He impurities, Diso in the low 3He
             concentration limit) and the thermal boundary resistance,
             2Rb. This analysis provides the basis for experiments to
             determine these parameters. Although past experiments to
             measure these properties have been carried out using dc and
             transient techniques, an ac technique offers significant
             noise reduction over these techniques. By sweeping the
             frequency, it is possible for an experimenter to clearly
             identify different components of the system response to the
             heat flux. For instance, if τ is the slowest fluid thermal
             response time, conventional Kapitza boundary effects
             dominate at frequencies, ωτ ≫ 1. These calculations
             reveal an interesting analogy to the "Piston Effect" for
             near-critical classical fluids. In Part I of this work, we
             used normal liquid 4He as a testing ground for developing
             models of ac heat transport. In Part III of this work, we
             will present results in which we apply this technique to
             measurements on dilute mixtures of 3He in superfluid
             4He.},
   Key = {Olafsen98}
}

@article{fds245617,
   Author = {Painter, BD and Behringer, RP},
   Title = {Effects of spatial disorder on the transition to Taylor
             vortex flow},
   Journal = {EPL (Europhysics Letters)},
   Volume = {44},
   Number = {5},
   Pages = {599-605},
   Year = {1998},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/epl/i1998-00515-8},
   Abstract = {Using particle imaging velocimetry (PIV), we investigate the
             effects of fixed spatial disorder in a Taylor-Couette system
             near the onset of Taylor-Vortex flow. We induce small
             spatially frozen variations in the local control parameter
             of the system by varying the radius of the inner cylinder
             along the cylinder axis, y. For a smooth inner cylinder the
             bifurcation to Taylor vortex rolls is instrumentally sharp.
             With a 12% variation in the local Reynolds number Re(y) we
             find localized rolls with an amplitude that varies
             exponentially in the spatially averaged Re. Smoothed
             bifurcations and localized flows have been seen in recent
             numerical studies of systems with spatially varying control
             parameters and in convection of a fluid in a porous medium.
             The secondary transition to wavy flew is significantly
             elevated in the system with spatially varying
             Re(y).},
   Doi = {10.1209/epl/i1998-00515-8},
   Key = {fds245617}
}

@booklet{Moon97,
   Author = {Moon, HT and Kim, S and Behringer, RP and Kuramoto,
             Y},
   Title = {Nonlinear dynamics and chaos},
   Journal = {International Journal of Bifurcation & Chaos},
   Volume = {7},
   Number = {4},
   Pages = {787-788},
   Year = {1997},
   Month = {April},
   ISSN = {0218-1274},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997XZ65200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Moon97}
}

@booklet{Behringer97,
   Author = {Behringer, RP},
   Title = {The scientist in the sandbox: Time-dependence, fractals and
             waves},
   Journal = {International Journal of Bifurcation and Chaos in Applied
             Sciences and Engineering},
   Volume = {7},
   Number = {5},
   Pages = {963-978},
   Year = {1997},
   Abstract = {Granular materials exhibit a rich variety of dynamical
             behavior, much of which is poorly understood. Fractal-like
             stress chains, convection, a variety of wave dynamics,
             including waves which resemble capillary waves, 1/f noise,
             and fractional Brownian motion provide examples. Although
             granular materials consist of collections of interacting
             particles, there are important differences between the
             dynamics of a collection of grains and the dynamics of a
             collection of molecules. In particular, the ergodic
             hypothesis is generally invalid for granular materials, so
             that ordinary statistical physics does not apply.
             Fluctuations on laboratory scales in such quantities as the
             stress can be very large - as much as an order of magnitude
             greater than the mean. Below is a brief review of some of
             the theoretical approaches to granular flow followed by a
             discussion of several recent experiments. These experiments
             focus on complex structures and fluctuations in the flow of
             granular materials in a hopper or in simple shear flow. The
             experimental work at Duke has been carried out in
             collaboration with a number of investigators, including G.
             W. Baxter, R. Leone, H. K. Pak, E. Van Doom, C. O'Hern, and
             B. Miller. Elsewhere in this issue, Pak et al. discuss
             experiments to characterize and better understand the
             convective flows which occur when granular materials are
             shaken with accelerations exceeding that of
             gravity.},
   Key = {Behringer97}
}

@booklet{Khosropour97,
   Author = {Khosropour, R and Zirinsky, J and Pak, HK and Behringer,
             RP},
   Title = {Convection and size segregation in a Couette flow of
             granular material},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {56},
   Number = {4},
   Pages = {4467-4473},
   Year = {1997},
   Abstract = {We have investigated the size segregation of a binary
             mixture of spherical glass particles in a Couette geometry,
             where the cylinders are made of smooth glass and the flow is
             generated by the shearing motion of the inner cylinder. The
             trajectories of 1, 2, and 3 mm glass particles, placed at
             the bottom of the cell, were followed as they moved through
             a 1 mm medium. We observe convective motion of the particles
             in which particles rise at the outer radius and fall at the
             inner radius. The horizontal and vertical speeds of 2 and 3
             mm glass particles, initially at the cell bottom, as a
             function of the inner cylinder speed were determined and the
             onset of turbulent motion measured by processing images.
             While in all cases the larger particles rose to the top and
             remained on the surface as rotation continued, the particles
             comprising the medium appear to go through a convectivelike
             motion. The effect of interstitial fluid, in this case air,
             was studied by repeating the experiments in vacuum. We did
             not detect any significant changes in the
             results.},
   Key = {Khosropour97}
}

@booklet{Olafsen97,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {Dynamic measurements of thermal transport coefficients and
             boundary resistance I. Normal4He},
   Journal = {Journal of Low Temperature Physics},
   Volume = {106},
   Number = {5-6},
   Pages = {673-704},
   Year = {1997},
   Abstract = {The thermal conductivity, κ, and the thermal diffusivity,
             DT, of normal liquid 4He have been obtained from the
             temperature response, T((ω), across a fluid layer of
             thickness, d, to an ac heat flux, Q(t) = Q0exp(iωt).
             Previous transient heat flux experiments measured the
             thermal relaxation of the fluid towards equilibrium and
             assumed the dominance of a single slowest mode. The present
             ac technique allows measurements under steady-state
             conditions while driving the system at a single frequency,
             ω. The response curve for T(ω)/Q0 yields data for κ, DT
             and the boundary resistance, Rb. Boundary effects appear at
             frequencies higher than τ-1 ≡ DT/d2 where the fluid is
             unresponsive to bulk heat transport. We use this fact to
             obtain Rb with high accuracy in the normal phase from the
             high frequency response. In addition, the apparatus permits
             the fluid thickness, d, to be varied continuously and in
             situ from zero to 3 nun, allowing for further consistency in
             the fluid measurements. This work also includes data for the
             onset of convection where Q0 &gt; Qc. and Qc corresponds to
             the heat amplitude at convective onset.},
   Key = {Olafsen97}
}

@booklet{Pak97,
   Author = {Pak, HK and Doorn, EV and Behringer, RP},
   Title = {Ambient gases and heaping instability of granular materials
             under vertical vibration},
   Journal = {International Journal of Bifurcation and Chaos in Applied
             Sciences and Engineering},
   Volume = {7},
   Number = {5},
   Pages = {1035-1041},
   Year = {1997},
   Abstract = {We consider layers of non-cohesive granular materials lying
             on a vertically vibrating surface. Above a threshold
             acceleration, Γ = Γc, internal convective motion begins,
             and the free surface of the granular material becomes
             unstable to the formation of a heap. As Γ increases
             further, there are several higher order instabilities,
             traveling surface waves, subharmonic bifurcations, and
             bubbling. We find that for particles of diameter d ≤ 1 mm,
             the pressure P of the surrounding gas plays a key role in
             the instabilities. We propose criteria to determine when gas
             effects are relevant.},
   Key = {Pak97}
}

@booklet{Howle97,
   Author = {Howle, LE and Behringer, RP and Georgiadis, JG},
   Title = {Convection and flow in porous media. Part 2. Visualization
             by shadowgraph},
   Journal = {Journal of Fluid Mechanics},
   Volume = {332},
   Pages = {247-262},
   Year = {1997},
   Abstract = {We present results for pattern formation at the onset of
             convection in fluid-saturated porous media obtained by a
             novel variation on the shadowgraphic technique (modified
             shadowgraphic technique). Both ordered and disordered media
             are used, each exhibiting distinct behaviour. Ordered porous
             media are constructed from grids of overlapping bars.
             Convective onset in this type of medium is characterized by
             a sharp, well-defined bifurcation to straight parallel
             rolls. The orientation of the convection rolls is determined
             by the number of bar layers, Nb; odd Nb leads to rolls with
             axes perpendicular to the direction of the top and bottom
             bars, and even Nb to rolls at 45° to the bars. Disordered
             porous layers are produced by stacking randomly drilled
             disks separated by spacers. In this system, we observe a
             rounded bifurcation to convection with localized convection
             near convective onset. More specifically, the flow patterns
             take on one of several different three-dimensional cellular
             structures after each cycling through convective onset.
             These observations may be described by two different
             mechanisms: random spatial fluctuations in the Rayleigh
             number (Zimmermann et al. 1993), and/or spatial variation in
             the thermal conductivity on the length scale of the
             convection wavelength (Braester &amp; Vadasz
             1993).},
   Key = {Howle97}
}

@booklet{Shattuck97,
   Author = {Shattuck, MD and Behringer, RP and Johnson, GA and Georgiadis,
             JG},
   Title = {Convection and flow in porous media. Part 1. Visualization
             by magnetic resonance imaging},
   Journal = {Journal of Fluid Mechanics},
   Volume = {332},
   Pages = {215-245},
   Year = {1997},
   Abstract = {We describe an experimental study of porous media convection
             (PMC) from onset to 8Rac. The goal of this work is to
             provide non-invasive imaging and high-precision heat
             transport measurements to test theories of convection in
             PMC. We obtain velocity information and visualize the
             convection patterns using magnetic resonance imaging (MRI).
             We study both ordered and disordered packings of
             mono-disperse spheres of diameter d = 3.204 ± 0.029 mm, in
             circular, rectangular, and hexagonal planforms. In general,
             the structure of the medium plays a role which is not
             predicted by theories which assume a homogeneous system.
             Disordered media are prepared by pouring mono-disperse
             spheres into the container. Large ordered regions of close
             packing for the spheres, with grain boundaries and isolated
             defects, characterize these media. The defects and grain
             boundaries play an important role in pattern formation in
             disordered media. Any deviation from close packing produces
             a region of larger porosity, hence locally larger
             permeability. The result is spatial variations in the
             Rayleigh number, Ra. We define the critical Ra, Rac, as the
             Rayleigh number at the onset of convection in the ordered
             regions. We find that stable localized convective regions
             exist around grain boundaries and defects at Ra &lt; Rac.
             These remain as pinning sites for the convection patterns in
             the ordered regions as Ra increases above Rac up to 5Rac,
             the highest Ra studied in the disordered media. In ordered
             media, spheres are packed such that the only deviations from
             close packing occur within a thin (&lt;d) region near the
             vertical walls. Stable localized convection begins at 0.5Rac
             in the wall regions but appears to play only a weak role in
             the pattern formation of the interior regions (bulk), since
             different stable patterns are observed in the bulk at the
             same Ra after each cycling of Ra below Rac, even for similar
             patterns of small rolls in the wall regions. The experiments
             provide a test of the following predictions for PMC: (i)
             that straight parallel rolls should be linearly stable for
             Rac &lt; Ra &lt; 5Rac; (ii) that at onset, the rolls should
             have a dimensionless wavevector qc = π; (iii) that at the
             upper end of this range rolls should lose stability to
             cross-rolls; (iv) that the initial slope of the Nusselt
             curve should be 2; (v) that there should be a rapid decay of
             vertical vorticity - hence no complex flows, such as those
             which occur for Rayleigh-Bénard convection (RBC) within the
             nominal regime of stable parallel rolls. These predictions
             are in partial agreement with our findings for the bulk
             convection in the ordered media. We observe roll-like
             structures which relax rapidly to stable patterns between
             Rac and 5Rac. However we find a wavenumber which is 0.7π
             compared to π derived from linear stability theory. We find
             an asymmetry between the size of the upflowing regions and
             downflowing regions as Ra grows above Rac. The ratio of the
             volume of the upflowing to the volume of the downflowing
             regions decreases as Ra increases and leads to a novel
             time-dependent state, which does not consist of cross-rolls.
             This time-dependent state begins at 6Rac and is observed up
             to 8Rac, the largest Ra which we studied. It seems likely
             that the occurrence of this state is linked to departures
             from the Boussinesq approximation at higher Ra. We also find
             that the slope of the Nusselt curve is 0.7, which does not
             agree with the predicted value of 2.},
   Key = {Shattuck97}
}

