%% Papers Published @article{fds245439, Author = {Goellner, G and Behringer, R and Meyer, H}, Title = {Thermodynamic properties of liquid^{3}He-^{4}He 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<X<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 liquid^{3}He-^{4}He 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<T - Tt<0.53 K and -9<Δ - Δt<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<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 a^{3}He-^{4}He 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 of^{3}He 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>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<∼R<∼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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800124&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Behringer80a} } @booklet{Agosta80, Author = {AGOSTA, C and JAN, J and SHAUMEYER, J and BEHRINGER, RP}, Title = {TIME-DEPENDENT FLOW IN RAYLEIGH-BENARD CONVECTION}, Journal = {Bulletin- American Physical Society}, Volume = {25}, Number = {4}, Pages = {531-531}, Year = {1980}, ISSN = {0003-0503}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800341&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Agosta80} } @booklet{Behringer80, Author = {Behringer, RP and Agosta, C and Jan, JS and Shaumeyer, JN}, Title = {Time-dependent Rayleigh-Bénard convection and instrumental attenuation}, Journal = {Physics Letters A}, Volume = {80}, Number = {4}, Pages = {273-276}, Year = {1980}, ISSN = {0375-9601}, url = {http://dx.doi.org/10.1016/0375-9601(80)90020-1}, Abstract = {We present new thermal data on time-dependent convection in a cylindrically confined layer of helium with aspect ratio Γ=7.87 (Γ≡layer radius/layer height). Experimental data and an analysis of attenuation effects indicate broadband spectral features obtained by a global probe tend to be independent of Γ for Γ≳5. © 1980.}, Doi = {10.1016/0375-9601(80)90020-1}, Key = {Behringer80} } @booklet{Shaumeyer80, Author = {SHAUMEYER, JN and BEHRINGER, RP and BAIERLEIN, R}, Title = {LINEAR GROWTH-RATES FOR THE RAYLEIGH-BENARD INSTABILITY IN CYLINDRICAL GEOMETRY}, Journal = {Bulletin- American Physical Society}, Volume = {25}, Number = {4}, Pages = {531-531}, Year = {1980}, ISSN = {0003-0503}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1980JM68800342&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Shaumeyer80} } @booklet{Shaumeyer81, Author = {SHAUMEYER, JN and BEHRINGER, RP and BAIERLEIN, R}, Title = {LINEAR GROWTH-RATES FOR THE RAYLEIGH-BENARD INSTABILITY IN CYLINDRICAL GEOMETRY}, Journal = {Journal of Fluid Mechanics}, Volume = {109}, Number = {AUG}, Pages = {339-348}, Year = {1981}, ISSN = {0022-1120}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1981MH72200021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1017/S0022112081001109}, Key = {Shaumeyer81} } @booklet{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 liquid^{3}He-^{4}He mixtures. II. Superfluid phase}, Journal = {Journal of Low Temperature Physics}, Volume = {46}, Number = {5-6}, Pages = {435-450}, Year = {1982}, ISSN = {0022-2291}, url = {http://dx.doi.org/10.1007/BF00683909}, Abstract = {Relaxation measurements in superfluid3He-4He mixtures when a heat flux across a horizontal layer is switched on or off provide a quantitative test for the solutions of Khalatnikov's hydrodynamic equations. On the basis of these equations we predict that the relaxation times τ in a layer of height d can be expressed by a simple scaled relation that is a function of static and transport properties. Relaxation experiments on five mixtures are in good agreement with these predictions. In an appendix we discuss the viscous penetration depth λp and show that it is small enough for the Khalatnikov expressions to be valid under our experimental conditions. © 1982 Plenum Publishing Corporation.}, Doi = {10.1007/BF00683909}, Key = {Behringer82c} } @booklet{Behringer82b, Author = {BEHRINGER, RP and MEYER, H}, Title = {DIFFUSIVE RELAXATION PROCESSES IN LIQUID HE-3-HE-4 MIXTURES .1. NORMAL PHASE}, Journal = {Journal of Low Temperature Physics}, Volume = {46}, Number = {5-6}, Pages = {407-434}, Year = {1982}, ISSN = {0022-2291}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1982NK12900003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/BF00683908}, Key = {Behringer82b} } @booklet{Behringer82a, Author = {Behringer, RP and Shaumeyer, JN and Clark, CA and Agosta, CC}, Title = {Turbulent onset in moderately large convecting layers}, Journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, Volume = {26}, Number = {6}, Pages = {3723-3726}, Year = {1982}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.26.3723}, Abstract = {We present long-time thermal data on turbulent evolution in Rayleigh-Bénard convection for cylindrical containers of aspect ratios =6.22 and 7.87 and Prandtl numbers near 0.6. The first time dependence observed was more complex than the intermittent flows reported by Ahlers and Walden for =4.72, although the periodicity they observed was reproduced for =7.87. The turbulent onset for =6.22, showing substantial regimes of periodicity, was quite different from that for =7.87 or 4.72. We conclude that changes of order unity in strongly affect turbulent onset, even for moderately large aspect ratios. © 1982 The American Physical Society.}, Doi = {10.1103/PhysRevA.26.3723}, Key = {Behringer82a} } @article{fds320092, Author = {Behringer, RP and Meyer, H}, Title = {Diffusive relaxation processes in liquid^{3}He-^{4}He 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<Γ<13 show that near onset the first time dependence is always periodic and associated with changes in the heat transport. The dominant periodicity has a nonzero amplitude, A, and vanishing frequency at onset. Changes in A with Γ show wave-number effects. Except for the time dependence, the transition is consistent with predictions for the skew-varicose instability. © 1983 The American Physical Society.}, Doi = {10.1103/PhysRevLett.50.1199}, Key = {Behringer83} } @booklet{Clark83, Author = {CLARK, C and SHAUMEYER, J and AGOSTA, C and BEHRINGER, RP}, Title = {THE ONSET OF CONVECTIVE TURBULENCE IN LARGE ASPECT RATIO LAYERS}, Journal = {Physica A: Statistical Mechanics and its Applications}, Volume = {118}, Number = {1-3}, Pages = {442-442}, Year = {1983}, ISSN = {0378-4371}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1983QK91000038&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1016/0378-4371(83)90220-0}, Key = {Clark83} } @booklet{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< <22. For all, there is a first transition at a Rayleigh number R1>Rc where convection begins at Rc. Time dependence occurs for R>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 superfluid^{3}He-^{4}He 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<1, p=1, and p>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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1986AZG3200002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/BF00681317}, Key = {Behringer86} } @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 a^{3}He-superfluid-^{4}He 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:^{3}He and^{3}He-^{4}He 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<NPr<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<T<2.0 K, implying an accessible Prandtl-number range near onset of at least 0.04<NPr<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<NPr<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<T<2.0 K, implying an accessible Prandtl-number range near onset of at least 0.04<NPr<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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1990EG22500006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/BF00683153}, Key = {Behringer90a} } @booklet{Behringer90, Author = {BEHRINGER, RP}, Title = {THERMAL RESPONSE OF A HE-3-SUPERFLUID-HE-4 MIXTURE}, Journal = {Journal of Low Temperature Physics}, Volume = {81}, Number = {1-2}, Pages = {1-17}, Year = {1990}, Month = {October}, ISSN = {0022-2291}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1990EG22500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/BF00683148}, Key = {Behringer90} } @article{fds245445, Author = {Shattuck, M and Behringer, R and Geordiadis, J and Johnson, GA}, Title = {Magnetic resonance imaging of interstitial velocity distributions in porous media}, Journal = {American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED}, Volume = {125}, Pages = {39-45}, Year = {1991}, Abstract = {In this article we report on a promising application of Magnetic Resonance Imaging (MRI), which can measure local interstitial velocity distributions inside fully-saturated porous media. We have extended the standard three-dimensional MRI sequence to include local velocity information. During flow, the moving spins of the fluid (in this case water) accumulate phase in the presence of magnetic field gradients. This phase is proportional to the local velocity. By repeating the measurement under the influence of different magnetic gradient strengths, we can reconstruct the velocity distribution in each volume element (voxel). Using this technique to study pressure-driven flow through a fully-saturated, cylindrical packed bed, we have observed flow channeling near the walls and an exponential distribution of velocities.