## Publications of Robert P. Behringer    :recent first  alphabetical  combined listing:

%% Papers Published
@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}
}

@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{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{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}
}

@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},
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},
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},
Key = {Shaumeyer80}
}

@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},
Doi = {10.1017/S0022112081001109},
Key = {Shaumeyer81}
}

@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},
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{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},
Doi = {10.1016/0378-4371(83)90220-0},
Key = {Clark83}
}

@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{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}
}

@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{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},
Doi = {10.1007/BF00681317},
Key = {Behringer86}
}

@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{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{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{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{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{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{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{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-BÃ©nard 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. Â© 1990 The American Physical
Society.},
Doi = {10.1103/PhysRevA.41.5735},
Key = {Metcalfe90}
}

@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{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},
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},
Doi = {10.1007/BF00683148},
Key = {Behringer90}
}

@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
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},
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
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}
}

@article{fds332215,
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},
Month = {January},
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 = {fds332215}
}

@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{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}
}

@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}
}

@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}
}

@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},
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{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},
Doi = {10.1007/BF00682012},
Key = {Metcalfe93}
}

@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},
Doi = {10.1209/0295-5075/21/5/011},
Key = {Baxter93}
}

@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}
}

@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{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{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,
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},
Doi = {10.1038/374015a0},
Key = {Behringer95}
}

@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}
}

@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{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}
}

@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{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},
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},
Doi = {10.1017/S0022112096000134},
Key = {Metcalfe96a}
}

@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{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
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
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
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{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},
Key = {Moon97}
}

@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}
}

@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{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{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{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{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.
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},
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
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{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}
}

@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}
}

@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{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},
Doi = {10.1023/A:1021809821766},
Key = {Olafsen99}
}

@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}
}

@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{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{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{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, Î“, = A,Ï‰2,/g, for shaking of the form s,
= A, cos(Ï‰l + Ï†,), 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; Î“v.h &gt;
1.6. We consider first the case Î“v = 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 Îµ =
(Î“h-Î“hc)/Î“hc, from the appropriate transition
points, i.e. as Ï„ Î± Îµ-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 Î“v &gt; Î™. 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, Ï†h - Ï†v, shifts over
time.},
Key = {fds245631}
}

@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{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{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{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{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{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{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
2002.},
Doi = {10.1007/s10035-001-0098-7},
Key = {fds245634}
}

@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{fds304520,
Author = {Behringer, B},
Title = {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{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{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{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{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
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 45Â°, 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. Â©
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
Doi = {10.1016/S0167-2789(03)00137-4},
Key = {fds304524}
}

@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{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{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
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
mechanics.},
Doi = {10.1209/epl/i2004-10061-5},
Key = {fds245641}
}

@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{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{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
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.
anisotropy in the diffusivity that is a property of dense
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{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{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{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{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{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
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{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},
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,
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
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
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{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{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{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{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{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{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}
}

@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{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}
}

@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
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}
}

@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},
Editor = {T. Aste and T. De Matteo and A. Tordesillas},
Year = {2007},
Key = {fds139760}
}

@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}
}

@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}
}

@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{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{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{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{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{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{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{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{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{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},
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
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}
}

@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{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}
}

@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{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
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{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
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{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{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
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
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
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
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
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
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
rights reserved.},
Doi = {10.1016/j.jmps.2010.10.007},
Key = {fds304526}
}

@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{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{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{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
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{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{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{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{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{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},
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},
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},
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},
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},
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},
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},
Doi = {10.1063/1.4811968},
Key = {fds245434}
}

@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{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{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
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{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{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{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{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{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{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{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{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{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},
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{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{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},
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{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{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{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{fds292207,
Author = {Mort, P and Michaels, J and Behringer, R and Campbell, C and Kondic, L and Kheiripour Langroudi and M and Shattuck, M and Tang, J and Tardos, G 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{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{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{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
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{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{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{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{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,
J},
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,
J},
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,
J},
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,
J},
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,
J},
Year = {2017},
url = {http://dx.doi.org/10.1051/epjconf/201714006014},
Doi = {10.1051/epjconf/201714006014},
Key = {fds329764}
}

@article{fds333316,
Author = {Zhang, Y and Behringer, R},
Title = {Pulling an intruder from a granular material: a novel
depinning experiment},
Journal = {EPJ Web of Conferences},
Volume = {140},
Pages = {03040-03040},
Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
J},
Year = {2017},
url = {http://dx.doi.org/10.1051/epjconf/201714003040},
Doi = {10.1051/epjconf/201714003040},
Key = {fds333316}
}