@booklet{Vandoorn97a,
   Author = {Doorn, EV and Behringer, RP},
   Title = {Onset and evolution of a wavy instability in shaken
             sand},
   Journal = {Physics Letters, Section A: General, Atomic and Solid State
             Physics},
   Volume = {235},
   Number = {5},
   Pages = {469-474},
   Year = {1997},
   Abstract = {A novel small wavelength instability occurs in experiments
             for vertically shaken (z = a cos(ωt)) sand, for small
             particle diameters d and when gas effects are important. At
             onset, the energy (aω)2/gd is proportional to a/d, as
             previously found for traveling waves. The instability begins
             as a surface perturbation with wavelength λ0 ∼ 6 mm;
             subsequently λ grows exponentially in time. © 1997
             Published by Elsevier Science B.V.},
   Key = {Vandoorn97a}
}

@booklet{Vandoorn97,
   Author = {Doorn, EV and Behringer, RP},
   Title = {Dilation of a vibrated granular layer},
   Journal = {EPL (Europhysics Letters)},
   Volume = {40},
   Number = {4},
   Pages = {387-392},
   Year = {1997},
   ISSN = {0295-5075},
   url = {http://dx.doi.org/10.1209/epl/i1997-00476-x},
   Abstract = {We report measurements of the dilation, δh, of a vertically
             shaken sand heap in the presence of air. These measurements
             were carried out for dimensionless accelerations 1.0 ≤ Γ
             ≤ 2.7, for particle diameters of 0.05 mm ≤ d ≤ 1.0 mm,
             for layer height to particle diameter ratios of 80 ≤ h0/d
             ≤ 140, and for shaking amplitudes of 0.66 mm ≤ a ≤
             6.65 mm. δh is mostly limited to a thin avalanching surface
             layer. The vertical motion of this layer is well described
             by a simple model of an inelastic bouncing ball, independent
             of other complex motion elsewhere.},
   Doi = {10.1209/epl/i1997-00476-x},
   Key = {Vandoorn97}
}

@booklet{Miller96,
   Author = {Miller, B and O'Hern, C and Behringer, RP},
   Title = {Stress Fluctuations for Continuously Sheared Granular
             Materials.},
   Journal = {Physical Review Letters},
   Volume = {77},
   Number = {15},
   Pages = {3110-3113},
   Year = {1996},
   Month = {October},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10062136},
   Doi = {10.1103/PhysRevLett.77.3110},
   Key = {Miller96}
}

@booklet{Metcalfe96,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Convection in He-3-superfluid-He-4 mixtures .1. A Boussinesq
             analogue},
   Journal = {Journal of Fluid Mechanics},
   Volume = {307},
   Pages = {269-296},
   Year = {1996},
   Month = {January},
   ISSN = {0022-1120},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996TV26300012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1017/S0022112096000122},
   Key = {Metcalfe96}
}

@booklet{Metcalfe96a,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Convection in He-3-superfluid-He-4 mixtures .2. A survey of
             instabilities},
   Journal = {Journal of Fluid Mechanics},
   Volume = {307},
   Pages = {297-331},
   Year = {1996},
   Month = {January},
   ISSN = {0022-1120},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996TV26300013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1017/S0022112096000134},
   Key = {Metcalfe96a}
}

@article{fds245451,
   Author = {Behringer, RP},
   Title = {Dynamics of granular materials},
   Journal = {NASA Conference Publication},
   Number = {3338},
   Pages = {245-250},
   Year = {1996},
   Abstract = {Granular materials exhibit a rich variety of dynamical
             behavior, much of which is poorly understood. Fractal-like
             stress chains, convection, a variety of wave dynamics,
             including waves which resemble capillary waves, 1/f noise,
             and fractional Brownian motion provide examples. Work
             beginning at Duke will focus on gravity driven convection,
             mixing, and gravitational collapse. Although granular
             materials consist of collections of interacting particles,
             there are important differences between the dynamics of a
             collections of grains and the dynamics of a collections of
             molecules. In particular, the ergodic hypothesis is
             generally invalid for granular materials, so that ordinary
             statistical physics does not apply. In the absence of a
             steady energy input, granular materials undergo a rapid
             collapse which is strongly influenced by the presence of
             gravity. Fluctuations on laboratory scales in such
             quantities as the stress can be very large-as much as an
             order of magnitude greater than the mean.},
   Key = {fds245451}
}

@booklet{Jaeger96a,
   Author = {Jaeger, HM and Nagel, SR and Behringer, RP},
   Title = {The physics of granular materials},
   Journal = {Physics Today},
   Volume = {49},
   Number = {4},
   Pages = {32-38},
   Year = {1996},
   Key = {Jaeger96a}
}

@booklet{Jaeger96,
   Author = {Jaeger, HM and Nagel, SR and Behringer, RP},
   Title = {Granular solids, liquids, and gases},
   Journal = {Reviews of Modern Physics},
   Volume = {68},
   Number = {4},
   Pages = {1259-1273},
   Year = {1996},
   url = {http://dx.doi.org/10.1103/RevModPhys.68.1259},
   Abstract = {Granular materials are ubiquitous in the world around us.
             They have properties that are different from those commonly
             associated with either solids, liquids, or gases. In this
             review the authors select some of the special properties of
             granular materials and describe recent research
             developments.},
   Doi = {10.1103/RevModPhys.68.1259},
   Key = {Jaeger96}
}

@article{fds287562,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Convection in 3He-superfluid-4He
             mixtures. Part 2. A survey of instabilities},
   Journal = {Journal of Fluid Mechanics},
   Volume = {307},
   Pages = {297-331},
   Year = {1996},
   Abstract = {Dilute mixtures of 3He in superfluid 4He have Prandtl
             numbers easily tunable between those of liquid metals and
             water: 0.04 &lt; Pr &lt; 2. Moreover, superfluid mixture
             convection is closely analogous to classical
             Rayleigh-Bénard convection, i.e. superfluid mixtures
             convect as if they were classical, single-component fluids.
             This work has two goals. The first, accomplished in Part 1,
             is to experimentally validate the superfluid mixture
             convection analogue to Rayleigh-Bénard convection. With
             superfluid effects understood and under control, the second
             goal is to identify and characterize time-dependence and
             chaos and to discover new dynamical behaviour in strongly
             nonlinear convective flows. In this paper, Part 2, we
             exploit the unique Pr range of superfluid mixtures and the
             variable aspect ratio (Γ) capabilities of our experiment to
             survey convective instabilities in the broad, and heretofore
             largely unexplored, parameter space 0.12 &lt; Pr &lt; 1.4
             and 2 &lt; Γ &lt; 95. Within this large parameter space, we
             have focused on small to moderate Γ and Pr and on large Γ
             with Pr ≈ 1. The novel behaviour uncovered in the survey
             includes the following. Changing attractors: at Γ= 6.0 and
             Pr = 0.3, we observe intermittent bursting destabilizing a
             fully developed chaotic state. Above the onset of bursting
             the average length of a burst-free interval and the average
             length of a burst vary as power laws. At Γ = 4.25 and Pr =
             0.12 we observe a particularly novel reversible switching
             transition involving two chaotic attractors. Instability
             competition: near the codimension-2 point at the crossing of
             the skewed-varicose and oscillatory instabilities we find
             that the effects of instability competition greatly increase
             the complexity and multiplicity of states. A heat-pulse
             method allows selection of the active state. Decreasing Γ
             suppresses the available complexity. Superfluid turbulence:
             we find that the large-amplitude noisy states, previously
             believed due to superfluid turbulence, are confined to small
             values of Γ and Pr and are not consistent with superfluid
             turbulence. Changing instabilities: at Pr = 0.19 a
             wavevector detuning changes the type of secondary
             instability from oscillatory to saddle-node, with an unusual
             3/4 exponent time scaling. Very large Γ : at Pr = 1.3 for
             Γ increasing from 44 to 90, we observe the onset of
             convection changing from ordered and stationary to
             disordered and time-dependent. At the beginning of the
             crossover there are hysteretic transitions to coherent
             oscillations close to the onset of convection. By the end of
             the crossover convection is time-dependent and irregular at
             onset with the fluctuation amplitude correlated with the
             mean Nusselt number.},
   Key = {fds287562}
}

@article{fds287563,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Convection in 3He-superfluid-4He
             mixtures. Part 1. A Boussinesq analogue},
   Journal = {Journal of Fluid Mechanics},
   Volume = {307},
   Pages = {269-296},
   Year = {1996},
   Abstract = {Dilute mixtures of 3He in superfluid 4He have Prandtl
             numbers easily tunable between those of liquid metals and
             water: 0.04 &lt; Pr &lt; 2. Moreover, owing to the tight
             coupling of the temperature and concentration fields,
             superfluid mixture convection is closely analogous to
             classical Rayleigh-Bénard convection, i.e. superfluid
             mixtures convect as if they were classical, single-component
             fluids, well described by the Boussinesq equations. This
             work has two goals. The first is to put the theory of
             superfluid mixture convection on a firmer basis. We
             accomplish this by combining experiment and analysis to
             measure superfluid effects on the onset of convection. In
             the process, we demonstrate quantitative control over
             superfluid effects and, in particular, that deviations from
             classical convective behaviour can be made small or at worst
             no larger than finite aspect ratio effects. The size of
             superfluid effects at convective onset can be less than a
             few percent for temperatures 1 &lt; T &lt; 2 K. Comparison
             of the measured properties of superfluid mixture roll
             instabilities above the onset of convection (e.g. skewed
             varicose, oscillatory, and particularly near the
             codimension-2 point) to the properties predicted by
             Boussinesq calculations further verifies that superfluid
             mixtures convect as classical fluids. With superfluid
             effects understood and under control, the second goal,
             presented in Part 2, is to exploit the unique Pr range of
             superfluid mixtures and the variable aspect ratio (Γ)
             capabilities of our experiment to survey convective
             instabilities in the broad, and heretofore largely
             unexplored, parameter space 0.12 &lt; Pr &lt; 1.4 and 2 &lt;
             Γ &lt; 95. The aim is to identify and characterize
             time-dependence and chaos, and to discover new dynamical
             behaviour in strongly nonlinear convective
             flows.},
   Key = {fds287563}
}

@booklet{Shattuck95,
   Author = {Shattuck, MD and Behringer, RP and Johnson, GA and Georgiadis,
             JG},
   Title = {Onset and Stability of Convection in Porous Media:
             Visualization by Magnetic Resonance Imaging.},
   Journal = {Physical Review Letters},
   Volume = {75},
   Number = {10},
   Pages = {1934-1937},
   Year = {1995},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10059166},
   Doi = {10.1103/PhysRevLett.75.1934},
   Key = {Shattuck95}
}

@booklet{Olafsen95,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {Temporal response of the thermal boundary resistance in
             superfluid helium.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {52},
   Number = {1},
   Pages = {61-63},
   Year = {1995},
   Month = {July},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9979569},
   Key = {Olafsen95}
}

@booklet{Pak95,
   Author = {Pak, HK and Van Doorn E, and Behringer, RP},
   Title = {Effects of ambient gases on granular materials under
             vertical vibration.},
   Journal = {Physical Review Letters},
   Volume = {74},
   Number = {23},
   Pages = {4643-4646},
   Year = {1995},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10058562},
   Doi = {10.1103/PhysRevLett.74.4643},
   Key = {Pak95}
}

@article{fds245449,
   Author = {Behringer, RP},
   Title = {Scientist in the sandbox: complexity and dynamics in
             granular flow},
   Journal = {Materials Research Society Symposium - Proceedings},
   Volume = {367},
   Pages = {461-469},
   Year = {1995},
   Abstract = {Granular materials exhibit a rich variety of dynamical
             behavior, much of which is poorly understood. Although
             granular materials consist of collections of interacting
             particles, there are important differences between the
             dynamics of a collection of grains and the dynamics of a
             collection of molecules. In particular, the ergodic
             hypothesis is generally invalid for granular materials,
             hence ordinary physics does not apply. In this article, the
             recent insights on this phenomena are emphasised to provide
             an understanding of the dynamical behavior of these
             materials.},
   Key = {fds245449}
}

@booklet{Behringer95,
   Author = {Behringer, RP},
   Title = {Mixed predictions},
   Journal = {Nature},
   Volume = {374},
   Number = {6517},
   Pages = {15-},
   Year = {1995},
   ISSN = {0028-0836},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1995QK07900027&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1038/374015a0},
   Key = {Behringer95}
}

@booklet{Metcalfe94,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Transition to large aspect ratio convection.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {49},
   Number = {5},
   Pages = {R3572-R3575},
   Year = {1994},
   Month = {May},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9961787},
   Key = {Metcalfe94}
}