}, Key = {fds245445} } @article{fds245446, Author = {Shattuck, M and Behringer, R and Geordiadis, J and Johnson, GA}, Title = {Magnetic resonance imaging of interstitial velocity distributions in porous media}, Year = {1991}, Abstract = {In this article we report on a promising application of Magnetic Resonance Imaging (MRI), which can measure local interstitial velocity distributions inside fully-saturated porous media. We have extended the standard three-dimensional MRI sequence to include local velocity information. During flow, the moving spins of the fluid (in this case water) accumulate phase in the presence of magnetic field gradients. This phase is proportional to the local velocity. By repeating the measurement under the influence of different magnetic gradient strengths, we can reconstruct the velocity distribution in each volume element (voxel). Using this technique to study pressure-driven flow through a fully-saturated, cylindrical packed bed, we have observed flow channeling near the walls and an exponential distribution of velocities. (A)}, Key = {fds245446} } @booklet{Baxter91, Author = {Baxter, GW and Behringer, RP}, Title = {Cellular automata models for the flow of granular materials}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {51}, Number = {1-3}, Pages = {465-471}, Year = {1991}, ISSN = {0167-2789}, url = {http://dx.doi.org/10.1016/0167-2789(91)90252-5}, Abstract = {The importance of particle irregularity in the flow of granular material can be demonstrated using simple experiments. We introduce cellular automata which model nonspherical particles using rules derived from experiments. These automata can reproduce many features of the physical flows including the alignment of the particles, the formation of a complex channel region, the shape of the upper free surface, and the formation of defects in the body of the material. © 1991.}, Doi = {10.1016/0167-2789(91)90252-5}, Key = {Baxter91} } @booklet{Baxter91a, Author = {BAXTER, GW and LEONE, R and JOHNSON, GA and BEHRINGER, RP}, Title = {TIME-DEPENDENCE, SCALING AND PATTERN-FORMATION FOR FLOWING SAND}, Journal = {European Journal of Mechanics - B/Fluids}, Volume = {10}, Number = {2}, Pages = {181-186}, Year = {1991}, ISSN = {0997-7546}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1991FR81800029&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Baxter91a} } @booklet{Metcalfe91, Author = {Metcalfe, G and Behringer, RP}, Title = {Using superfluid mixtures to probe convective instabilities}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {51}, Number = {1-3}, Pages = {520-530}, Year = {1991}, ISSN = {0167-2789}, Abstract = {When the height d of a convecting layer of a dilute solution of 3He in superfluid 4He is much greater than a characteristic dissipation length λ0, the superfluid mixture behaves as if it were a single-component classical fluid, but one with the extraordinarily broad and interesting Prandtl number range of 0.04 < Pr < 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 < T < 2.0 K. We also report a series of measurements near the crossing of the skewed-varicose and oscillatory instabilities showing the effects of instability competition. © 1991.}, Key = {Metcalfe91} } @booklet{Behringer91, Author = {Behringer, RP and Meyers, SD and Swinney, HL}, Title = {Chaos and mixing in a geostrophic flow}, Journal = {Physics of fluids. A, Fluid dynamics}, Volume = {3}, Number = {5}, Pages = {1243-1249}, Year = {1991}, ISSN = {0899-8213}, Abstract = {Experiments on Rossby waves on an azimuthal jet in a rapidly rotating annular tank reveal a striking barrier to mixing across the jet. A model based on the experiments assumes a two-dimensional incompressible flow described by a time-dependent streamfunction consisting of azimuthally propagating waves on a narrow jet. When there is only one wave, all Lagrangian particle trajectories are closed in the appropriate reference frame. When two independent waves are present, some trajectories are chaotic, and the size of the chaotic sea grows as the amplitude of the second wave is increased; however, at least one barrier to global transport - an invariant surface - prohibits trajectories from crossing the jet. The addition of a third wave is found to break the barrier only if the wave amplitudes exceed the width of the jet. In the experiment, the wave amplitude is typically about one-half the jet width, and the barrier to mixing persists even at the highest accessible Reynolds numbers. © 1991 American Institute of Physics.}, Key = {Behringer91} } @booklet{Anderson91, Author = {Anderson, KE and Behringer, RP}, Title = {Traveling wave convection patterns in an annular cell}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {51}, Number = {1-3}, Pages = {444-449}, Year = {1991}, ISSN = {0167-2789}, Abstract = {Fast traveling wave convection rolls, localized rolls, non-uniform velocity rolls and slow rolls are four distinct patterns observed during the evolution of convection patterns in an ethanol-water binary mixture. These Rayleigh-Bénard experiments were carried out in an annular cell with an aspect ratio of 80:2:1. The mixture has a separation ratio value of ψ {reversed tilde equals} -0.09. The convection was driven by a constant heat flux less than 5% above the onset heat flux. © 1991.}, Key = {Anderson91} } @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 in^{3}He-superfluid-^{4}He mixtures}, Journal = {Journal of Low Temperature Physics}, Volume = {90}, Number = {1-2}, Pages = {95-117}, Year = {1993}, ISSN = {0022-2291}, url = {http://dx.doi.org/10.1007/BF00682012}, Abstract = {The equations of motion for convection in dilute3He-superfluid-4He mixtures are the same as those for convection in a conventional pure fluid with the addition of several correction terms. Fetter has considered, for a horizontally infinite layer with realistic boundary conditions, the effect of these corrections on the critical Rayleigh number, Rc. The results are a perturbation expansion for Rc to lowest order in three perturbation terms, ε1, ε2, ε3. In order to make a comparison with recent precise experiments which have yielded Rc as a function of the layer height d, we have carried out several calculations. First we show that the analysis can be recast as an expansion in inverse powers of d2. We then carry out a complete expansion to O(d-6). Up to O(d-4), the expansion involves only the ratio (λ0/d) where λ0 is a length scale which is intrinsic to superfluid mixtures. We consider the effect of the superfluid perturbations on both the critical Rayleigh numbers and wavevectors. These are shifted very little as long as λ0/d is small; the crossover from large to small occurs for λ0/d∼0.1. We also solve a simplified version of the stability problem which contains the dominant superfluid effect. The simplified problem is Hermitian, and is therefore amenable to an exact solution. A comparison with experimental data for Rc and the simplified model shows excellent agreement with the calculations. © 1993 Plenum Publishing Corporation.}, Doi = {10.1007/BF00682012}, Key = {fds245499} } @booklet{Behringer93, Author = {BEHRINGER, RP}, Title = {THE DYNAMICS OF FLOWING SAND}, Volume = {3}, Number = {3}, Pages = {1-&}, Year = {1993}, ISSN = {0938-9008}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993MN18200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Behringer93} } @booklet{Howle93, Author = {Howle, L and Behringer, RP and Georgiadis, J}, Title = {Visualization of convective fluid flow in a porous medium}, Journal = {Nature}, Volume = {362}, Number = {6417}, Pages = {230-232}, Year = {1993}, Abstract = {WHEN a horizontal layer of fluid is heated from below, it may undergo Rayleigh-Bénard convection (RBC), leading to the spontaneous appearance of regular patterns of fluid flow1. The shadowgraph technique2, which allows visualization of the convection patterns, has assisted in developing an understanding of RBC. Related to RBC is convection in a fluid permeating a porous medium (called Horton-Rodgers-Lapwood convection or HRLC) when it is heated from below3-7. HRLC is relevant to geothermal applications and to flow in soils. Pattern formation in HRLC is less easily visualized by shadowgraph techniques because of the difficulties of transmitting light through the porous medium. Here we show how these difficulties can be overcome by constructing porous media in which the interfaces between solid and liquid are either parallel or perpendicular to the confining boundaries of the experimental system. Convection in such a medium can be visualized using conventional shadowgraph methods, and we compare the stationary flow patterns observed against measurements of heat transport.}, Key = {Howle93} } @booklet{Metcalfe93, Author = {METCALFE, G and BEHRINGER, RP}, Title = {SUPERFLUID EFFECTS AT THE ONSET OF CONVECTION IN HE-3-SUPERFLUID-HE-4 MIXTURES}, Journal = {Journal of Low Temperature Physics}, Volume = {90}, Number = {1-2}, Pages = {95-117}, Year = {1993}, Month = {January}, ISSN = {0022-2291}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993KL83500005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/BF00682012}, Key = {Metcalfe93} } @booklet{Baxter93, Author = {BAXTER, GW and LEONE, R and BEHRINGER, RP}, Title = {EXPERIMENTAL TEST OF TIME SCALES IN FLOWING SAND}, Journal = {EPL (Europhysics Letters)}, Volume = {21}, Number = {5}, Pages = {569-574}, Year = {1993}, Month = {February}, ISSN = {0295-5075}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993KN37200011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1209/0295-5075/21/5/011}, Key = {Baxter93} } @booklet{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, hence ordinary physics does not apply. In this article, the recent insights on this phenomena are emphasised to provide an understanding of the dynamical behavior of these materials.}, Key = {fds245449} } @booklet{Behringer95, Author = {Behringer, RP}, Title = {Mixed predictions}, Journal = {Nature}, Volume = {374}, Number = {6517}, Pages = {15-}, Year = {1995}, ISSN = {0028-0836}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1995QK07900027&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1038/374015a0}, Key = {Behringer95} } @booklet{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^{3}He-superfluid-^{4}He 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 < Pr < 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 < Pr < 1.4 and 2 < Γ < 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^{3}He-superfluid-^{4}He 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 < Pr < 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 < T < 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 < Pr < 1.4 and 2 < Γ < 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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996TV26300012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1017/S0022112096000122}, Key = {Metcalfe96} } @booklet{Metcalfe96a, Author = {Metcalfe, G and Behringer, RP}, Title = {Convection in He-3-superfluid-He-4 mixtures .2. A survey of instabilities}, Journal = {Journal of Fluid Mechanics}, Volume = {307}, Pages = {297-331}, Year = {1996}, Month = {January}, ISSN = {0022-1120}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996TV26300013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1017/S0022112096000134}, Key = {Metcalfe96a} } @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. Normal^{4}He}, 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 > Qc. and Qc corresponds to the heat amplitude at convective onset.