@article{fds333317,
Author = {Barés, J and Zhao, Y and Renouf, M and Dierichs, K and Behringer,
R},
Title = {Structure of hexapod 3D packings: understanding the global
stability from the local organization},
Journal = {EPJ Web of Conferences},
Volume = {140},
Pages = {06021-06021},
Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
J},
Year = {2017},
url = {http://dx.doi.org/10.1051/epjconf/201714006021},
Doi = {10.1051/epjconf/201714006021},
Key = {fds333317}
}

@article{fds332933,
Author = {Stevens Bester and C and Behringer, RP},
Title = {Collisional model of the drag force of granular
impact},
Journal = {EPJ Web of Conferences},
Volume = {140},
Pages = {03017-03017},
Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
J},
Year = {2017},
url = {http://dx.doi.org/10.1051/epjconf/201714003017},
Doi = {10.1051/epjconf/201714003017},
Key = {fds332933}
}

@article{fds332934,
Author = {Xu, Y and Barés, J and Zhao, Y and Behringer, RP},
Title = {Jamming Transition: Heptagons, Pentagons, and
Discs},
Journal = {EPJ Web of Conferences},
Volume = {140},
Pages = {06010-06010},
Editor = {Radjai, F and Nezamabadi, S and Luding, S and Delenne,
J},
Year = {2017},
url = {http://dx.doi.org/10.1051/epjconf/201714006010},
Doi = {10.1051/epjconf/201714006010},
Key = {fds332934}
}

@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{fds331483,
Author = {Lim, MX and Barés, J and Zheng, H and Behringer,
RP},
Title = {Force and Mass Dynamics in Non-Newtonian
Suspensions.},
Journal = {Physical Review Letters},
Volume = {119},
Number = {18},
Pages = {184501},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1103/physrevlett.119.184501},
Abstract = {Above a certain solid fraction, dense granular suspensions
in water exhibit non-Newtonian behavior, including
impact-activated solidification. Although it has been
suggested that solidification depends on boundary
interactions, quantitative experiments on the boundary
forces have not been reported. Using high-speed video,
tracer particles, and photoelastic boundaries, we determine
the impactor kinematics and the magnitude and timings of
impactor-driven events in the body and at the boundaries of
cornstarch suspensions. We observe mass shocks in the
suspension during impact. The shock front dynamics are
strongly correlated to those of the intruder. However, the
total momentum associated with this shock never approaches
the initial impactor momentum. We also observe a faster
second front associated with the propagation of pressure to
the boundaries of the suspension. The two fronts depend
differently on the initial impactor speed v_{0} and the
suspension packing fraction. The speed of the pressure wave
is at least an order of magnitude smaller than (linear)
ultrasound speeds obtained for much higher frequencies,
pointing to complex amplitude and frequency response of
cornstarch suspensions to compressive strains.},
Doi = {10.1103/physrevlett.119.184501},
Key = {fds331483}
}

@article{fds332796,
Author = {Lim, MX and Behringer, RP},
Title = {Topology of force networks in granular media under
impact},
Journal = {EPL (Europhysics Letters)},
Volume = {120},
Number = {4},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1209/0295-5075/120/44003},
Abstract = {© EPLA, 2018. We investigate the evolution of the force
network in experimental systems of twodimensional granular
materials under impact. We use the first Betti number, β 1
, and persistence diagrams, as measures of the topological
properties of the force network. We show that the structure
of the network has a complex, hysteretic dependence on both
the intruder acceleration and the total force response of
the granular material. β 1 can also distinguish between the
nonlinear formation and relaxation of the force network. In
addition, using the persistence diagram of the force
network, we show that the size of the loops in the force
network has a Poisson-like distribution, the characteristic
size of which changes over the course of the
impact.},
Doi = {10.1209/0295-5075/120/44003},
Key = {fds332796}
}

@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 = {5-1},
Pages = {052902},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1103/physreve.96.052902},
Abstract = {We present the experimental and numerical studies of a
two-dimensional sheared amorphous material composed of
bidisperse photoelastic disks. We analyze the statistics of
avalanches during shear including the local and global
fluctuations in energy and changes in particle positions and
orientations. We find scale-free distributions for these
global and local avalanches denoted by power laws whose
cutoffs vary with interparticle friction and packing
fraction. Different exponents are found for these power laws
depending on the quantity from which variations are
extracted. An asymmetry in time of the avalanche shapes is
evidenced along with the fact that avalanches are mainly
triggered by the shear bands. A simple relation independent
of the intensity is found between the number of local
avalanches and the global avalanches they form. We also
compare these experimental and numerical results for both
local and global fluctuations to predictions from mean-field
and depinning theories.},
Doi = {10.1103/physreve.96.052902},
Key = {fds329760}
}

%% Papers Accepted
@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}
}

@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{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{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{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{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{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}
}

%% Papers Submitted
@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}
}

@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{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{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{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{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{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{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{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{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{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}
}

%% Preprints
@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}
}

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

@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}
}

%% 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}
}

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