@article{fds245448,
   Author = {Pak, HK and Behringer, PR},
   Title = {Bubbling in vertically vibrated granular
             materials},
   Journal = {Nature},
   Volume = {371},
   Number = {6494},
   Pages = {231-233},
   Year = {1994},
   url = {http://dx.doi.org/10.1038/371231a0},
   Abstract = {Granular materials show both fluid-like and solid-like
             behaviour. Under weak shear they deform plastically; under
             high shear they flow. These materials exhibit other unusual
             kinds of behaviour, including segregation, density waves,
             convection and anomalous sound propagation. Their dynamical
             properties are important in many industrial applications. In
             particular, the shaking of granular materials is used to
             mix, segregate and transport them. Vertically shaken
             granular materials undergo a transition to a convective
             state. Here we describe experiments which show that such
             convective motion can involve bubbling - the formation and
             upward motion of voids. The presence of gas between the
             grains is essential for bubbling to occur, and the
             instability shows characteristics of a Hopf bifurcation such
             as is seen at the onset of chaos. This bubbling behaviour
             may be analogous to that observed in fluidized beds, and
             might be expected to occur when soils are fluidized during
             earthquakes.},
   Doi = {10.1038/371231a0},
   Key = {fds245448}
}

@booklet{Olafsen94,
   Author = {Olafsen, JS and Behringer, RP},
   Title = {Thermal response of normal and superfluid helium to an AC
             heat flux},
   Journal = {Physica B: Condensed Matter},
   Volume = {194-196},
   Number = {PART 1},
   Pages = {595-596},
   Year = {1994},
   ISSN = {0921-4526},
   Abstract = {Measurements of the thermal response, ΔT(ω), across a
             layer of helium in its normal and superfluid phases have
             been made for an AC heat source, Q(t)=Qoexp(iωt). Previous
             DC measurements below Tλ have indicated a dependence on the
             layer thickness, d, for κeff at low concentrations, X,
             suggesting an intrinsic length scale within the fluid. A
             ΔT(ω) profile is ideally suited to reveal any internal
             length scales of the fluid. The apparatus also permits d to
             be varied continuously and in situ from zero to 3mm. ©
             1994.},
   Key = {Olafsen94}
}

@booklet{Pak93,
   Author = {Pak, HK and Behringer, RP},
   Title = {Surface waves in vertically vibrated granular
             materials.},
   Journal = {Physical Review Letters},
   Volume = {71},
   Number = {12},
   Pages = {1832-1835},
   Year = {1993},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10054511},
   Doi = {10.1103/PhysRevLett.71.1832},
   Key = {Pak93}
}

@booklet{Baxter93,
   Author = {BAXTER, GW and LEONE, R and BEHRINGER, RP},
   Title = {EXPERIMENTAL TEST OF TIME SCALES IN FLOWING
             SAND},
   Journal = {EPL (Europhysics Letters)},
   Volume = {21},
   Number = {5},
   Pages = {569-574},
   Year = {1993},
   Month = {February},
   ISSN = {0295-5075},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993KN37200011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1209/0295-5075/21/5/011},
   Key = {Baxter93}
}

@booklet{Metcalfe93,
   Author = {METCALFE, G and BEHRINGER, RP},
   Title = {SUPERFLUID EFFECTS AT THE ONSET OF CONVECTION IN
             HE-3-SUPERFLUID-HE-4 MIXTURES},
   Journal = {Journal of Low Temperature Physics},
   Volume = {90},
   Number = {1-2},
   Pages = {95-117},
   Year = {1993},
   Month = {January},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993KL83500005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/BF00682012},
   Key = {Metcalfe93}
}

@article{fds245447,
   Author = {Howle, LE and Behringer, RP and Georgiadis, JG},
   Title = {Visualization of natural convection in ordered and
             disordered porous layers},
   Journal = {American Society of Mechanical Engineers, Fluids Engineering
             Division (Publication) FED},
   Volume = {172},
   Pages = {387-395},
   Year = {1993},
   Abstract = {The recent Modified Shadowgraphic Technique is used to study
             pattern formation of convecting flows in fluid saturated
             porous layers. Both regular and random media are explored,
             each exhibiting distinct primary bifurcation behavior. In
             regular porous layers, consisting of grids of overlapping
             bars, the preferred wave pattern at onset is parallel rolls
             with roll orientation determined by bar orientation at the
             upper and lower boundaries. The random medium shows a
             different disorganized convection pattern with each cycling
             through the onset of convection. The experimental work is
             complemented by large scale numerical simulation of large
             aspect ratio convection in porous layers with uniform
             permeability and with spatially varying permeability. The
             influence of the permeability field on pattern selection is
             explored.},
   Key = {fds245447}
}

@article{fds245499,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Superfluid effects at the onset of convection
             in3He-superfluid-4He
             mixtures},
   Journal = {Journal of Low Temperature Physics},
   Volume = {90},
   Number = {1-2},
   Pages = {95-117},
   Year = {1993},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00682012},
   Abstract = {The equations of motion for convection in
             dilute3He-superfluid-4He mixtures are the same as those for
             convection in a conventional pure fluid with the addition of
             several correction terms. Fetter has considered, for a
             horizontally infinite layer with realistic boundary
             conditions, the effect of these corrections on the critical
             Rayleigh number, Rc. The results are a perturbation
             expansion for Rc to lowest order in three perturbation
             terms, ε1, ε2, ε3. In order to make a comparison with
             recent precise experiments which have yielded Rc as a
             function of the layer height d, we have carried out several
             calculations. First we show that the analysis can be recast
             as an expansion in inverse powers of d2. We then carry out a
             complete expansion to O(d-6). Up to O(d-4), the expansion
             involves only the ratio (λ0/d) where λ0 is a length scale
             which is intrinsic to superfluid mixtures. We consider the
             effect of the superfluid perturbations on both the critical
             Rayleigh numbers and wavevectors. These are shifted very
             little as long as λ0/d is small; the crossover from large
             to small occurs for λ0/d∼0.1. We also solve a simplified
             version of the stability problem which contains the dominant
             superfluid effect. The simplified problem is Hermitian, and
             is therefore amenable to an exact solution. A comparison
             with experimental data for Rc and the simplified model shows
             excellent agreement with the calculations. © 1993 Plenum
             Publishing Corporation.},
   Doi = {10.1007/BF00682012},
   Key = {fds245499}
}

@booklet{Behringer93,
   Author = {BEHRINGER, RP},
   Title = {THE DYNAMICS OF FLOWING SAND},
   Volume = {3},
   Number = {3},
   Pages = {1-&},
   Year = {1993},
   ISSN = {0938-9008},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993MN18200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Behringer93}
}

@booklet{Howle93,
   Author = {Howle, L and Behringer, RP and Georgiadis, J},
   Title = {Visualization of convective fluid flow in a porous
             medium},
   Journal = {Nature},
   Volume = {362},
   Number = {6417},
   Pages = {230-232},
   Year = {1993},
   Abstract = {WHEN a horizontal layer of fluid is heated from below, it
             may undergo Rayleigh-Bénard convection (RBC), leading to
             the spontaneous appearance of regular patterns of fluid
             flow1. The shadowgraph technique2, which allows
             visualization of the convection patterns, has assisted in
             developing an understanding of RBC. Related to RBC is
             convection in a fluid permeating a porous medium (called
             Horton-Rodgers-Lapwood convection or HRLC) when it is heated
             from below3-7. HRLC is relevant to geothermal applications
             and to flow in soils. Pattern formation in HRLC is less
             easily visualized by shadowgraph techniques because of the
             difficulties of transmitting light through the porous
             medium. Here we show how these difficulties can be overcome
             by constructing porous media in which the interfaces between
             solid and liquid are either parallel or perpendicular to the
             confining boundaries of the experimental system. Convection
             in such a medium can be visualized using conventional
             shadowgraph methods, and we compare the stationary flow
             patterns observed against measurements of heat
             transport.},
   Key = {Howle93}
}

@booklet{Anderson92,
   Author = {Anderson, KE and Shattuck, MD and Behringer, RP},
   Title = {Novel cross-roll state in a cylindrical convection cell with
             thermally conducting sidewalls.},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {46},
   Number = {10},
   Pages = {R6143-R6146},
   Year = {1992},
   Month = {November},
   ISSN = {1050-2947},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9907998},
   Key = {Anderson92}
}

@booklet{Metcalfe92,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Observation of chaotic bursting and attractor switching in a
             fluid.},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {46},
   Number = {2},
   Pages = {R711-R714},
   Year = {1992},
   Month = {July},
   ISSN = {1050-2947},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9908229},
   Key = {Metcalfe92}
}

@article{fds245498,
   Author = {Behringer, RP and Baxter, GW},
   Title = {Pattern formation and time-dependence in flowing
             sand},
   Journal = {Proceedings of Engineering Mechanics},
   Pages = {1028-1030},
   Year = {1992},
   Abstract = {The authors present results for a number of experiments on
             flowing granular materials and a novel cellular automata
             model for the flow of these materials when the grains are
             long and thin. In the first experiment, they present results
             for the time-dependent stress associated with sand flow in a
             hopper. In a second set of experiments they show the
             existence of propagating fronts. These results imply that an
             additional degree of freedom, not included in conventional
             models, may be necessary, to describe the experiments. The
             authors describe experimental observations for the flow of
             materials with long thin grains; these experiments form the
             basis for the cellular automata model.},
   Key = {fds245498}
}

@article{fds245425,
   Author = {Behringer, R and Timp, G and Baranger, HU and Cunningham,
             JE},
   Title = {Quantum-mechanical features in the resistance of a submircon
             junction.},
   Journal = {Physical Review Letters},
   Volume = {66},
   Number = {7},
   Pages = {930-933},
   Year = {1991},
   Month = {February},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/physrevlett.66.930},
   Doi = {10.1103/physrevlett.66.930},
   Key = {fds245425}
}

@article{fds245445,
   Author = {Shattuck, M and Behringer, R and Geordiadis, J and Johnson,
             GA},
   Title = {Magnetic resonance imaging of interstitial velocity
             distributions in porous media},
   Journal = {American Society of Mechanical Engineers, Fluids Engineering
             Division (Publication) FED},
   Volume = {125},
   Pages = {39-45},
   Year = {1991},
   Abstract = {In this article we report on a promising application of
             Magnetic Resonance Imaging (MRI), which can measure local
             interstitial velocity distributions inside fully-saturated
             porous media. We have extended the standard
             three-dimensional MRI sequence to include local velocity
             information. During flow, the moving spins of the fluid (in
             this case water) accumulate phase in the presence of
             magnetic field gradients. This phase is proportional to the
             local velocity. By repeating the measurement under the
             influence of different magnetic gradient strengths, we can
             reconstruct the velocity distribution in each volume element
             (voxel). Using this technique to study pressure-driven flow
             through a fully-saturated, cylindrical packed bed, we have
             observed flow channeling near the walls and an exponential
             distribution of velocities.},
   Key = {fds245445}
}

@article{fds245446,
   Author = {Shattuck, M and Behringer, R and Geordiadis, J and Johnson,
             GA},
   Title = {Magnetic resonance imaging of interstitial velocity
             distributions in porous media},
   Year = {1991},
   Abstract = {In this article we report on a promising application of
             Magnetic Resonance Imaging (MRI), which can measure local
             interstitial velocity distributions inside fully-saturated
             porous media. We have extended the standard
             three-dimensional MRI sequence to include local velocity
             information. During flow, the moving spins of the fluid (in
             this case water) accumulate phase in the presence of
             magnetic field gradients. This phase is proportional to the
             local velocity. By repeating the measurement under the
             influence of different magnetic gradient strengths, we can
             reconstruct the velocity distribution in each volume element
             (voxel). Using this technique to study pressure-driven flow
             through a fully-saturated, cylindrical packed bed, we have
             observed flow channeling near the walls and an exponential
             distribution of velocities. (A)},
   Key = {fds245446}
}

@booklet{Baxter91,
   Author = {Baxter, GW and Behringer, RP},
   Title = {Cellular automata models for the flow of granular
             materials},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {51},
   Number = {1-3},
   Pages = {465-471},
   Year = {1991},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/10.1016/0167-2789(91)90252-5},
   Abstract = {The importance of particle irregularity in the flow of
             granular material can be demonstrated using simple
             experiments. We introduce cellular automata which model
             nonspherical particles using rules derived from experiments.
             These automata can reproduce many features of the physical
             flows including the alignment of the particles, the
             formation of a complex channel region, the shape of the
             upper free surface, and the formation of defects in the body
             of the material. © 1991.},
   Doi = {10.1016/0167-2789(91)90252-5},
   Key = {Baxter91}
}

@booklet{Baxter91a,
   Author = {BAXTER, GW and LEONE, R and JOHNSON, GA and BEHRINGER,
             RP},
   Title = {TIME-DEPENDENCE, SCALING AND PATTERN-FORMATION FOR FLOWING
             SAND},
   Journal = {European Journal of Mechanics - B/Fluids},
   Volume = {10},
   Number = {2},
   Pages = {181-186},
   Year = {1991},
   ISSN = {0997-7546},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1991FR81800029&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Baxter91a}
}