}, Key = {Olafsen97} } @booklet{Pak97, Author = {Pak, HK and Doorn, EV and Behringer, RP}, Title = {Ambient gases and heaping instability of granular materials under vertical vibration}, Journal = {International Journal of Bifurcation and Chaos in Applied Sciences and Engineering}, Volume = {7}, Number = {5}, Pages = {1035-1041}, Year = {1997}, Abstract = {We consider layers of non-cohesive granular materials lying on a vertically vibrating surface. Above a threshold acceleration, Γ = Γc, internal convective motion begins, and the free surface of the granular material becomes unstable to the formation of a heap. As Γ increases further, there are several higher order instabilities, traveling surface waves, subharmonic bifurcations, and bubbling. We find that for particles of diameter d ≤ 1 mm, the pressure P of the surrounding gas plays a key role in the instabilities. We propose criteria to determine when gas effects are relevant.}, Key = {Pak97} } @booklet{Howle97, Author = {Howle, LE and Behringer, RP and Georgiadis, JG}, Title = {Convection and flow in porous media. Part 2. Visualization by shadowgraph}, Journal = {Journal of Fluid Mechanics}, Volume = {332}, Pages = {247-262}, Year = {1997}, Abstract = {We present results for pattern formation at the onset of convection in fluid-saturated porous media obtained by a novel variation on the shadowgraphic technique (modified shadowgraphic technique). Both ordered and disordered media are used, each exhibiting distinct behaviour. Ordered porous media are constructed from grids of overlapping bars. Convective onset in this type of medium is characterized by a sharp, well-defined bifurcation to straight parallel rolls. The orientation of the convection rolls is determined by the number of bar layers, Nb; odd Nb leads to rolls with axes perpendicular to the direction of the top and bottom bars, and even Nb to rolls at 45° to the bars. Disordered porous layers are produced by stacking randomly drilled disks separated by spacers. In this system, we observe a rounded bifurcation to convection with localized convection near convective onset. More specifically, the flow patterns take on one of several different three-dimensional cellular structures after each cycling through convective onset. These observations may be described by two different mechanisms: random spatial fluctuations in the Rayleigh number (Zimmermann et al. 1993), and/or spatial variation in the thermal conductivity on the length scale of the convection wavelength (Braester & Vadasz 1993).}, Key = {Howle97} } @booklet{Shattuck97, Author = {Shattuck, MD and Behringer, RP and Johnson, GA and Georgiadis, JG}, Title = {Convection and flow in porous media. Part 1. Visualization by magnetic resonance imaging}, Journal = {Journal of Fluid Mechanics}, Volume = {332}, Pages = {215-245}, Year = {1997}, Abstract = {We describe an experimental study of porous media convection (PMC) from onset to 8Rac. The goal of this work is to provide non-invasive imaging and high-precision heat transport measurements to test theories of convection in PMC. We obtain velocity information and visualize the convection patterns using magnetic resonance imaging (MRI). We study both ordered and disordered packings of mono-disperse spheres of diameter d = 3.204 ± 0.029 mm, in circular, rectangular, and hexagonal planforms. In general, the structure of the medium plays a role which is not predicted by theories which assume a homogeneous system. Disordered media are prepared by pouring mono-disperse spheres into the container. Large ordered regions of close packing for the spheres, with grain boundaries and isolated defects, characterize these media. The defects and grain boundaries play an important role in pattern formation in disordered media. Any deviation from close packing produces a region of larger porosity, hence locally larger permeability. The result is spatial variations in the Rayleigh number, Ra. We define the critical Ra, Rac, as the Rayleigh number at the onset of convection in the ordered regions. We find that stable localized convective regions exist around grain boundaries and defects at Ra < 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 (<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 < Ra < 5Rac; (ii) that at onset, the rolls should have a dimensionless wavevector qc = π; (iii) that at the upper end of this range rolls should lose stability to cross-rolls; (iv) that the initial slope of the Nusselt curve should be 2; (v) that there should be a rapid decay of vertical vorticity - hence no complex flows, such as those which occur for Rayleigh-Bénard convection (RBC) within the nominal regime of stable parallel rolls. These predictions are in partial agreement with our findings for the bulk convection in the ordered media. We observe roll-like structures which relax rapidly to stable patterns between Rac and 5Rac. However we find a wavenumber which is 0.7π compared to π derived from linear stability theory. We find an asymmetry between the size of the upflowing regions and downflowing regions as Ra grows above Rac. The ratio of the volume of the upflowing to the volume of the downflowing regions decreases as Ra increases and leads to a novel time-dependent state, which does not consist of cross-rolls. This time-dependent state begins at 6Rac and is observed up to 8Rac, the largest Ra which we studied. It seems likely that the occurrence of this state is linked to departures from the Boussinesq approximation at higher Ra. We also find that the slope of the Nusselt curve is 0.7, which does not agree with the predicted value of 2.}, Key = {Shattuck97} } @booklet{Vandoorn97a, Author = {Doorn, EV and Behringer, RP}, Title = {Onset and evolution of a wavy instability in shaken sand}, Journal = {Physics Letters, Section A: General, Atomic and Solid State Physics}, Volume = {235}, Number = {5}, Pages = {469-474}, Year = {1997}, Abstract = {A novel small wavelength instability occurs in experiments for vertically shaken (z = a cos(ωt)) sand, for small particle diameters d and when gas effects are important. At onset, the energy (aω)2/gd is proportional to a/d, as previously found for traveling waves. The instability begins as a surface perturbation with wavelength λ0 ∼ 6 mm; subsequently λ grows exponentially in time. © 1997 Published by Elsevier Science B.V.}, Key = {Vandoorn97a} } @booklet{Vandoorn97, Author = {Doorn, EV and Behringer, RP}, Title = {Dilation of a vibrated granular layer}, Journal = {EPL (Europhysics Letters)}, Volume = {40}, Number = {4}, Pages = {387-392}, Year = {1997}, ISSN = {0295-5075}, url = {http://dx.doi.org/10.1209/epl/i1997-00476-x}, Abstract = {We report measurements of the dilation, δh, of a vertically shaken sand heap in the presence of air. These measurements were carried out for dimensionless accelerations 1.0 ≤ Γ ≤ 2.7, for particle diameters of 0.05 mm ≤ d ≤ 1.0 mm, for layer height to particle diameter ratios of 80 ≤ h0/d ≤ 140, and for shaking amplitudes of 0.66 mm ≤ a ≤ 6.65 mm. δh is mostly limited to a thin avalanching surface layer. The vertical motion of this layer is well described by a simple model of an inelastic bouncing ball, independent of other complex motion elsewhere.}, Doi = {10.1209/epl/i1997-00476-x}, Key = {Vandoorn97} } @booklet{Moon97, Author = {Moon, HT and Kim, S and Behringer, RP and Kuramoto, Y}, Title = {Nonlinear dynamics and chaos}, Journal = {International Journal of Bifurcation & Chaos}, Volume = {7}, Number = {4}, Pages = {787-788}, Year = {1997}, Month = {April}, ISSN = {0218-1274}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997XZ65200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {Moon97} } @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 < Γh.v < 1.6. Phenomena include the spontaneous formation of a static heap at Γhs (Γv,) when Γv < 1, convective flow for Γhe > 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^{3}He-Superfluid^{4}He 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. ©1999 The American Physical Society.}, Key = {Veje99} } @booklet{Tennakoon99, Author = {Tennakoon, SGK and Kondic, L and Behringer, RP}, Title = {Onset of flow in a horizontally vibrated granular bed: Convection by horizontal shearing}, Journal = {EPL (Europhysics Letters)}, Volume = {45}, Number = {4}, Pages = {470-475}, Year = {1999}, ISSN = {0295-5075}, url = {http://dx.doi.org/10.1209/epl/i1999-00190-3}, Abstract = {We present experimental observations of the onset of flow for horizontally vibrated 3D granular systems. For accelerations Γ above Γ*, the top layers of granular material flow, leading to convection with motion both parallel and transverse to the shaking; the lower part of the layer moves with the shaker in solid body motion. With increasing Γ, more of the layer becomes liquefied. The initial bifurcation is backward, but a small amount of fluidization by gas flow lifts the hysteresis. A new convective mechanism, which we explore both experimentally and computationally, associated with horizontal shearing at the walls, is identified as the mechanism driving the transverse convective flow.