@booklet{Metcalfe91,
   Author = {Metcalfe, G and Behringer, RP},
   Title = {Using superfluid mixtures to probe convective
             instabilities},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {51},
   Number = {1-3},
   Pages = {520-530},
   Year = {1991},
   ISSN = {0167-2789},
   Abstract = {When the height d of a convecting layer of a dilute solution
             of 3He in superfluid 4He is much greater than a
             characteristic dissipation length λ0, the superfluid
             mixture behaves as if it were a single-component classical
             fluid, but one with the extraordinarily broad and
             interesting Prandtl number range of 0.04 &lt; Pr &lt; 1.5.
             We have made the first direct measurements of λ0 by
             observing its effect on the critical Rayleigh number Rc,
             thus determining quantitatively how closely superfluid
             mixture convection matches standard Rayleigh-Bénard
             convection. Two-fluid effects can be only a few percent for
             1.0 &lt; T &lt; 2.0 K. We also report a series of
             measurements near the crossing of the skewed-varicose and
             oscillatory instabilities showing the effects of instability
             competition. © 1991.},
   Key = {Metcalfe91}
}

@booklet{Behringer91,
   Author = {Behringer, RP and Meyers, SD and Swinney, HL},
   Title = {Chaos and mixing in a geostrophic flow},
   Journal = {Physics of fluids. A, Fluid dynamics},
   Volume = {3},
   Number = {5},
   Pages = {1243-1249},
   Year = {1991},
   ISSN = {0899-8213},
   Abstract = {Experiments on Rossby waves on an azimuthal jet in a rapidly
             rotating annular tank reveal a striking barrier to mixing
             across the jet. A model based on the experiments assumes a
             two-dimensional incompressible flow described by a
             time-dependent streamfunction consisting of azimuthally
             propagating waves on a narrow jet. When there is only one
             wave, all Lagrangian particle trajectories are closed in the
             appropriate reference frame. When two independent waves are
             present, some trajectories are chaotic, and the size of the
             chaotic sea grows as the amplitude of the second wave is
             increased; however, at least one barrier to global transport
             - an invariant surface - prohibits trajectories from
             crossing the jet. The addition of a third wave is found to
             break the barrier only if the wave amplitudes exceed the
             width of the jet. In the experiment, the wave amplitude is
             typically about one-half the jet width, and the barrier to
             mixing persists even at the highest accessible Reynolds
             numbers. © 1991 American Institute of Physics.},
   Key = {Behringer91}
}

@booklet{Anderson91,
   Author = {Anderson, KE and Behringer, RP},
   Title = {Traveling wave convection patterns in an annular
             cell},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {51},
   Number = {1-3},
   Pages = {444-449},
   Year = {1991},
   ISSN = {0167-2789},
   Abstract = {Fast traveling wave convection rolls, localized rolls,
             non-uniform velocity rolls and slow rolls are four distinct
             patterns observed during the evolution of convection
             patterns in an ethanol-water binary mixture. These
             Rayleigh-Bénard experiments were carried out in an annular
             cell with an aspect ratio of 80:2:1. The mixture has a
             separation ratio value of ψ {reversed tilde equals} -0.09.
             The convection was driven by a constant heat flux less than
             5% above the onset heat flux. © 1991.},
   Key = {Anderson91}
}

@booklet{Behringer90a,
   Author = {BEHRINGER, RP and ONUKI, A and MEYER, H},
   Title = {THERMAL EQUILIBRATION OF FLUIDS NEAR THE LIQUID-VAPOR
             CRITICAL-POINT - HE-3 AND HE-3-HE-4 MIXTURES},
   Journal = {Journal of Low Temperature Physics},
   Volume = {81},
   Number = {1-2},
   Pages = {71-102},
   Year = {1990},
   Month = {October},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1990EG22500006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/BF00683153},
   Key = {Behringer90a}
}

@booklet{Behringer90,
   Author = {BEHRINGER, RP},
   Title = {THERMAL RESPONSE OF A HE-3-SUPERFLUID-HE-4
             MIXTURE},
   Journal = {Journal of Low Temperature Physics},
   Volume = {81},
   Number = {1-2},
   Pages = {1-17},
   Year = {1990},
   Month = {October},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1990EG22500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/BF00683148},
   Key = {Behringer90}
}

@booklet{Baxter90,
   Author = {Baxter, GW and Behringer, RP},
   Title = {Cellular automata models of granular flow.},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {42},
   Number = {2},
   Pages = {1017-1020},
   Year = {1990},
   Month = {July},
   ISSN = {1050-2947},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9904123},
   Key = {Baxter90}
}

@booklet{Metcalfe90,
   Author = {Metcalfe, GP and Behringer, RP},
   Title = {Convection in 3He-superfluid-4He mixtures: Measurement of
             the superfluid effects.},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {41},
   Number = {10},
   Pages = {5735-5738},
   Year = {1990},
   Month = {May},
   ISSN = {1050-2947},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9902969},
   Abstract = {Dilute superfluid mixtures bridge the Prandtl number range
             between liquid metals and water: 0.04&lt;NPr&lt;2. The
             convective equations of motion for superfluid mixtures are
             the equations for Rayleigh-Bénard convection in a normal
             single-component fluid plus additional superfluid terms. We
             have measured the latter through their effect on the
             critical Rayleigh number Rc. The corrections can be only a
             few percent for 1.0&lt;T&lt;2.0 K, implying an accessible
             Prandtl-number range near onset of at least
             0.04&lt;NPr&lt;1.5. © 1990 The American Physical
             Society.},
   Doi = {10.1103/PhysRevA.41.5735},
   Key = {Metcalfe90}
}

@booklet{Anderson90,
   Author = {Anderson, KE and Behringer, RP},
   Title = {Long time scales in traveling wave convection
             patterns},
   Journal = {Physics Letters A},
   Volume = {145},
   Number = {6-7},
   Pages = {323-328},
   Year = {1990},
   ISSN = {0375-9601},
   url = {http://dx.doi.org/10.1016/0375-9601(90)90942-H},
   Abstract = {Rayleigh-Bénard experiments using an ethanol-water mixture
             in an annular cell, have shown that the patterns which occur
             at the onset of traveling wave convection can evolve in a
             complex fashion over hundreds of hours. We describe a 500
             hour transition from a group of three convecting roll pairs
             to thirty-nine pairs which filled the cell. ©
             1990.},
   Doi = {10.1016/0375-9601(90)90942-H},
   Key = {Anderson90}
}

@booklet{Metcalfe90a,
   Author = {Metcalfe, GP and Behringer, RP},
   Title = {Critical Rayleigh numbers for cryogenic experiments},
   Journal = {Journal of Low Temperature Physics},
   Volume = {78},
   Number = {3-4},
   Pages = {231-246},
   Year = {1990},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00686102},
   Abstract = {We give critical Rayleigh numbers, Rc, and the corresponding
             critical wavevectors, ac, for the onset of Rayleigh-Bénard
             convection for thermal conditions on the horizontal
             boundaries that model physical experiments, particularly
             those carried out at low temperatures with liquid helium. We
             assume that a fluid layer, satisfying the Boussinesq
             approximation, is bounded above and below by rigid plates
             with finite, nonzero vertical thicknesses and finite thermal
             conductivities. The effect of sidewalls on Rc is not likely
             to be important for many experiments and so is not
             considered here; specifically, we assume a horizontally
             infinite layer. At the top of the top plate and the bottom
             of the bottom plate, we consider boundary conditions for
             which a linear combination of the convective temperature
             field and its vertical derivative vanishes. For these
             boundary conditions, the growth rates of the linear
             stability problem are necessarily real. We find that Rc only
             deviates significantly from 1708 and ac only deviates
             significantly from 3.11, when the thermal conductivity of
             the fluid is comparable to or larger than that of the
             boundaries, or when the plates are exceptionally thin. In
             particular a fixed heat flux applied to highly conducting
             plates (a configuration frequently used in cryogenic
             experiments) does not cause Rc to vary much from the
             standard value, 1708. © 1990 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00686102},
   Key = {Metcalfe90a}
}

@article{fds287566,
   Author = {Behringer, RP},
   Title = {Thermal response of a3He-superfluid-4He
             mixture},
   Journal = {Journal of Low Temperature Physics},
   Volume = {81},
   Number = {1-2},
   Pages = {1-17},
   Year = {1990},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00683148},
   Abstract = {The response of a layer of superfluid mixture to an ac heat
             source, Q(t)=Q0 exp (iωt), is determined. In the
             low-frequency regime, the temperature response at the heated
             side of a superfluid layer is essentially identical to that
             of an ordinary fluid having a thermal conductivity κeff and
             a thermal diffusion coefficient Γ0/2. Here κeff is the
             effective conductivity of Khalatnikov, and Γ0 is the
             diffusion coefficient of Griffin. At much higher
             frequencies, the results are more complicated. The
             low-frequency regime is defined in terms of the second sound
             velocity u2 by ω≪u22/Γ0. The ac response function is
             valuable in a number of ways. It can be used to obtain the
             system response to more complicated time-dependent
             variations in Q such as step changes in Q. A knowledge of
             the response function in the low-frequency regime provides a
             mechanism for directly determining the Kapitza resistance in
             mixtures. Finally, a knowledge of the response function
             provides an additional opportunity to test two-fluid
             hydrodynamics. Alternative tests of superfluid hydrodynamics
             are of particular interest in light of recent experiments
             that show anomalous values for κeff in the low3He
             concentration limit © 1990 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00683148},
   Key = {fds287566}
}

@article{fds287567,
   Author = {Behringer, RP and Onuki, A and Meyer, H},
   Title = {Thermal equilibration of fluids near the liquid-vapor
             critical point:3He and3He-4He
             mixtures},
   Journal = {Journal of Low Temperature Physics},
   Volume = {81},
   Number = {1-2},
   Pages = {71-102},
   Year = {1990},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00683153},
   Abstract = {We study the temperature-equilibration process of fluids at
             constant volume in a thermal conductivity cell, where an
             initial temperature gradient relaxes to zero. The
             calculation is performed in the linear approximation for a
             pure fluid and a binary mixture. Near the critical point of
             the pure fluid, the adiabatic heating process, which takes
             place at constant volume V, causes equilibration to proceed
             four times faster when CP/CV≫1 than for the process at
             constant pressure P. For the mixtures, the relaxation rate
             enhancement at constant V compared with constant P is
             restricted to a temperature region where the coupling
             between temperature and mass diffusion is small. The
             predictions are compared with experimental results for3He
             and for two3He-4He mixtures along their critical isochores.
             Finally, we discuss the thermal relaxation in the two-phase
             (liquid-gas) and one-phase (gas) regimes at the critical
             density, as measured with a conductivity and a calorimetry
             cell. The contrasting behavior for3He and a3He-4He mixture
             in these two regimes and under these different constraints
             is pointed out and discussed. © 1990 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00683153},
   Key = {fds287567}
}

@article{fds304527,
   Author = {Metcalfe, GP and Behringer, RP},
   Title = {Convection in -43He mixtures: Measurement of the superfluid
             effects},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {41},
   Number = {10},
   Pages = {5735-5738},
   Year = {1990},
   ISSN = {1050-2947},
   url = {http://dx.doi.org/10.1103/PhysRevA.41.5735},
   Abstract = {Dilute superfluid mixtures bridge the Prandtl number range
             between liquid metals and water: 0.04&lt;NPr&lt;2. The
             convective equations of motion for superfluid mixtures are
             the equations for Rayleigh-Bénard convection in a normal
             single-component fluid plus additional superfluid terms. We
             have measured the latter through their effect on the
             critical Rayleigh number Rc. The corrections can be only a
             few percent for 1.0&lt;T&lt;2.0 K, implying an accessible
             Prandtl-number range near onset of at least
             0.04&lt;NPr&lt;1.5. © 1990 The American Physical
             Society.},
   Doi = {10.1103/PhysRevA.41.5735},
   Key = {fds304527}
}

@booklet{Baxter89,
   Author = {Baxter, GW and Behringer, RP and Fagert, T and Johnson,
             GA},
   Title = {Pattern formation in flowing sand.},
   Journal = {Physical Review Letters},
   Volume = {62},
   Number = {24},
   Pages = {2825-2828},
   Year = {1989},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10040101},
   Doi = {10.1103/PhysRevLett.62.2825},
   Key = {Baxter89}
}

@booklet{Motsay88,
   Author = {Motsay, RW and Anderson, KE and Behringer, RP},
   Title = {The onset of convection and turbulence in rectangular layers
             of normal liquid 4He.},
   Journal = {J. FLUID MECH.},
   Volume = {189 , Apr. 1988},
   Pages = {263-286},
   Year = {1988},
   Abstract = {Heat transport in rectangular layers of convecting normal
             liquid helium-4 with Prandtl numbers 0.52 and 0.70 was
             measured. The effect of sidewalls on steady convection and
             the nature of secondary instabilities on the convective
             rolls leading to the onset of turbulence were studied.
             Results near the onset of convection, the critical Rayleigh
             numbers and the initial slopes of the Nusselt curve were in
             agreement with theory and other experimental
             work.},
   Key = {Motsay88}
}

@booklet{Gao87,
   Author = {Gao, H and Behringer, RP},
   Title = {Onset of time dependence at the secondary instability of a
             convecting binary mixture: Implications for wave-number
             selection.},
   Journal = {Physical review. A, General physics},
   Volume = {35},
   Number = {9},
   Pages = {3993-3996},
   Year = {1987},
   Month = {May},
   ISSN = {0556-2791},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9898638},
   Key = {Gao87}
}

@booklet{Gao87a,
   Author = {Gao, H and Metcalfe, G and Jung, T and Behringer,
             RP},
   Title = {HEAT-FLOW EXPERIMENTS IN LIQUID **4He WITH A VARIABLE
             CYLINDRICAL GEOMETRY.},
   Journal = {Journal of Fluid Mechanics},
   Volume = {174},
   Pages = {209-231},
   Year = {1987},
   Abstract = {This paper first describes an apparatus for measuring the
             Nusselt number N versus the Rayleigh number R of convecting
             normal liquid **4He layers. The most important feature of
             the apparatus is its ability to provide layers of different
             heights d, and hence different aspect ratios GAMMA . The
             horizontal cross-section of each layer is circular, and
             GAMMA is defined by GAMMA equals D/2d where D is the
             diameter of the layer. Results are reported for 2. 4 less
             than equivalent to GAMMA less than equivalent to 16 and for
             Prandtl numbers Pr spanning 0. 5. and 0. 9. These results
             are presented in terms of the slope N//1 equals R//cdN/dR
             evaluated just above the onset of convection at R//c. Study
             results are discussed.},
   Key = {Gao87a}
}

@booklet{Gao86,
   Author = {Gao, H and Behringer, RP},
   Title = {Convective instabilities of a normal liquid 3He-4He
             mixture.},
   Journal = {Physical review. A, General physics},
   Volume = {34},
   Number = {1},
   Pages = {697-700},
   Year = {1986},
   Month = {July},
   ISSN = {0556-2791},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9897319},
   Key = {Gao86}
}

@booklet{Shaumeyer86,
   Author = {Shaumeyer, JN and Behringer, RP},
   Title = {Unexpected observation in measurements of transport
             coefficients in 3He-4He mixtures near T lambda.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {33},
   Number = {5},
   Pages = {3553-3555},
   Year = {1986},
   Month = {March},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9938751},
   Key = {Shaumeyer86}
}

@booklet{Behringer86,
   Author = {BEHRINGER, RP},
   Title = {HYDRODYNAMIC HEAT-FLOW IN VERY DILUTE SUPERFLUID HE-3-HE-4
             MIXTURES},
   Journal = {Journal of Low Temperature Physics},
   Volume = {62},
   Number = {1-2},
   Pages = {15-26},
   Year = {1986},
   Month = {January},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1986AZG3200002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/BF00681317},
   Key = {Behringer86}
}

@article{fds287565,
   Author = {Behringer, RP},
   Title = {Hydrodynamic heat flow in very dilute superfluid3He-4He
             mixtures},
   Journal = {Journal of Low Temperature Physics},
   Volume = {62},
   Number = {1-2},
   Pages = {15-26},
   Year = {1986},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00681317},
   Abstract = {The superfluid hydrodynamics of heat flow is examined for
             very small mass concentrations c of3He in4He in an effort to
             better understand recent results for the effective heat
             conductivity κeff, which appear to be in conflict with
             predictions. The full hydrodynamics contains a thermal
             boundary layer; within this layer the temperature and
             concentration gradients differ from those in the bulk fluid.
             An examination of finite heating effects based on the ansatz
             κeff ∝c-pfor small c shows distinctly different behavior
             for experimental determinations of κeff when p&lt;1, p=1,
             and p&gt;1. Thus, finite heating can be used as a probe to
             evaluate the exponent p. © 1986 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00681317},
   Key = {fds287565}
}

@booklet{Behringer85,
   Author = {Behringer, RP},
   Title = {Rayleigh-Bénard convection and turbulence in liquid
             helium},
   Journal = {Reviews of Modern Physics},
   Volume = {57},
   Number = {3},
   Pages = {657-687},
   Year = {1985},
   ISSN = {0034-6861},
   url = {http://dx.doi.org/10.1103/RevModPhys.57.657},
   Abstract = {Recent advances in the understanding of Rayleigh-Bénard
             convection and turbulence are reviewed in light of work
             using liquid helium. The discussion includes both
             experiments which have probed the steady flows preceding
             time dependence and experiments which have been directed
             toward understanding the ways in which turbulence evolves.
             Comparison is made where appropriate to the many important
             contributions which have been obtained using
             room-temperature fluids, and a discussion is given
             explaining the advantages of cryogenic techniques. Brief
             reviews are given for recent experimental investigations of
             convection in He3-He4 mixtures in both the superfluid and
             the normal states and investigations of convection in
             rotating layers of liquid helium. © 1985 The American
             Physical Society.},
   Doi = {10.1103/RevModPhys.57.657},
   Key = {Behringer85}
}

@booklet{Gao84,
   Author = {Gao, H and Behringer, RP},
   Title = {Onset of convective time dependence in cylindrical
             containers},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {30},
   Number = {5},
   Pages = {2837-2839},
   Year = {1984},
   ISSN = {1050-2947},
   url = {http://dx.doi.org/10.1103/PhysRevA.30.2837},
   Abstract = {Thermal measurements probe time dependence in a convecting
             helium layer with cylindrical geometry and aspect ratios
             radiusheight in the range 2.4&lt; &lt;22. For all, there is
             a first transition at a Rayleigh number R1&gt;Rc where
             convection begins at Rc. Time dependence occurs for R&gt;R1
             when 4. The character of the transition at R1 is identified
             over the full range of. As becomes large R1Rc 1.09, a value
             which is difficult to reconcile with predictions for the
             expected skewed varicose instability. © 1984 The American
             Physical Society.},
   Doi = {10.1103/PhysRevA.30.2837},
   Key = {Gao84}
}

@booklet{Behringer83,
   Author = {Behringer, RP and Gao, H and Shaumeyer, JN},
   Title = {Time dependence in rayleigh-Bénard convection with a
             variable cylindrical geometry},
   Journal = {Physical Review Letters},
   Volume = {50},
   Number = {16},
   Pages = {1199-1202},
   Year = {1983},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/PhysRevLett.50.1199},
   Abstract = {Studies of the first time dependence in Rayleigh-Bénard
             convection in He4 are reported. The aspect ratio Γ could be
             varied continuously. Data at 31 Γ values with 4&lt;Γ&lt;13
             show that near onset the first time dependence is always
             periodic and associated with changes in the heat transport.
             The dominant periodicity has a nonzero amplitude, A, and
             vanishing frequency at onset. Changes in A with Γ show
             wave-number effects. Except for the time dependence, the
             transition is consistent with predictions for the
             skew-varicose instability. © 1983 The American Physical
             Society.},
   Doi = {10.1103/PhysRevLett.50.1199},
   Key = {Behringer83}
}

@booklet{Clark83,
   Author = {CLARK, C and SHAUMEYER, J and AGOSTA, C and BEHRINGER,
             RP},
   Title = {THE ONSET OF CONVECTIVE TURBULENCE IN LARGE ASPECT RATIO
             LAYERS},
   Journal = {Physica A: Statistical Mechanics and its
             Applications},
   Volume = {118},
   Number = {1-3},
   Pages = {442-442},
   Year = {1983},
   ISSN = {0378-4371},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1983QK91000038&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1016/0378-4371(83)90220-0},
   Key = {Clark83}
}

@booklet{Behringer82,
   Author = {Behringer, RP and Ahlers, G},
   Title = {HEAT TRANSPORT AND TEMPORAL EVOLUTION OF FLUID FLOW NEAR THE
             RAYLEIGH-BENARD INSTABILITY IN CYLINDRICAL
             CONTAINERS.},
   Journal = {Journal of Fluid Mechanics},
   Volume = {125},
   Number = {DEC},
   Pages = {219-258},
   Year = {1982},
   Abstract = {The paper describes in detail an apparatus for
             heat-transport measurements in shallow horizontal layers of
             fluid at low temperatures. High-precision results of
             convective heat transports as a function of the Rayleigh
             number R are presented for cylindrical cells of aspect ratio
             L equals 2. 08, 4. 72 and 57. The paper concentrates on the
             long-time behavior of Boussinesq systems. The measurements
             show that the convective onset near the critical Rayleigh
             number R//c is sharp within the experimental resolution of
             about 0. 1% of the Nusselt number N, even in laterally
             finite containers. Values of R//c, and of the initial slopes
             of N(R), are obtained and compared with predictions for
             different flow patterns. Refs.},
   Key = {Behringer82}
}

@booklet{Behringer82c,
   Author = {Behringer, RP and Meyer, H},
   Title = {Diffusive relaxation processes in liquid3He-4He
             mixtures. II. Superfluid phase},
   Journal = {Journal of Low Temperature Physics},
   Volume = {46},
   Number = {5-6},
   Pages = {435-450},
   Year = {1982},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00683909},
   Abstract = {Relaxation measurements in superfluid3He-4He mixtures when a
             heat flux across a horizontal layer is switched on or off
             provide a quantitative test for the solutions of
             Khalatnikov's hydrodynamic equations. On the basis of these
             equations we predict that the relaxation times τ in a layer
             of height d can be expressed by a simple scaled relation
             that is a function of static and transport properties.
             Relaxation experiments on five mixtures are in good
             agreement with these predictions. In an appendix we discuss
             the viscous penetration depth λp and show that it is small
             enough for the Khalatnikov expressions to be valid under our
             experimental conditions. © 1982 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00683909},
   Key = {Behringer82c}
}

@booklet{Behringer82b,
   Author = {BEHRINGER, RP and MEYER, H},
   Title = {DIFFUSIVE RELAXATION PROCESSES IN LIQUID HE-3-HE-4 MIXTURES
             .1. NORMAL PHASE},
   Journal = {Journal of Low Temperature Physics},
   Volume = {46},
   Number = {5-6},
   Pages = {407-434},
   Year = {1982},
   ISSN = {0022-2291},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1982NK12900003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/BF00683908},
   Key = {Behringer82b}
}

@booklet{Behringer82a,
   Author = {Behringer, RP and Shaumeyer, JN and Clark, CA and Agosta,
             CC},
   Title = {Turbulent onset in moderately large convecting
             layers},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {26},
   Number = {6},
   Pages = {3723-3726},
   Year = {1982},
   ISSN = {1050-2947},
   url = {http://dx.doi.org/10.1103/PhysRevA.26.3723},
   Abstract = {We present long-time thermal data on turbulent evolution in
             Rayleigh-Bénard convection for cylindrical containers of
             aspect ratios =6.22 and 7.87 and Prandtl numbers near 0.6.
             The first time dependence observed was more complex than the
             intermittent flows reported by Ahlers and Walden for =4.72,
             although the periodicity they observed was reproduced for
             =7.87. The turbulent onset for =6.22, showing substantial
             regimes of periodicity, was quite different from that for
             =7.87 or 4.72. We conclude that changes of order unity in
             strongly affect turbulent onset, even for moderately large
             aspect ratios. © 1982 The American Physical
             Society.},
   Doi = {10.1103/PhysRevA.26.3723},
   Key = {Behringer82a}
}