}, Doi = {10.1209/epl/i1999-00190-3}, Key = {Tennakoon99} } @booklet{Vanel99, Author = {Vanel, L and Howell, D and Clark, D and Behringer, RP and Clément, E}, Title = {Memories in sand: Experimental tests of construction history on stress distributions under sandpiles}, Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics}, Volume = {60}, Number = {5 A}, Pages = {R5040-R5043}, Year = {1999}, ISSN = {1063-651X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000083870700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Abstract = {We report experiments on piles of cohesionless granular materials showing the effect of construction history on static stress distributions. Stresses under piles are monitored by sensitive capacitive techniques. The piles are formed either by pouring granular material from a funnel with a small outlet (localized source), or from a large sieve (homogeneous rain). Localized sources yield stress profiles with a clear stress dip near the center of the pile; the homogeneous rain profiles have no stress dip. We show that the stress profiles scale linearly with the pile height. Experiments on wedge-shaped piles show similar but weaker effects.}, Doi = {10.1103/PhysRevE.60.R5040}, Key = {Vanel99} } @article{fds245621, Author = {Howell, D and Behringer, RP and Veje, C}, Title = {Stress fluctuations in a 2D granular Couette experiment: A continuous transition}, Journal = {Physical Review Letters}, Volume = {82}, Number = {26 I}, Pages = {5241-5244}, Year = {1999}, Abstract = {Experiments on a slowly sheared 2D granular material show a continuous transition as the packing fraction γ passes through γc ≃ 0.776. The mean stress, σ̄, plays the role of an order parameter. As γ → γc from above, (1) the compressibility becomes large, (2) a slowing down of the mean velocity occurs, (3) the force distributions change, and (4) the network of stress chains changes from intermittent long radial chains near γc to a tangled dense network for larger γ. © 1999 The American Physical Society.}, Key = {fds245621} } @article{fds245625, Author = {Behringer, RP and Howell, D and Kondic, L and Tennakoon, S and Veje, C}, Title = {Predictability and granular materials}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {133}, Number = {1-4}, Pages = {1-17}, Year = {1999}, Abstract = {Granular materials present a number of challenges to predictability. The classical description of a dense granular material is based on Coulomb friction. For a static array of grains, the Coulomb friction forces are typically underdetermined. If we are to make useful statements about such arrays, we must develop new approaches, including the development of statistical descriptions. Granular materials also show large fluctuations in the local forces. These fluctuations are quite sensitive to small perturbations in the packing geometry of the grains. In the past, they have typically been ignored. However, recent experiments and models are beginning to shed new light on their characteristics. This article briefly reviews some of this new work, and in particular presents experimental results characterizing fluctuations and the role of friction in granular materials. © 1999 Elsevier Science B.V.}, Key = {fds245625} } @article{fds287564, Author = {Olafsen, JS and Behringer, RP}, Title = {AC Thermal Conductivity Measurements in Dilute Mixtures of^{3}He in Superfluid^{4}He}, 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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000082955500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1023/A:1021809821766}, Key = {Olafsen99} } @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 > Γv.h > 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 > 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 > Î“v.h > 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 > 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 the present analysis. © Springer-Verlag 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 number of collisions. © 2002 Published by Elsevier B.V.}, Doi = {10.1016/S0167-2789(02)00566-3}, Key = {fds245535} } @article{fds245616, Author = {Kondic, L and Hartley, RR and Tennakoon, SGK and Painter, B and Behringer, RP}, Title = {Segregation by friction}, Journal = {Europhysics Letters}, Volume = {61}, Number = {6}, Pages = {742-748}, Year = {2003}, url = {http://dx.doi.org/10.1209/epl/i2003-00291-y}, Abstract = {Granular materials are known to separate by size under a variety of circumstances. Experiments presented here and elucidated by modeling and MD simulation document a new segregation mechanism, namely segregation by friction. The experiments are carried out by placing steel spheres on a horizontal plane enclosed by rectangular sidewalls, and subjecting them to horizontal shaking. Half the spheres are highly smooth; the remainder are identical to the first half, except that their surfaces have been roughened by chemical etching, giving them higher coefficients of friction. Segregation due to this difference in friction occurs, particularly when the grains have a relatively long mean free path. In the presence of an appropriately chosen small "hill" in the middle of the container, the grains can be made to completely segregate by friction type.}, Doi = {10.1209/epl/i2003-00291-y}, Key = {fds245616} } @article{fds245645, Author = {Geng, J and Behringer, RP and Reydellet, G and Clement, E}, Title = {Green's Function Measurements in2D Granualr Materials}, Journal = {Physica D}, Volume = {182}, Number = {3-4}, Pages = {274-303}, Year = {2003}, url = {http://dx.doi.org/10.1016/S0167-2789(03)00137-4}, Abstract = {We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amounts of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Eur. Phys. J. E 4 (2001) 451] and Socolar et al. [Eur. Phys. J. E 7 (2002) 353] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Phys. Rev. Lett. 89 (2002) 084302]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Da Silva and Rajchenbach [Nature 406 (2000) 708] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 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© 2003 Elsevier Science B.V. All rights reserved.}, Doi = {10.1016/S0167-2789(03)00137-4}, Key = {fds245645} } @article{fds304524, Author = {Geng, J and Reydellet, G and Clément, E and Behringer, RP}, Title = {Green's function measurements of force transmission in 2D granular materials}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {182}, Number = {3-4}, Pages = {274-303}, Year = {2003}, url = {http://dx.doi.org/10.1016/S0167-2789(03)00137-4}, Abstract = {We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amounts of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Eur. Phys. J. E 4 (2001) 451] and Socolar et al. [Eur. Phys. J. E 7 (2002) 353] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Phys. Rev. Lett. 89 (2002) 084302]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Da Silva and Rajchenbach [Nature 406 (2000) 708] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 45°, corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction of the chains, with an exponent of -0.81. The response to forces is the strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction. © 2003 Elsevier Science B.V. All rights reserved.}, Doi = {10.1016/S0167-2789(03)00137-4}, Key = {fds304524} } @article{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 lead to the development of steady-profile two-dimensional traveling wave fingers. Using an infrared laser and scanning mirror, we impose thermal perturbations with a known wavelength to an initially uniform advancing fluid front. As the front advances in the experiment, we observe convergence to fingers with the initially prescribed wavelength. Experiments and numerical computations show that this family of solutions arises from a subcritical bifurcation.}, Doi = {10.1103/PhysRevLett.93.247803}, Key = {fds245640} } @article{fds245641, Author = {Kondic, L and Behringer, RP}, Title = {Elastic energy, fluctuations and temperature for granular materials}, Journal = {Europhysics Letters}, Volume = {67}, Number = {2}, Pages = {205-211}, Year = {2004}, url = {http://dx.doi.org/10.1209/epl/i2004-10061-5}, Abstract = {We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough P/Ey (pressure/Young's modulus) and P/v2 (P/kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, Tg, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This Tg is roughly consistent with a temperature adapted from equilibrium statistical mechanics.}, Doi = {10.1209/epl/i2004-10061-5}, Key = {fds245641} } @article{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 particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.}, Doi = {10.1103/PhysRevE.69.031308}, Key = {fds245642} } @article{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 lead to the development of steady-profile two-dimensional traveling wave fingers. Using an infrared laser and scanning mirror, we impose thermal perturbations with a known wavelength to an initially uniform advancing fluid front. As the front advances in the experiment, we observe convergence to fingers with the initially prescribed wavelength. Experiments and numerical computations show that this family of solutions arises from a subcritical bifurcation.}, Doi = {10.1103/PhysRevLett.93.247803}, Key = {fds303629} } @article{fds245435, Author = {Herrmann, HJ and Gudehus, G and Luding, S and Sommer, K and Parsons, M and McNamara, S and García-Rojo, R and Adams, MJ and Allersma, HGB and Ancey, C and Bardet, JP and Behringer, RP and Bideau, D and Bolton, M and Bouvard, D and Cambou, B and Chang, CS and Darve, F and Evesque, P and Ghadiri, M and Goddard, J and Gourves, R and Gudehus, G and Herrmann, HJ and Hidaka, J and Jaeger, HM and Jenkins, JT and Khakhar, DV and Kishino, Y and Lanier, J and Luding, S and Luong, MP and Matsuoka, H and Mehta, A and Muehlhaus, H and Nakagawa, M and Nova, R and Oda, M and Oger, L and Ottino, JM and Rasmussen, K and Satake, M et al.}, Title = {Preface}, Journal = {Powders and Grains 2005 - Proceedings of the 5th International Conference on Micromechanics of Granular Media}, Volume = {1}, Pages = {XXI-XXII}, Year = {2005}, Key = {fds245435} } @proceedings{fds245436, Author = {Behringer, RP and Clement, E and Geng, J and Hartley, R and Howell, D and Reydellet, G and Utter, B}, Title = {Statistical properties of dense granular matter}, Journal = {TRAFFIC AND GRANULAR FLOW '03}, Pages = {431-444}, Booktitle = {Proceedings of Traffic and Granular Flow, Delft}, Year = {2005}, ISBN = {3-540-25814-0}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000232132800044&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/3-540-28091-X_44}, Key = {fds245436} } @article{fds245464, Author = {Wambaugh, JF and Behringer, RP}, Title = {Asymmetry-induced circulation in granular hopper flows}, Journal = {Powders and Grains 2005 - Proceedings of the 5th International Conference on Micromechanics of Granular Media}, Volume = {2}, Pages = {915-918}, Booktitle = {Powders and Grains, 2005}, Publisher = {Balkema}, Editor = {R. Garcia-Rojo, and H. J. Herrmann}, Year = {2005}, Abstract = {The Jenike radial solutions have long been used to describe granular hopper flow by modeling particle paths as radial lines converging upon the vertex of a hopper. A finite-element simulation, based upon the Jenike solutions, has recently been developed and predicts that if the symmetry of the hopper is perturbed, a swirling, secondary-circulation flow arises in addition to the radial flow out of the hopper. (Gremaud et al. 2003) Additionally, increasing the roughness of the hopper walls is predicted to change the direction of this secondary-circulation and suppress its magnitude. Our experimental study tests for secondary-circulation in a hopper tilted to various angles, by tracking tracer grains within the flowing sand through windows in the side of the test hopper. Results indicate that perturbing the hopper by tilting with respect to gravity does indeed cause secondary-circulation. We do not, however, observe that varying the roughness of the hopper walls affects the secondary- circulation. © 2005 Taylor & Francis Group.}, Key = {fds245464} } @article{fds245465, Author = {Geng, J and Behringer, RP}, Title = {Slow drag in two-dimensional granular media}, Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, Volume = {71}, Number = {1}, Year = {2005}, ISSN = {1539-3755}, url = {http://dx.doi.org/10.1103/PhysRevE.71.011302}, Abstract = {We study the drag force experienced by an object slowly moving at constant velocity through a two-dimensional granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three important control parameters for the system: the packing fraction, the drag velocity and the size of the tracer particle. We find that the mean drag force increases as a power law (exponent of 1.5) in the reduced packing fraction, (γ-γ c)/γ c as γ passes through a critical packing fraction, γ c. By comparison, the mean drag grows slowly (basically logarithmic) with the drag velocity, showing a weak rate dependence. We also find that the mean drag force depends nonlinearly on the diameter, a of the tracer particle when a is comparable to the surrounding particles' size. However, the system nevertheless exhibits strong statistical invariance in the sense that many physical quantities collapse onto a single curve under appropriate scaling: force distributions P(f) collapse with appropriate scaling by the mean force, the power spectra P(ω) collapse when scaled by the drag velocity, and the avalanche size and duration distributions collapse when scaled by the mean avalanche size and duration. We also show that the system can be understood using simple failure models, which reproduce many experimental observations. These observations include the following: a power law variation of the spectrum with frequency characterized by an exponent α=-2, exponential distributions for both the avalanche size and duration, and an exponential fall-off at large forces for the force distributions. These experimental data and simulations indicate that fluctuations in the drag force seem to be associated with the force chain formation and breaking in the system. Moreover, our simulations suggest that the logarithmic increase of the mean drag force with rate can be accounted for if slow relaxation of the force chain networks is included. © 2005 The American Physical Society.}, Doi = {10.1103/PhysRevE.71.011302}, Key = {fds245465} } @article{fds245466, Author = {Wilkinson, RA and Behringer, RP and Jenkins, JT and Louge, MY}, Title = {Granular materials and the risks they pose for success on the moon and mars}, Journal = {AIP Conference Proceedings}, Volume = {746}, Pages = {1216-1223}, Booktitle = {Proceedings, STAIF}, Year = {2005}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.1867248}, Abstract = {Working with soil, sand, powders, ores, cement and sintered bricks, excavating, grading construction sites, driving off-road, transporting granules in chutes and pipes, sifting gravel, separating solids from gases, and using hoppers are so routine that it seems straightforward to do it on the Moon and Mars as we do it on Earth. This paper brings to the fore how little these processes are understood and the millennia-long trial-and-error practices that lead to today's massive over-design, high failure rate, and extensive incremental scaling up of industrial processes because of the inadequate predictive tools for design. We present a number of pragmatic scenarios where granular materials play a role, the risks involved, and what understanding is needed to greatly reduce the risks. © 2005 American Institute of Physics.}, Doi = {10.1063/1.1867248}, Key = {fds245466} } @article{fds245467, Author = {Majmudar, TS and Behringer, RP}, Title = {Contact forces and stress induced anisotropy}, Journal = {Powders and Grains 2005 - Proceedings of the 5th International Conference on Micromechanics of Granular Media}, Volume = {1}, Pages = {65-68}, Booktitle = {Powders and Grains, 2005}, Publisher = {Balkema}, Editor = {R. Garcia-Rojo, and H. J. Herrmann}, Year = {2005}, Abstract = {We present experiments measuring vector contact forces in a two-dimensional (2D) granular system consisting of bi-disperse, photoelastic disks. Using a bi-axial test apparatus, we study the response of the system to isotropic compression, uniaxial compression and pure shear. We obtain normal and tangential force distributions for each case and find that different loading conditions give rise to different force chain structures and different normal force distributions. © 2005 Taylor & 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 & 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 & 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 & 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 & Francis Group.}, Key = {fds245471} } @article{fds245544, Author = {Behringer, RP}, Title = {A grain of a good idea}, Journal = {Nature}, Volume = {437}, Pages = {1069}, Year = {2005}, Key = {fds245544} } @article{fds245548, Author = {Atman, APF and Brunet, P and Geng, J and Reydellet, G and Combe, G and Claudin, P and Behringer, RP and Clément, E}, Title = {Sensitivity of the stress response function to packing preparation}, Journal = {Journal of Physics Condensed Matter}, Volume = {17}, Number = {24}, Pages = {S2391-S2403}, Year = {2005}, url = {http://dx.doi.org/10.1088/0953-8984/17/24/002}, Abstract = {A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression and shearing. We show, using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected, and in most cases significant departures from isotropy should be observed. This suggests a new path towards a non-intrusive test of granular material constitutive properties. © 2005 IOP Publishing Ltd.}, Doi = {10.1088/0953-8984/17/24/002}, Key = {fds245548} } @article{fds245549, Author = {Behringer, RP and Shearer, M}, Title = {Preface to the Special Issue "Nonlinear Dynamics of Thin Films and Fluid Interfaces}, Journal = {Physica D}, Volume = {209}, Number = {1-4 SPEC. ISS.}, Pages = {vii-viii}, Year = {2005}, url = {http://dx.doi.org/10.1016/j.physd.2005.08.003}, Doi = {10.1016/j.physd.2005.08.003}, Key = {fds245549} } @article{fds245551, Author = {Bowen, M and Sur, J and Bertozzi, AL and Behringer, RP}, Title = {Nonlinear dynamics of two-dimensional undercompressive shocks}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {209}, Number = {1-4 SPEC. ISS.}, Pages = {36-48}, Year = {2005}, ISSN = {0167-2789}, url = {http://dx.doi.org/10.1016/j.physd.2005.06.011}, Abstract = {We consider the problem of a thin film driven by a thermal gradient with an opposing gravitational force. Under appropriate conditions, an advancing film front develops a leading undercompressive shock followed by a trailing compressive shock. Here, we investigate the nonlinear dynamics of these shock structures that describe a surprisingly stable advancing front. We compare two-dimensional simulations with linear stability theory, shock theory, and experimental results. The theory/experiment considers the propagation of information through the undercompressive shock towards the trailing compressive shock. We show that a local perturbation interacting with the undercompressive shock leads to nonlocal effects at the compressive shock. © 2005 Elsevier B.V. All rights reserved.}, Doi = {10.1016/j.physd.2005.06.011}, Key = {fds245551} } @article{fds304525, Author = {Behringer, RP and Shearer, M}, Title = {Physica D: Nonlinear Phenomena: Preface}, Journal = {Physica D: Nonlinear Phenomena}, Volume = {209}, Number = {1-4 SPEC. ISS.}, Pages = {vii-viii}, Year = {2005}, url = {http://dx.doi.org/10.1016/j.physd.2005.08.003}, Doi = {10.1016/j.physd.2005.08.003}, Key = {fds304525} } @article{fds318409, Author = {Daniels, KE and Behringer, RP}, Title = {Characterization of a freezing/melting transition in a vibrated and sheared granular medium}, Journal = {Powders and Grains 2005 - Proceedings of the 5th International Conference on Micromechanics of Granular Media}, Volume = {1}, Pages = {357-360}, Year = {2005}, Abstract = {We describe experiments on monodisperse spherical particles in an annular cell geometry, vibrated from below and sheared from above. This system shows a freezing/melting transition such that under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. We characterize the hysteretic transition between these two states, and observe features reminiscent of both a jamming transition and critical phenomena. © 2005 Taylor & 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 deform. A shadow-graph method is used to follow the pattern formation in time. The patterns are mainly composed of polygons and rolls. The mean pattern size first decreases slightly, and then gradually increases during the evolution. Evaporation affects the pattern formation mainly at the early stages and the local evaporation rate tends to become spatially uniform at the film surface. The Soret effect becomes important at the later stages and affects the mixture for a large mean solute concentration where the Soret number is significantly above zero. The strength of convection increases with the initial solute concentration and the substrate temperature. Our findings differ from the theoretical predictions in which evaporation is neglected. © 2007 The American Physical Society.