@article{fds320092,
   Author = {Behringer, RP and Meyer, H},
   Title = {Diffusive relaxation processes in liquid3He-4He
             mixtures. I. Normal phase},
   Journal = {Journal of Low Temperature Physics},
   Volume = {46},
   Number = {5-6},
   Pages = {407-434},
   Year = {1982},
   url = {http://dx.doi.org/10.1007/BF00683908},
   Abstract = {When a heat flux is switched on across a fluid binary
             mixture, steady state conditions for the temperature and
             mass concentration gradients ∇T and ∇c are reached via a
             diffusive transient process described by a series of terms
             "modes" involving characteristic times τn. These are
             determined by static and transport properties of the
             mixture, and by the boundary conditions. We present a
             complete mathematical solution for the relaxation process in
             a binary normal liquid layer of height d and infinite
             diameter, and discuss in particular the role of the
             parameter A=kT2(∂μ/∂c)T,P/TCP,c coupling the mass and
             thermal diffusion. Here kT is the thermal diffusion ratio,
             (∂μ/∂c)T,P-1 is the concentration susceptibility, μ is
             the chemical potential difference between the components,
             and CP,c is the specific heat. We present examples of
             special situations found in relaxation experiments. When A
             is small, the observable times τ(∇T) and τ(∇c) for
             temperature and concentration equilibration are different,
             but they tend to the same value as A increases. We present
             experimental results on four examples of liquid helium of
             different3He mole fraction X, and discuss these results on
             the basis of the preceding analysis. In the simple case for
             pure3He (i.e., in the absence of mass diffusion) we find the
             observed τ(∇T) to be in good agreement with that
             calculated from the thermal diffusivity. For all the
             investigated3He-4He mixtures, we observe τ(∇c) and
             τ(∇T) to be different when A is small, a situation
             occurring at high enough temperatures. As A increases with
             decreasing T, they become equal, as predicted. For the
             mixtures with mole fractions X(3He)=0.510 and 0.603, we
             derive the mass diffusion D from the analysis of τ(∇c)
             and demonstrate that it diverges strongly with an exponent
             of about 1/3 in the critical region near the superfluid
             transition. As the tricritical point (Tt, Xt) is approached
             for the mixture X=Xt0.675, D tends to zero with an exponent
             of roughly 0.4. These results are consistent with
             predictions and also with the D derived from sound
             attenuation data. We discuss the difficulties of the
             analysis in the regime close to Tλ and Tt, with special
             emphasis on the situation created by the onset of a
             superfluid film along the wall of the cell for X=0.603 and
             0.675. © 1982 Plenum Publishing Corporation.},
   Doi = {10.1007/BF00683908},
   Key = {fds320092}
}

@booklet{Shaumeyer81,
   Author = {SHAUMEYER, JN and BEHRINGER, RP and BAIERLEIN,
             R},
   Title = {LINEAR GROWTH-RATES FOR THE RAYLEIGH-BENARD INSTABILITY IN
             CYLINDRICAL GEOMETRY},
   Journal = {Journal of Fluid Mechanics},
   Volume = {109},
   Number = {AUG},
   Pages = {339-348},
   Year = {1981},
   ISSN = {0022-1120},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1981MH72200021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1017/S0022112081001109},
   Key = {Shaumeyer81}
}

@booklet{Behringer80a,
   Author = {BEHRINGER, RP and RUPPEINER, G and MEYER, H},
   Title = {RELAXATION-TIMES IN LIQUID HE-3-HE-4 MIXTURES},
   Journal = {Bulletin- American Physical Society},
   Volume = {25},
   Number = {4},
   Pages = {498-498},
   Year = {1980},
   ISSN = {0003-0503},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800124&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Behringer80a}
}

@booklet{Agosta80,
   Author = {AGOSTA, C and JAN, J and SHAUMEYER, J and BEHRINGER,
             RP},
   Title = {TIME-DEPENDENT FLOW IN RAYLEIGH-BENARD CONVECTION},
   Journal = {Bulletin- American Physical Society},
   Volume = {25},
   Number = {4},
   Pages = {531-531},
   Year = {1980},
   ISSN = {0003-0503},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800341&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Agosta80}
}

@booklet{Behringer80,
   Author = {Behringer, RP and Agosta, C and Jan, JS and Shaumeyer,
             JN},
   Title = {Time-dependent Rayleigh-Bénard convection and instrumental
             attenuation},
   Journal = {Physics Letters A},
   Volume = {80},
   Number = {4},
   Pages = {273-276},
   Year = {1980},
   ISSN = {0375-9601},
   url = {http://dx.doi.org/10.1016/0375-9601(80)90020-1},
   Abstract = {We present new thermal data on time-dependent convection in
             a cylindrically confined layer of helium with aspect ratio
             Γ=7.87 (Γ≡layer radius/layer height). Experimental data
             and an analysis of attenuation effects indicate broadband
             spectral features obtained by a global probe tend to be
             independent of Γ for Γ≳5. © 1980.},
   Doi = {10.1016/0375-9601(80)90020-1},
   Key = {Behringer80}
}

@booklet{Shaumeyer80,
   Author = {SHAUMEYER, JN and BEHRINGER, RP and BAIERLEIN,
             R},
   Title = {LINEAR GROWTH-RATES FOR THE RAYLEIGH-BENARD INSTABILITY IN
             CYLINDRICAL GEOMETRY},
   Journal = {Bulletin- American Physical Society},
   Volume = {25},
   Number = {4},
   Pages = {531-531},
   Year = {1980},
   ISSN = {0003-0503},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800342&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {Shaumeyer80}
}

@article{fds245443,
   Author = {Ahlers, G and Behringer, RP},
   Title = {Evolution of turbulence from the Rayleigh-Bénard
             instability},
   Journal = {Physical Review Letters},
   Volume = {40},
   Number = {11},
   Pages = {712-716},
   Year = {1978},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/PhysRevLett.40.712},
   Abstract = {Measurements of heat transport through horizontal layers of
             fluid heated from below are reported for three aspect ratios
             Γ(Γ=D2d,D=diameter,d=height of the cylindrical cells).
             They show that for Γ=57 the fluid flow is turbulent, in the
             sense that it has an a nonperiodic time dependence, for
             numbers R&gt;Rt with Rt≅Rc(Rc) is the critical R for onset
             of fluid flow). For Γ=4.72, we find Rt≅2Rc. For Γ=2.08,
             a quasiperiodic state exists for Rp&lt;∼R&lt;∼Rt, with
             Rp≅10Rc and Rt≅11Rc. © 1978 The American Physical
             Society.},
   Doi = {10.1103/PhysRevLett.40.712},
   Key = {fds245443}
}

@article{fds245442,
   Author = {Behringer, RP and Ahlers, G},
   Title = {Heat transport and critical slowing down near the
             Rayleigh-Bénard instability in cylindrical
             containers},
   Journal = {Physics Letters A},
   Volume = {62},
   Number = {5},
   Pages = {329-331},
   Year = {1977},
   ISSN = {0375-9601},
   url = {http://dx.doi.org/10.1016/0375-9601(77)90431-5},
   Abstract = {Measurements of heat transport across layers of liquid He I
             heated from below show a sharp transition to fluid flow at
             the gravitationally driven Rayleigh-Bénard instability. The
             effective thermal conductivity of the convecting fluid is
             found to be a linear function of the reduced Rayleigh number
             (R - Rc)/Rc and to have a slope which agrees with
             calculations. Critical slowing down near Rc is measured and
             found to be in excellent agreement with theory. ©
             1977.},
   Doi = {10.1016/0375-9601(77)90431-5},
   Key = {fds245442}
}

@article{fds245438,
   Author = {Riedel, EK and Meyer, H and Behringer, RP},
   Title = {Thermodynamic properties of liquid3He-4He
             mixtures near the tricritical point. II. Data analysis by
             the scaling-field method},
   Journal = {Journal of Low Temperature Physics},
   Volume = {22},
   Number = {3-4},
   Pages = {369-402},
   Year = {1976},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00654713},
   Abstract = {The scaling theory for tricritical phenomena by Riedel is
             applied to the analysis of thermodynamic properties of
             liquid3He-4He mixtures near the tricritical point. Within
             this theory experimental data for the phase diagram, the3He
             molar concentration X, and the concentration susceptibility
             (∂X/∂Δ)T are discussed in terms of two scaling fields
             that are functions of the temperature T and the difference
             Δ= {Mathematical expression}3- {Mathematical expression}4
             of the chemical potentials of the two helium isotopes. The
             quantities X and (∂X/∂Δ)T in terms of the fields T and
             Δ as independent variables are obtained for the intervals
             -0.1&lt;T - Tt&lt;0.53 K and -9&lt;Δ - Δt&lt;0.8 J/mole,
             from vapor pressure and calorimetric data described in a
             previous paper by Goellner, Behringer, and Meyer. The
             transformed data are analyzed to yield the tricritical
             exponents, amplitudes, scaling fields, and scaling
             functions. The values of the tricritical exponents are found
             to agree with those predicted by the renormalization-group
             theory of Riedel and Wegner. (Logarithmic corrections are
             beyond the precision of the present experiment.) Relations
             between amplitudes are derived and tested experimentally.
             The (linear) scaling fields are determined by using their
             relationship to geometrical features of the phase diagram.
             The data for X and (∂X/∂Δ)T are found to scale in terms
             of these generalized scaling variables. The sizes of the
             tricritical scaling regions in the normal and superfluid
             phases are estimated; the range of apparent tricritical
             scaling is found to be appreciably larger in the
             normal-fluid phase than in the superfluid phase. The
             tricritical scaling function for the concentration
             susceptibility is compared with the analogous scaling
             function for the compressibility of pure3He near the
             critical gas-liquid phase transition. Finally, when the
             critical line near the tricritical point is approached along
             a path of constant Δ&lt;Δt, the experimental data are
             found to exhibit the onset of the crossover from tricritical
             to critical behavior in qualitative agreement with crossover
             scaling. © 1976 Plenum Publishing Corporation.},
   Doi = {10.1007/BF00654713},
   Key = {fds245438}
}

@article{fds245440,
   Author = {Doiron, T and Behringer, RP and Meyer, H},
   Title = {Equation of state of a3He-4He mixture
             near its liquid-vapor critical point},
   Journal = {Journal of Low Temperature Physics},
   Volume = {24},
   Number = {3-4},
   Pages = {345-363},
   Year = {1976},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00655263},
   Abstract = {Measurements of the pressure coefficient (∂P/∂T)ρ,x are
             reported for a3He-4He mixture with a mole fraction X=0.805
             of3He in the neighborhood of the liquid-vapor critical
             point. These include data on 16 isochores taken over the
             density interval -0.5≤Δρ≤0.5 and over the temperature
             range -0.1 ≤t≤0.1, where Δρ=(ρ-ρc)/ρc and
             t=(T-Tc)/Tc,with ρc and Tc,respectively, the critical
             density and temperature of the mixture. From the
             discontinuity of (∂P/∂T)ρ,x at the boundary between the
             two-phase and the one-phase regions we determine the
             dew-bubble curve near Tcwith better precision than was done
             in recent PVT experiments. From the extrapolation of data
             not approaching Tccloser than 1 mK, (∂P/∂T)ρ,x along
             the critical isochore appears to be discontinuous at
             Tc,while for the isochore ρ/ρc≃0.92, (∂P/∂T)ρ,x is
             continuous across the dew curve. It is found that this
             latter isochore cuts the dew curve at its highest
             temperature. These observations are discussed in terms of
             general thermodynamic arguments and theoretical predictions
             of the asymptotic behavior. We calculate (∂P/∂T)ρ,x
             from the scaling equation of state proposed by Leung and
             Griffiths for3He-4He mixtures, using their numerical
             parameters. In spite of some systematic deviations,
             especially in the two-phase region, there is in general good
             agreement with experimental results. In particular, the
             shape of the measured dew-bubble curve and the apparent
             discontinuity of (∂P/∂T)ρ,x along the critical isochore
             show excellent agreement with theory. © 1976 Plenum
             Publishing Corporation.},
   Doi = {10.1007/BF00655263},
   Key = {fds245440}
}

@article{fds245441,
   Author = {Behringer, RP and Doiron, T and Meyer, H},
   Title = {Equation of state of3He near its liquid-vapor
             critical point},
   Journal = {Journal of Low Temperature Physics},
   Volume = {24},
   Number = {3-4},
   Pages = {315-344},
   Year = {1976},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00655262},
   Abstract = {We report high-resolution measurements of the pressure
             coefficient (∂P/∂T)ρ for3He in both the one-phase and
             two-phase regions close to the critical point. These include
             data on 40 isochores over the intervals -0.1≤t≤+0.1 and
             -0.2≤Δρ≤+0.2, where t=(T-Tc)/Tcand Δρ=(ρ-ρc)/ρc.
             We have determined the discontinuity Δ(∂P/∂T)ρ of
             (∂P/∂T)ρ between the one-phase and the two-phase
             regions along the coexistence curve as a function of Δρ.
             The asymptotic behavior of (1/ρ) Δ(∂P/∂T)ρ versus
             Δρ near the critical point gives a power law with an
             exponent (γ+β-1)β-1=1.39±0.02 for 0.01≦Δρ≤0.2 or
             -1×10-2≤t≤-10-6, from which we deduce γ=1.14±0.01,
             using β=0.361 determined from the shape of the coexistence
             curve. An analysis of the discontinuity Δ(∂P/∂T)ρ with
             a correction-to-scaling term gives γ=1.17±0.02. The quoted
             errors are from statistics alone. Furthermore, we combine
             our data with heat capacity results by Brown and Meyer to
             calculate (∂μ/∂T)ρc as a function of t. In the
             two-phase region the slope (∂2μ/∂T2)ρc is different
             from that in the one-phase region. These findings are
             discussed in the light of the predictions from simple
             scaling and more refined theories and model calculations.
             For the isochores Δρ≠0 we form a scaling plot to test
             whether the data follow simple scaling, which assumes
             antisymmetry of μ-μ (ρc, t) as a function of Δγ on both
             sides of the critical isochore. We find that indeed this
             plot shows that the assumption of simple scaling holds
             reasonably well for our data over the range {norm of
             matrix}t{norm of matrix}≤0.1. A fit of our data to the
             "linear model" approximation is obtained for {norm of
             matrix}Δρ{norm of matrix}≤0.10 and t≤0.02, giving a
             value of γ=1.16±0.02. Beyond this range, deviations
             between the fit and the data are greater than the
             experimental scatter. Finally we discuss the (∂P/∂T)ρ
             data analysis for4He by Kierstead. A power law plot of
             (1/ρ) Δ∂P/∂T)ρ versus Δρ below Tcleads to
             γ=1.13±0.10. An analysis with a correction-to-scaling term
             gives γ=1.06±0.02. In contrast to3He, the slopes
             (∂2μ/∂T2)ρc above and below Tcare only marginally
             different. © 1976 Plenum Publishing Corporation.},
   Doi = {10.1007/BF00655262},
   Key = {fds245441}
}