}, Doi = {10.1103/PhysRevE.76.016306}, Key = {fds245475} } @article{fds245476, Author = {Behringer, RP and Wilkinson, A and Metzger, PT}, Title = {Grenular Matter: Editorial}, Journal = {Granular Matter}, Volume = {9}, Number = {5}, Pages = {293-294}, Year = {2007}, ISSN = {1434-5021}, url = {http://dx.doi.org/10.1007/s10035-007-0048-0}, Doi = {10.1007/s10035-007-0048-0}, Key = {fds245476} } @article{fds245537, Author = {Kondic, L and O'Hern, C and Behringer, RP}, Title = {Dense Granular Systems: From Theory to Applications}, Journal = {SIAM News}, Volume = {40}, Pages = {13-15}, Year = {2007}, Key = {fds245537} } @article{fds245540, Author = {Zhang, J and Behringer, RP and Oron, A}, Title = {Maragoni convection in binary mixtures}, Journal = {Phys. Rev. E}, Volume = {76}, Pages = {106307}, Year = {2007}, Key = {fds245540} } @incollection{fds139760, Author = {R.P. Behringer}, Title = {Fluctuations in Granular Materials}, Volume = {8}, Series = {Lecture Notes in Complex Systems}, Pages = {187-215}, Booktitle = {Granular and Complex Materials}, Publisher = {World Scientific}, Address = {Singapore}, Editor = {T. Aste and T. De Matteo and A. Tordesillas}, Year = {2007}, Key = {fds139760} } @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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000273629400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1007/978-3-642-03578-4_3}, Key = {fds245437} } @article{fds245480, Author = {Tang, J and Sagdiphour, S and Behringer, RP}, Title = {Jamming and flow in 2D hoppers}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {515-518}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179975}, Abstract = {We consider jamming that occurs for the flow of dry granular materials from a hopper as the outlet size, D, is reduced relative to the particle size, d. We propose and test a model based on the simple idea that the probability of jamming on a short time, dt, is a constant, t. This leads to the prediction that the probability of surviving until time t without jamming is an exponentially decaying function, Ps(t) =exp(-t / t ). The important physical question is what determinest? Experiments to date have confirmed the exponential character of the survival probability. Work in progress characterizes t(D,d), fluctuations and their possible relation to the jamming process. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179975}, Key = {fds245480} } @article{fds245481, Author = {Kondic, L and Fang, X and Dybenko, OM and Behringer, RP}, Title = {Energy transport through dense granular matter}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {293-296}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179916}, Abstract = {In order to probe the process of energy propagation through dense granular systems, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. The soft-disk simulations are carried out in two spatial dimensions, and include the effects of energy loss due to inelasticity of collisions, frictional damping, rotations, and polydispersity. Our ability to control independently spatial and temporal properties of the imposed perturbations allows us to extract significant new information. In particular, Fourier analysis of the system response shows that properties of the propagating signal strongly depend on the spatial scales introduced by the perturbation itself. Then, we consider a sheared granular system and discuss how shearing influences the nature of the propagating signal. The simulations are carried out using realistic system sizes and material properties, allowing for direct experimental verification of the obtained results. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179916}, Key = {fds245481} } @article{fds245482, Author = {Dutt, M and Behringer, RP}, Title = {A particle-substrate numerical model for a quasi-2D driven dissipative granular gas}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {1112-1115}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179841}, Abstract = {A complete understanding of the microscopic dynamics of a monolayer of identical spheres moving on a substrate must encompass the effects of collisions and the substrate on the particles. We begin from first principles by considering collections of spherical frictional particles that roll and slip on a flat horizontally vibrated substrate. We present a numerical model which accounts for the substrate motion, collisional and surface frictional dissipation and their influence on particle dynamics for a quasi 2-dimensional dilute granular gas. In such systems, the ratio of the substrate acceleration to the particlesubstrate static frictional force (Kondic, Phys Rev. E (1999)) dominates the individual particle dynamics and the collision dynamics. This model is an extension of a previous numerical model which accounted for the influence of the collisional and substrate dissipation on a quasi two-dimensional cooling granular gas (Dutt Behringer, Phys. Rev. E (2004)). We willpresent results from our numerical experiments which highlight the progression of dynamical variables and fluctuation velocity distributions as a function of the initial conditions and the driving acceleration. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179841}, Key = {fds245482} } @article{fds245483, Author = {Hartley, RR and Behringer, RP and Henkes, S and Bi, D and Chakraborty, B}, Title = {Logarithmic strengthening of granular materials with shear rate}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {1089-1092}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179834}, Abstract = {Experiments on sheared granular materials show that the stresses grow as the first power of the log of the shear rate, γ. We suggest that this may be evidence of the stress ensemble recently proposed by Henkes, O'Hern, and Chakraborty. The picture that we propose is that under steady shearing, the local force network builds up over time, and then fails when the force on the network exceeds a characteristic value. In analogy to soft glassy rheology, we assume that this is an activated process, but now, with the Boltzmann factor replaced by the stress ensemble analogue. We assume that the probability that a local part of the network fails is proportional to exp[(σ- σm)/σo], where s is the local stress, sm is a failure threshold, and σo is related to the generalized temperature, α, of Henkes and Chakraborty. It is then possible to show that these assumptions lead to logarithmic increases in the stress as a function of γ. This contrasts with the SGR result that the stress grows as the square root of l og(γ). © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179834}, Key = {fds245483} } @article{fds245484, Author = {Utter, B and Behringer, RP}, Title = {Multiscale motion in the shear band of granular couette flow}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {339-342}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179928}, Abstract = {We probe the nature of slow flow in the shear band of a 2D granular Couette experiment. The experiment consists of an inner shearing wheel, an outer circular boundary, and particles which occupy the space between these two. The mean flow is strictly azimuthal, maximal at the shearing wheel, and decaying roughly exponentially with distance from wheel. In addition to the mean flow and its implied shear, there is also inherently stochastic non-affine motion that is associated with diffusion of the particles and not describable in terms of a smooth deformation. We represent the motion of particles in such small local regions over a short time by the sum of three parts: a mean flow, characterized by the exponential velocity profile; a smooth affine deformation; and a non-affine component. The key observation from this analysis is that each of these components has comparable magnitude. Displacements from mean, affine, and non-affine motion are all described within an O(1) scale factor by the same function of distance from the shearing wheel. The same function also describes the diffusivities determined from variance-vs.-time traces. The non-affine displacements are distributed according to a guassian-like function, except that the exponent is closer to 3/2 rather than 2. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179928}, Key = {fds245484} } @article{fds245485, Author = {Zhang, J and Behringer, RP and Majmudar, TS and Sperl, M}, Title = {Experiments on force fluctuations and the jamming transition}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {527-530}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179979}, Abstract = {Using photoelastic experimental techniques, we probe the nature of jamming in dense 2D granular systems. This approach allows a complete characterization of the system, including contact forces, and particle motion. Key findings for systems of disks include: force distributions that are sensitive to the stress state of the system (e.g. isotropic or not), The distributions have a roughly exponential tail following pure shear, but transition to a more gaussian-like distribution for isotropic compression. Near jamming, we find that the contact number per particle, Z, rises sharply as a function of packing fraction, f, at jamming, and then continues to rise above critical with an exponent that is consistent with 1/2. The pressure also rises as a function of f above jamming with an exponent slightly larger than 1.0, which is consistent with predictions. We also find that under cyclic shear, a dense granular material undergoes a different type of jamming transition, and we present initial results showing that P is a function of Z above this transition. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179979}, Key = {fds245485} } @article{fds245486, Author = {Kondic, L and Dybenko, OM and Behringer, RP}, Title = {Probing dense granular materials by space-time dependent perturbations}, Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, Volume = {79}, Number = {4}, Year = {2009}, ISSN = {1539-3755}, url = {http://dx.doi.org/10.1103/PhysRevE.79.041304}, Abstract = {The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping. © 2009 The American Physical Society.}, Doi = {10.1103/PhysRevE.79.041304}, Key = {fds245486} } @article{fds245487, Author = {Zhang, J and Ren, J and Farhadi, S and Behringer, RP and Majmudar, TS and Tordesillas, A}, Title = {A dense 2D granular material subject to cyclic pure shear}, Journal = {AIP Conference Proceedings}, Volume = {1145}, Pages = {553-556}, Year = {2009}, ISSN = {0094-243X}, url = {http://dx.doi.org/10.1063/1.3179985}, Abstract = {This work focuses on the evolution of fabric and stress tensors for an assembly of dense 2D photoelastic particles subjected to cyclic pure shear. The fabric and stress tensors are computed from the contact network and contact forces using particle tracking and photoelastic techniques. The system pressure, P, shear stress, t, and the mean contact number, Z fluctuate during the shear process. Their fluctuations are strongly correlated. We find, to a reasonable approximation, a functional relation between P, t and Z. By tracking the average contact number Z, we also find that there are jammed states at a packing fraction f = 0.758 below fc = 0.84 for the isotropic jamming transition in two dimensions. © 2009 American Institute of Physics.}, Doi = {10.1063/1.3179985}, Key = {fds245487} } @article{fds245489, Author = {Lois, G and Zhang, J and Majmudar, TS and Henkes, S and Chakraborty, B and O'Hern, CS and Behringer, RP}, Title = {Stress correlations in granular materials: An entropic formulation}, Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, Volume = {80}, Number = {6}, Year = {2009}, ISSN = {1539-3755}, url = {http://hdl.handle.net/10161/4281 Duke open access}, Abstract = {We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively. © 2009 The American Physical Society.}, Doi = {10.1103/PhysRevE.80.060303}, Key = {fds245489} } @article{fds245522, Author = {Krim, J and Behringer, RP}, Title = {Friction, force chains, and falling fruit}, Journal = {Physics today}, Volume = {62}, Number = {9}, Pages = {66-67}, Year = {2009}, ISSN = {0031-9228}, url = {http://dx.doi.org/10.1063/1.3226776}, Doi = {10.1063/1.3226776}, Key = {fds245522} } @article{fds245524, Author = {Kondic, L and Dybenko, OM and Behringer, RP}, Title = {Signal Propagation Through Dense Granular SystemsProbing dense granular materials by space-time dependent perturbations}, Journal = {Phys. Rev. E}, Volume = {79}, Pages = {041304}, Year = {2009}, Key = {fds245524} } @article{fds245527, Author = {Sanfratello, L and Fukushima, E and Behringer, RP}, Title = {Using MR elastography to image the 3D force chain structure of a quasi-static granular assembly}, Journal = {Granular Matter}, Volume = {11}, Number = {1}, Pages = {1-6}, Year = {2009}, ISSN = {1434-5021}, url = {http://dx.doi.org/10.1007/s10035-008-0112-4}, Abstract = {We have developed a magnetic resonance elastography (MRE) technique to experimentally investigate the force chain structure within a densely packed 3D granular assembly. MRE is an MRI technique whereby small periodic displacements within an elastic material are measured. We verified our MRE technique using a gel phantom and then extended the method to image the force carrying chain structure within a 3D granular assembly of particles under an initial pre-stressed condition, on top of which is superimposed a small-amplitude vibration. We find that significant coherent displacements form along force chains, where spin phase accumulates preferentially, allowing visualization. This work represents the first time that the internal force chain structure of a dry assembly of granular solids has been fully acquired in three dimensions. © 2008 Springer-Verlag.}, Doi = {10.1007/s10035-008-0112-4}, Key = {fds245527} } @article{fds245528, Author = {Tordesillas, A and Zhang, J and Behringer, R}, Title = {Buckling force chains in dense granular assemblies: Physical and numerical experiments}, Journal = {Geomechanics & Geoengineering: An International Journal}, Volume = {4}, Number = {1}, Pages = {3-16}, Year = {2009}, ISSN = {1748-6025}, url = {http://dx.doi.org/10.1080/17486020902767347}, Abstract = {This paper focuses on the columnar particle structures known as force chains, and their failure via buckling. The local kinematics and frictional dissipation of this failure mechanism are examined quantitatively for dense, cohesionless granular assemblies, under quasistatic and strain-controlled compression. Data are taken from a physical experiment and a discrete element simulation of bidisperse assemblies of circular particles undergoing shear banding. Particular attention is paid to the deformation and dissipation within a class of particle clusters, each composed of a buckled force chain segment and its laterally supporting neighbours. These particle clusters are found to be confined to the shear band. We establish measures of their local micropolar deformation, including nonaffine deformation, and the evolution of these quantities with strain. Temporally and spatially, the kinematics of this class of particles exhibits trends consistent with the particle motions that form the major contributors to deformation on the mesoscopic and macroscopic scales. The predominant mode of contact failure in a force chain undergoing buckling, and in the contacts with and within its laterally supporting neighbours, is frictional rolling. Rolling friction thus serves as one of, if not the main control valve for the energy flow from the force chain to its surrounding medium.}, Doi = {10.1080/17486020902767347}, Key = {fds245528} } @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 inward temperature gradient reveal the evolution of a radial height profile given by h(r) = A(t)r(α), where A(t) decays logarithmically with time, and [Formula: see text]. In the case where there is no rotation, small centrally placed drops show novel retraction behavior under a sufficiently strong temperature gradient. Using the same interferometric arrangement, we observed the onset of the fingering instability of small drops placed at the center of the rotating substrate in the absence of a temperature gradient. At the onset of the instability, the height profile for small drops is more complex than previously assumed.}, Doi = {10.1088/0953-8984/21/46/464123}, Key = {fds245523} } @article{fds245519, Author = {Zhang, J and Majmudar, TS and Sperl, M and Behringer, RP}, Title = {Jamming for a 2D granular material}, Journal = {Soft Matter}, Volume = {6}, Number = {13}, Pages = {2982-2991}, Year = {2010}, ISSN = {1744-683X}, url = {http://hdl.handle.net/10161/4125 Duke open access}, Abstract = {This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, . In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable which we identify with as c. It is possible to fit Z and P, to power law expressions in - c above c, and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near c. The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below c, where the application of shear strain at constant leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, τ. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant first leads to an increase of both τ and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only and τ, but also P. P, τ, and Z are all hysteretic functions of shear strain for fixed . However, we find that both P and τ are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, τ = μP. © 2010 The Royal Society of Chemistry.}, Doi = {10.1039/c000147c}, Key = {fds245519} } @article{fds245520, Author = {Zhang, J and Majmudar, TS and Tordesillas, A and Behringer, RP}, Title = {Statistical properties of a 2D granular material subjected to cyclic shear}, Journal = {Granular Matter}, Volume = {12}, Number = {2}, Pages = {159-172}, Year = {2010}, ISSN = {1434-5021}, url = {http://dx.doi.org/10.1007/s10035-010-0170-2}, Abstract = {This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, P, and the mean contact number, Z. This relationship applies to the shear stress τ , except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as P ,τ and Z are strongly hysteretic functions of the strain, e. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks. © Springer-Verlag 2010.}, Doi = {10.1007/s10035-010-0170-2}, Key = {fds245520} } @article{fds245521, Author = {Zhang, J and Behringer, RP and Goldhirsch, I}, Title = {Coarse-Graining of a Physical Granular System}, Journal = {Progress of Theoretical Physics}, Volume = {184}, Number = {SUPPL. 184}, Pages = {16-30}, Year = {2010}, ISSN = {0033-068X}, Abstract = {Results, including displacement, strain and stress fields, obtained by applying a resolution-controlled coarse-graining method to an experiment, comprised of a bidisperse system of photoelastic disks under pure shear, are presented. The paper reviews the experimental methods as well as the philosophical and technical bases of the coarse-graining methods employed in this study. Some fields reveal the emergence of a shear band while others do not. Correlations of the displacement fluctuations are shown to decay on a very small scale, of the order of a few particle diameters, even close to jamming. An unexpectedly simple relation between the particle rotation angles and the rotation field is reported. Implications of these and other findings are discussed.