@article{fds245439,
   Author = {Goellner, G and Behringer, R and Meyer, H},
   Title = {Thermodynamic properties of liquid3He-4He
             mixtures near the tricritical point. I. Vapor pressure
             measurements and their thermodynamic analysis},
   Journal = {Journal of Low Temperature Physics},
   Volume = {13},
   Number = {1-2},
   Pages = {113-147},
   Year = {1973},
   ISSN = {0022-2291},
   url = {http://dx.doi.org/10.1007/BF00654401},
   Abstract = {Sensitive vapor pressure (Psat) measurements of3He-4He
             mixtures by means of a low-temperature strain gauge are
             described over the temperature range 0.5-1.5 K and the range
             0.4&lt;X&lt;0.85, where X is the3He mole fraction in the
             liquid phase. The vapor pressure cell is flat, with a height
             of only 2 mm, in order to reduce concentration gradients
             near the tricritical point. The pressure-sensitive device,
             which resolves changes of about 5×10-8 atm, is described,
             and its advantages over a conventional manometer system are
             discussed. Data taken successively on mixtures of small mole
             fraction difference are used to locate the phase separation
             boundary in the T-X plane and also the lambda line from a
             change in (∂Psat/∂T)x at these transitions. The limiting
             slopes (dT/dX)σ and (dT/dX)λ of the phase separation curve
             and the lambda line in the vicinity of their junction point,
             the tricritical point, are presented and compared with
             previous work. From the vapor pressure data, the
             concentration susceptibility (∂X/∂Δ)T,P was obtained.
             Here Δ=μ3-μ4 is the chemical potential difference of the
             respective isotopic components3He and4He. It is shown that
             (∂X/∂Δ)t diverges as the tricritical point is
             approached along various paths in the T-X plane, and the
             relevant tricritical exponents are presented. The weak
             divergence of (∂X/∂Δ)T along the lambda line predicted
             from the postulates of Griffiths and Wheeler could not be
             detected and it is believed that such divergence has to
             occur in a temperature interval that is far too small to be
             resolved with present-day techniques. Furthermore, gravity
             effects might well prevent observation of the weak
             divergence. The lambda transition is well evidenced by a
             distinct "shoulder" in a plot of (∂X/∂Δ)T at constant X
             as a function of T. This "shoulder" becomes smaller and
             gradually gets topped by a peak as X decreases from the
             tricritical mole fraction Xt. From a combination of vapor
             pressure and calorimetric data the chemical potential
             difference [Δ(X, T)-Δt] is calculated between 0.78 and
             1.22 K. Here Δt is the value at the tricritical point. From
             this tabulation the critical line and its slope (dΔ/dT)λ
             are obtained and compared with previous values based on
             calorimetric experiments only and with calculations based on
             the excess chemical potentials μ3E and μ4E derived from
             saturated vapor pressure data. © 1973 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF00654401},
   Key = {fds245439}
}


%% Papers Accepted   
@article{fds245418,
   Author = {Walker, DM and Tordesillas, A and Zhang, J and Behringer, RP and Andò,
             E and Viggiani, G and Druckrey, A and Alshibli, K},
   Title = {Structural templates of disordered granular
             media},
   Journal = {International Journal of Solids and Structures},
   Volume = {54},
   Pages = {20-30},
   Year = {2015},
   Month = {February},
   ISSN = {0020-7683},
   url = {http://hdl.handle.net/10161/10934 Duke open
             access},
   Doi = {10.1016/j.ijsolstr.2014.11.013},
   Key = {fds245418}
}

@article{fds303622,
   Author = {Clark, AH and Petersen, AJ and Behringer, RP},
   Title = {Collisional Model for Granular Impact Dynamics},
   Journal = {Phys. Rev. E},
   Volume = {89},
   Pages = {012201},
   Year = {2013},
   Month = {October},
   url = {http://arxiv.org/abs/1310.3134v2},
   Abstract = {When an intruder strikes a granular material from above, the
             grains exert a stopping force which decelerates and stops
             the intruder. Many previous studies have used a macroscopic
             force law, including a drag force which is quadratic in
             velocity, to characterize the decelerating force on the
             intruder. However, the microscopic origins of the force law
             terms are still a subject of debate. Here, drawing from
             previous experiments with photoelastic particles, we present
             a model which describes the velocity-squared force in terms
             of repeated collisions with clusters of grains. From our
             high speed photoelastic data, we infer that `clusters'
             correspond to segments of the strong force network that are
             excited by the advancing intruder. The model predicts a
             scaling relation for the velocity-squared drag force that
             accounts for the intruder shape. Additionally, we show that
             the collisional model predicts an instability to rotations,
             which depends on the intruder shape. To test this model, we
             perform a comprehensive experimental study of the dynamics
             of two-dimensional granular impacts on beds of photoelastic
             disks, with different profiles for the leading edge of the
             intruder. We particularly focus on a simple and useful case
             for testing shape effects by using triangular-nosed
             intruders. We show that the collisional model effectively
             captures the dynamics of intruder deceleration and rotation;
             i.e., these two dynamical effects can be described as two
             different manifestations of the same grain-scale physical
             processes.},
   Doi = {10.1103/PhysRevE.89.012201},
   Key = {fds303622}
}

@article{fds245507,
   Author = {Ren, J and Dijksman, JA and Behringer, RP},
   Title = {Reynolds pressure and relaxation in a sheared granular
             system.},
   Journal = {Physical Review Letters},
   Volume = {110},
   Number = {1},
   Pages = {018302},
   Year = {2013},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23383846},
   Abstract = {We describe experiments that probe the evolution of shear
             jammed states, occurring for packing fractions [symbol: see
             text](S) ≤ [symbol: see text] ≤ [symbol: see text] J,
             for frictional granular disks, where above [symbol: see
             text]J there are no stress-free static states. We use a
             novel shear apparatus that avoids the formation of
             inhomogeneities known as shear bands. This fixed [symbol:
             see text] system exhibits coupling between the shear strain,
             γ, and the pressure, P, which we characterize by the
             "Reynolds pressure" and a "Reynolds coefficient," R([symbol:
             see text]) = (∂(2)P/∂γ(2))/2. R depends only on
             [symbol: see text] and diverges as R ~ ([symbol: see text])c
             - )(α), where [symbol: see text](c) ~/= [symbol: see
             text](J) and α ~/= -3.3. Under cyclic shear, this system
             evolves logarithmically slowly towards limit cycle dynamics,
             which we characterize in terms of pressure relaxation at
             cycle n: ΔP ~/= -βln (n/n(0)). β depends only on the
             shear cycle amplitude, suggesting an activated process where
             β plays a temperaturelike role.},
   Doi = {10.1103/PhysRevLett.110.018302},
   Key = {fds245507}
}

@article{fds220989,
   Author = {R.P. Behringer},
   Title = {Forces in Static Packings},
   Journal = {Handbook of Granular Materials},
   Year = {2013},
   Key = {fds220989}
}

@article{fds220991,
   Author = {Karin Dahmen and R.P. Behringer},
   Title = {Avalanches in Slowly Sheared Disordered Materials},
   Journal = {Handbook of Granular Materials},
   Year = {2013},
   Key = {fds220991}
}

@article{fds220993,
   Author = {C. Coulais and R. P. Behringer and O. Dauchot},
   Title = {How the ideal Jamming point illuminates the world of
             granular media},
   Journal = {Soft Matter},
   Year = {2013},
   Key = {fds220993}
}

@article{fds212514,
   Author = {R.P. Behringer},
   Title = {Forces and Packings for Granular Materials},
   Booktitle = {Handbook of Granular Materials},
   Year = {2012},
   Key = {fds212514}
}

@article{fds212515,
   Author = {Karin Dahmen and R.P. Behringer},
   Title = {Avalanches in Slowly Sheared Disordered Materials,},
   Booktitle = {Handbook of Granular Materials},
   Year = {2012},
   Key = {fds212515}
}

@article{fds245508,
   Author = {Zheng, H and Dijksman, JA and Behringer, RP},
   Title = {On the application of photoelasticity techniques in
             geotechnical engineering},
   Journal = {Forum on Urban Geoenvironment and Sustainable
             Development},
   Year = {2012},
   Key = {fds245508}
}

@article{fds245646,
   Author = {Hartley, RR and Behringer, RP},
   Title = {Logarithmic rate dependence of force networks in sheared
             granular materials.},
   Journal = {Nature},
   Volume = {421},
   Number = {6926},
   Pages = {928-931},
   Year = {2003},
   Month = {February},
   ISSN = {0028-0836},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12606996},
   Abstract = {Many models of slow, dense granular flows assume that the
             internal stresses are independent of the shearing rate. In
             contrast, logarithmic rate dependence is found in
             solid-on-solid friction, geological settings and elsewhere.
             Here we investigate the rate dependence of stress in a
             slowly sheared two-dimensional system of photoelastic disks,
             in which we are able to determine forces on the granular
             scale. We find that the mean (time-averaged) stress displays
             a logarithmic dependence on the shear rate for plastic
             (irreversible) deformations. However, there is no
             perceivable dependence on the driving rate for elastic
             (reversible) deformations, such as those that occur under
             moderate repetitive compression. Increasing the shearing
             rate leads to an increase in the strength of the force
             network and stress fluctuations. Qualitatively, this
             behaviour resembles the changes associated with an increase
             in density. Increases in the shearing rate also lead to
             qualitative changes in the distributions of stress build-up
             and relaxation events. If shearing is suddenly stopped,
             stress relaxations occur with a logarithmic functional form
             over long timescales. This slow collective relaxation of the
             stress network provides a mechanism for rate-dependent
             strengthening.},
   Doi = {10.1038/nature01394},
   Key = {fds245646}
}


%% Papers Submitted   
@article{fds245417,
   Author = {Walker, DM and Tordesillas, A and Brodu, N and Dijksman, JA and Behringer, RP and Froyland, G},
   Title = {Self-assembly in a near-frictionless granular material:
             conformational structures and transitions in uniaxial cyclic
             compression of hydrogel spheres.},
   Journal = {Soft Matter},
   Volume = {11},
   Number = {11},
   Pages = {2157-2173},
   Year = {2015},
   Month = {March},
   ISSN = {1744-683X},
   url = {http://dx.doi.org/10.1039/c4sm02384f},
   Abstract = {We use a Markov transition matrix-based analysis to explore
             the structures and structural transitions in a
             three-dimensional assembly of hydrogel spheres under cyclic
             uniaxial compression. We apply these methods on experimental
             data obtained from a packing of nearly frictionless hydrogel
             balls. This allows an exploration of the emergence and
             evolution of mesoscale internal structures - a key
             micromechanical property that governs self-assembly and
             self-organization in dense granular media. To probe the
             mesoscopic force network structure, we consider two
             structural state spaces: (i) a particle and its contacting
             neighbours, and (ii) a particle's local minimal cycle
             topology summarized by a cycle vector. In both spaces, our
             analysis of the transition dynamics reveals which structures
             and which sets of structures are most prevalent and most
             likely to transform into each other during the
             compression/decompression of the material. In compressed
             states, structures rich in 3-cycle or triangle topologies
             form in abundance. In contrast, in uncompressed states,
             transitions comprising poorly connected structures are
             dominant. An almost-invariant transition set within the
             cycle vector space is discovered that identifies an
             intermediate set of structures crucial to the material's
             transition from weakly jammed to strongly jammed, and vice
             versa. Preferred transition pathways are also highlighted
             and discussed with respect to thermo-micro-mechanical
             constitutive formulations.},
   Doi = {10.1039/c4sm02384f},
   Key = {fds245417}
}

@article{fds245416,
   Author = {Behringer, RP},
   Title = {Jamming in granular materials},
   Journal = {Comptes Rendus Physique},
   Volume = {16},
   Number = {1},
   Pages = {10-25},
   Year = {2015},
   Month = {January},
   ISSN = {1631-0705},
   url = {http://dx.doi.org/10.1016/j.crhy.2015.02.001},
   Doi = {10.1016/j.crhy.2015.02.001},
   Key = {fds245416}
}

@article{fds245421,
   Author = {Clark, AH and Behringer, RP},
   Title = {Jet-induced 2-D crater formation with horizontal symmetry
             breaking},
   Journal = {Granular Matter},
   Volume = {16},
   Number = {4},
   Pages = {433-440},
   Year = {2014},
   Month = {January},
   ISSN = {1434-5021},
   url = {http://dx.doi.org/10.1007/s10035-014-0501-9},
   Abstract = {We investigate the formation of a crater in a 2-D bed of
             granular material by a jet of impinging gas, motivated by
             the problem of a retrograde rocket landing on a planetary
             surface. The crater is characterized in terms of depth and
             shape as it evolves, as well as by the horizontal position
             of the bottom of the crater. The crater tends to grow
             logarithmically in time, a result which is common in related
             experiments. We also observe a horizontal symmetry breaking
             at certain well-defined conditions which, as we will
             demonstrate, could be of considerable practical concern for
             lunar or planetary landers. We present data on the evolution
             of these asymmetric states and attempt to give insights into
             the mechanism behind the symmetry-breaking bifurcation. ©
             2014 Springer-Verlag Berlin Heidelberg.},
   Doi = {10.1007/s10035-014-0501-9},
   Key = {fds245421}
}

@article{fds225622,
   Author = {Abram H. Clark and Alec J. Petersen and Lou Kondic and R.P.
             Behringer},
   Title = {Nonlinear Sound During Granular Impact},
   Journal = {Physical Review Letters},
   Year = {2014},
   Key = {fds225622}
}

@article{fds225623,
   Author = {Nicolas Brodu and Joshua A. Dijksman and R.P.
             Behringer},
   Title = {Spanning the Scales of Granular Materials: Microscopic Force
             Imaging},
   Journal = {Nature Communications},
   Year = {2014},
   Key = {fds225623}
}

@article{fds225624,
   Author = {Nicolas Brodu and Joshua A. Dijksman and R.P.
             Behringer},
   Title = {Simulation scheme for modeling dense granular
             media},
   Journal = {Phys. Rev. E},
   Year = {2014},
   Key = {fds225624}
}

@article{fds225627,
   Author = {R.P. Behringer},
   Title = {How Do Granular Materials Jam, and How Do They
             Fail?},
   Journal = {Published Proceedings, ESMC, 2015},
   Year = {2014},
   Key = {fds225627}
}

@article{fds303623,
   Author = {Farhadi, S and Behringer, RP and Zhu, AZ},
   Title = {Stress relaxation for granular materials near Jamming under
             cyclic compression},
   Year = {2013},
   Month = {September},
   url = {http://arxiv.org/abs/1309.7147v1},
   Abstract = {We have explored isotropically jammed states of semi-2D
             granular materials through cyclic compression. In each
             compression cycle, systems of either identical ellipses or
             bi-disperse disks, transition between jammed and unjammed
             states. We determine the evolution of the average pressure,
             P, and structure through consecutive jammed states. We
             observe a transition point, {\phi}m, above which P persists
             over many cycles; below {\phi}m, P relaxes slowly. The
             relaxation time scale associated with P increases with
             packing fraction, while the relaxation time scale for
             collective particle motion remains constant. The collective
             motion of the ellipses is hindered compared to disks, due to
             the rotational constraints on elliptical
             particles.},
   Key = {fds303623}
}

@article{fds220994,
   Author = {Hu Zheng and Joshua A. Dijksman and R. P. Behringer},
   Title = {On the application of photoelasticity techniques in
             geotechnical engineering},
   Journal = {G´eotechnique Letters},
   Year = {2013},
   Key = {fds220994}
}

@article{fds220996,
   Author = {R. P. Behringer and Daping Bi and Bulbul Chakraborty and Abram Clark and Joshua Dijksman and Jie Ren and Jie Zhang},
   Title = {Statistical Properties of Granular Materials near
             Jamming},
   Journal = {J. Stat.},
   Year = {2013},
   Key = {fds220996}
}

@article{fds220997,
   Author = {David M. Walker and Antoinette Tordesillas and Michael Small and Robert P. Behringer and Chi K. Tse},
   Title = {A complex systems analysis of stick-slip dynamics of a
             laboratory fault},
   Journal = {Chaos},
   Year = {2013},
   Key = {fds220997}
}

@article{fds220998,
   Author = {David M.Walker and Antoinette Tordesill and Jie Ren and Joshua A.
             Dijksman and Robert P. Behringer},
   Title = {Uncovering temporal transitions and aging dynamics in
             granular materials under cyclic shear using quadrant
             scans},
   Journal = {Physical Review Letters},
   Year = {2013},
   Key = {fds220998}
}

@article{fds220999,
   Author = {Somayeh Farhadi and Robert P. Behringer},
   Title = {Anomalous Dynamics for Sheared Granular Materials},
   Journal = {Physical Review Letters},
   Year = {2013},
   Key = {fds220999}
}

@article{fds303633,
   Author = {Clark, AH and Behringer, RP},
   Title = {Granular Impact Model as an Energy-Depth
             Relation},
   Journal = {EPL},
   Volume = {101},
   Pages = {64001},
   Year = {2012},
   Month = {October},
   url = {http://arxiv.org/abs/1210.6692v5},
   Abstract = {Velocity-squared drag forces are common in describing an
             object moving through a granular material. The resulting
             force law is a nonlinear differential equation, and
             closed-form solutions of the dynamics are typically obtained
             by making simplifying assumptions. Here, we consider a
             generalized version of such a force law which has been used
             in many studies of granular impact. We show that recasting
             the force law into an equation for the kinetic energy versus
             depth, K(z), yields a linear differential equation, and thus
             general closed-form solutions for the velocity versus depth.
             This approach also has several advantages in fitting such
             models to experimental data, which we demonstrate by
             applying it to data from 2D impact experiments. We also
             present new experimental results for this model, including
             shape and depth dependence of the velocity-squared drag
             force.},
   Doi = {10.1209/0295-5075/101/64001},
   Key = {fds303633}
}

@article{fds212516,
   Author = {Abram Clark and Lou Kondic and R.P. Behringer},
   Title = {Granular Impact Dynamics: Fluctuations at Short Time
             Scales},
   Booktitle = {Powders and Grains, 2013},
   Year = {2012},
   Key = {fds212516}
}

@article{fds245536,
   Author = {Wambaugh, JF and Hartley, RR and Behringer, RP},
   Title = {Force networks and elasticity in granular
             silos.},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {32},
   Number = {2},
   Pages = {135-145},
   Year = {2010},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20582447},
   Abstract = {We have made experimental observations of the force networks
             within a two-dimensional granular silo similar to the
             classical system of Janssen. Models like that of Janssen
             predict that pressure within a silo saturates with depth as
             the result of vertical forces being redirected to the walls
             of the silo where they can then be carried by friction. We
             use photoelastic particles to obtain information not
             available in previous silo experiments --the internal force
             structure. We directly compare various predictions with the
             results obtained by averaging ensembles of experimentally
             obtained force networks. We identify several differences
             between the mean behavior in our system and that predicted
             by Janssen-like models: We find that the redirection
             parameter describing how the force network transfers
             vertical forces to the walls varies with depth. We find that
             changes in the preparation of the material can cause the
             pressure within the silo to either saturate or to continue
             building with depth. Most strikingly, we observe a nonlinear
             response to overloads applied to the top of the material in
             the silo. For larger overloads we observe the previously
             reported "giant overshoot" effect where overload pressure
             decays only after an initial increase (G. Ovarlez et al.,
             Phys. Rev. E 67, 060302(R) (2003)). For smaller overloads we
             find that additional pressure propagates to great depth.
             Analysis of the differences between the inter-grain contact
             and force networks suggests that, for our system, when the
             load and the particle weight are comparable, particle
             elasticity acts to stabilize the force network, allowing
             deep propagation. For larger loads, the force network
             rearranges, resulting in the expected, Janssen-like
             behavior. Thus, a meso-scale network phenomenon results in
             an observable nonlinearity in the mean pressure
             profile.},
   Doi = {10.1140/epje/i2010-10608-1},
   Key = {fds245536}
}

@article{fds245562,
   Author = {Lätzel, M and Luding, S and Herrmann, HJ and Howell, DW and Behringer,
             RP},
   Title = {Comparing simulation and experiment of a 2D granular Couette
             shear device.},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {11},
   Number = {4},
   Pages = {325-333},
   Year = {2003},
   Month = {August},
   ISSN = {1292-8941},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15011035},
   Abstract = {We present experiments along with molecular-dynamics (MD)
             simulations of a two-dimensional (2D) granular material in a
             Couette cell undergoing slow shearing. The grains are disks
             confined between an inner, rotating wheel and a fixed outer
             ring. The simulation results are compared to experimental
             studies and quantitative agreement is found. Tracking the
             positions and orientations of individual particles allows us
             to obtain density distributions, velocity and particle
             rotation rates for the system. The key issue of this paper
             is to show the extent to which quantitative agreement
             between an experiment and MD simulations is possible.
             Besides many differences in model details and the
             experiment, the qualitative features are nicely reproduced.
             We discuss the quantitative agreement/disagreement, give
             possible reasons, and outline further research
             perspectives.},
   Doi = {10.1140/epje/i2002-10160-7},
   Key = {fds245562}
}

@article{fds17073,
   Author = {Junfei Geng and R.P. Behringer},
   Title = {Diffusion, mobility and temperature in a dense granular
             material},
   Year = {2002},
   Month = {December},
   Key = {fds17073}
}

@article{fds17079,
   Author = {Brian Utter and R.P. Behringer},
   Title = {Diffusion in 2D Granular Couette Flow},
   Year = {2002},
   Month = {December},
   Key = {fds17079}
}

@article{fds39238,
   Author = {Junfei Geng and R.P. Behringer and G. Reydellet and E.
             Clement},
   Title = {Green's Function Measurements of 2D Granular
             Materials},
   Journal = {Physica D},
   Year = {2002},
   Month = {December},
   Key = {fds39238}
}


%% Preprints   
@article{fds184683,
   Author = {A.H. Clark and J. Brandenburg and R.P. Behringer},
   Title = {Jet-Induced Crater Formation: Horizontal Symmetry
             Breaking},
   Journal = {to be submitted to Nature Physics},
   Year = {2012},
   Key = {fds184683}
}

@article{fds139352,
   Author = {M. Carey and M. Steen and R.P. Behringer},
   Title = {Binary convection in a porous medium},
   Year = {2007},
   Key = {fds139352}
}

@article{fds139350,
   Author = {J. F. Wambaugh and T. S. Majmudar and B.P. Tighe and J.E. S. Socolar and R.P. Behringer},
   Title = {Scaling and anisotropy in dense granular
             matter},
   Year = {2006},
   Key = {fds139350}
}

@article{fds3947,
   Author = {Brian Utter and R.P. Behringer},
   Title = {Transients in 2D granular shear},
   Year = {2002},
   Month = {December},
   Key = {fds3947}
}

@article{fds3950,
   Author = {Meenakshi Dutt and R.P. Behringer},
   Title = {Effects of Surface Friction on a Two-Dimensional Granular
             System: I, Cooling of a Bound System},
   Year = {2002},
   Month = {December},
   Key = {fds3950}
}

@article{fds3951,
   Author = {Meenakshi Dutt and R.P. Behringer},
   Title = {Effects of Surface Friction on a Two-Dimensional Granular
             System: II, Numerical Model of a Granular Collider
             Experiment},
   Year = {2002},
   Month = {December},
   Key = {fds3951}
}

@article{fds3952,
   Author = {M. Carey and M. Steen and R.P. Behringer},
   Title = {Binary Convection in a Porous Medium},
   Year = {2002},
   Month = {December},
   Key = {fds3952}
}

@article{fds3953,
   Author = {R.R. Hartley and R.P. Behringer},
   Title = {The Dynamics of Shaken Granular Materials: Onset of
             Convection},
   Year = {2002},
   Month = {December},
   Key = {fds3953}
}


%% Other   
@misc{fds3956,
   Author = {R.P. Behringer},
   Title = {Fluctuations and Phase Transitions in GranularMaterials},
   Journal = {AIAA Conference on International Space Station
             Utilization},
   Year = {2001},
   Month = {October},
   Key = {fds3956}
}