}, Key = {fds245521} } @article{fds318408, Author = {Zhang, J and Behringer, RP and Goldhirsch, I}, Title = {Coarse-graining of a physical granular system}, Journal = {Progress of Theoretical Physics Supplement}, Number = {184}, Pages = {16-30}, Year = {2010}, Abstract = {Results, including displacement, strain and stress fields, obtained by applying a resolution-controlled coarse-graining method to an experiment, comprised of a bidisperse system of photoelastic disks under pure shear, are presented. The paper reviews the experimental methods as well as the philosophical and technical bases of the coarse-graining methods employed in this study. Some fields reveal the emergence of a shear band while others do not. Correlations of the displacement fluctuations are shown to decay on a very small scale, of the order of a few particle diameters, even close to jamming. An unexpectedly simple relation between the particle rotation angles and the rotation field is reported. Implications of these and other findings are discussed.}, Key = {fds318408} } @article{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 monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading. Â© 2010 2010 Elsevier Ltd. All rights reserved.}, Doi = {10.1016/j.jmps.2010.10.007}, Key = {fds245513} } @article{fds245514, Author = {Walker, DM and Tordesillas, A and Thornton, C and Behringer, RP and Zhang, J and Peters, JF}, Title = {Percolating contact subnetworks on the edge of isostaticity}, Journal = {Granular Matter}, Volume = {13}, Number = {3}, Pages = {233-240}, Year = {2011}, ISSN = {1434-5021}, url = {http://dx.doi.org/10.1007/s10035-011-0250-y}, Abstract = {We search for a percolating, strong subnetwork of contacts in a quasi-statically deforming, frictional granular material. Of specific interest in this study is that subnetwork which contributes to the majority of the total deviator stress and is, or is on the edge of being, isostatic. We argue that a subnetwork derived from the minimal spanning trees of a graph - optimized to include as many elastic contacts as possible and which bear normal contact forces above a given threshold delivers such a network. Moreover adding the strong 3-force-cycles to the spanning tree introduces a level of redundancy required to achieve a network that is almost if not isostatic. Results are shown for assemblies of non-uniformly sized circular particles under biaxial compression, in two-dimensions: a discrete element (DEM) simulation of monotonic loading under constant confining pressure, and cyclic loading of photoelastic disks under constant volume. © 2011 Springer-Verlag.}, Doi = {10.1007/s10035-011-0250-y}, Key = {fds245514} } @article{fds245517, Author = {Zhang, J and Oron, A and Behringer, RP}, Title = {Novel pattern forming states for Marangoni convection in volatile binary liquids}, Journal = {Physics of Fluids}, Volume = {23}, Number = {7}, Pages = {072102}, Year = {2011}, ISSN = {1070-6631}, url = {http://dx.doi.org/10.1063/1.3609287}, Abstract = {We describe experiments on Marangoni convection in thin evaporating liquid films. The films are binary mixtures of ethanol and water exposed to the ambient room air during all experimental runs. These experiments exhibit a variety of different, often novel, patterns, depending on the concentration (weight fraction) c of ethanol. Among these are mobile circular convective patterns, which have not been previously observed, to our knowledge. The convective patterns evolve due to the evaporation of both the solvent and the solute, and their size increases substantially with the initial concentration c. The patterns reported here differ from those found in binary mixtures of NaCl and water, where only water evaporates. © 2011 American Institute of Physics.}, Doi = {10.1063/1.3609287}, Key = {fds245517} } @article{fds245518, Author = {Krim, J and Yu, P and Behringer, RP}, Title = {Stick-Slip and the Transition to Steady Sliding in a 2D Granular Medium and a Fixed Particle Lattice}, Journal = {pure and applied geophysics}, Volume = {168}, Number = {12}, Pages = {2259-2275}, Year = {2011}, ISSN = {0033-4553}, url = {http://dx.doi.org/10.1007/s00024-011-0364-5}, Abstract = {We report an experimental study of the stick-slip to steady sliding behavior of a solid object pulled, via a spring, across 2D granular substrates of photoelastic disks that are either fixed in a solid lattice (granular solid) or unconstrained, forming a granular bed. We observe a progression of friction regimes with increasing sliding speed, including single-slip, double-slip, and mixed stick-slip regimes, steady sliding, and inertial oscillations. For the case of the granular bed, we report a detailed analysis of frictional behavior for the low speed stick-slip regime, including spring and elastic energy dependencies during the stick and slip portions of the motion. For the case of the granular solid, we explore friction in the presence and absence of externally applied vibrations, and compare it with sliding on a granular bed, which is intrinsically disordered. We observe that external vibration reduces transition values for both the single-slip to double-slip transition and the stick-slip to steady sliding transition. Moreover, we observe that the effect of packing disorder on granular friction seems similar to the effect of vibration-induced disorder, a result that, to our knowledge, has not been reported previously in the experimental literature. © 2011 Springer Basel AG.}, Doi = {10.1007/s00024-011-0364-5}, Key = {fds245518} } @article{fds304526, Author = {Tordesillas, A and Lin, Q and Zhang, J and Behringer, RP and Shi, J}, Title = {Structural stability and jamming of self-organized cluster conformations in dense granular materials}, Journal = {Journal of the Mechanics and Physics of Solids}, Volume = {59}, Number = {2}, Pages = {265-296}, Year = {2011}, ISSN = {0022-5096}, url = {http://dx.doi.org/10.1016/j.jmps.2010.10.007}, Abstract = {We examine emergent, self-organized particle cluster conformations in quasistatically deforming dense granular materials from the perspective of structural stability. A structural mechanics approach is employed, first, to devise a new stability measure for such conformations in equilibrium and, second, to use this measure to explore the evolving stability of jammed states of specific cluster conformations, i.e. particles forming force chains and minimal contact cycles. Knowledge gained on (a) the spatial and temporal evolution of stability of individual jammed conformations and (b) their relative stability levels, offer valuable clues on the rheology and, in particular, self-assembly of granular materials. This study is undertaken using data from assemblies of nonuniformly sized circular particles undergoing 2D deformation in two biaxial compression tests: a discrete element simulation of monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading. © 2010 2010 Elsevier Ltd. All rights reserved.}, Doi = {10.1016/j.jmps.2010.10.007}, Key = {fds304526} } @article{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 spheres. © Copyright EPLA, 2012.}, Doi = {10.1209/0295-5075/100/44005}, Key = {fds245492} } @article{fds245493, Author = {Tordesillas, A and Walker, DM and Froyland, G and Zhang, J and Behringer, RP}, Title = {Transition dynamics and magic-number-like behavior of frictional granular clusters}, Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, Volume = {86}, Number = {1}, Pages = {011306}, Year = {2012}, ISSN = {1539-3755}, url = {http://www.ncbi.nlm.nih.gov/pubmed/23005410}, Abstract = {Force chains, the primary load-bearing structures in dense granular materials, rearrange in response to applied stresses and strains. These self-organized grain columns rely on contacts from weakly stressed grains for lateral support to maintain and find new stable states. However, the dynamics associated with the regulation of the topology of contacts and strong versus weak forces through such contacts remains unclear. This study of local self-organization of frictional particles in a deforming dense granular material exploits a transition matrix to quantify preferred conformations and the most likely conformational transitions. It reveals that favored cluster conformations reside in distinct stability states, reminiscent of "magic numbers" for molecular clusters. To support axial loads, force chains typically reside in more stable states of the stability landscape, preferring stabilizing trusslike, three-cycle contact triangular topologies with neighboring grains. The most likely conformational transitions during force chain failure by buckling correspond to rearrangements among, or loss of, contacts which break the three-cycle topology. © 2012 American Physical Society.}, Doi = {10.1103/PhysRevE.86.011306}, Key = {fds245493} } @article{fds245505, Author = {Kondic, L and Goullet, A and O'Hern, CS and Kramar, M and Mischaikow, K and Behringer, RP}, Title = {Topology of force networks in compressed granular media}, Journal = {EPL (Europhysics Letters)}, Volume = {97}, Number = {5}, Pages = {54001}, Year = {2012}, ISSN = {0295-5075}, url = {http://dx.doi.org/10.1209/0295-5075/97/54001}, Abstract = {Using numerical simulations, we investigate the evolution of the structure of force networks in slowly compressed model granular materials in two spatial dimensions. We quantify the global properties of the force networks using the zeroth Betti number B0, which is a topological invariant. We find that B0 can distinguish among force networks in systems with frictionless vs. frictional disks and varying size distributions. In particular, we show that 1) the force networks in systems composed of frictionless, monodisperse disks differ significantly from those in systems with frictional, polydisperse disks and we isolate the effect (friction, polydispersity) leading to the differences; 2) the structural properties of force networks change as the system passes through the jamming transition; and 3) the force network continues to evolve as the system is compressed above jamming, e.g., the size of connected clusters with forces larger than a given threshold decreases significantly with increasing packing fraction. © Europhysics Letters Association, 2012.}, Doi = {10.1209/0295-5075/97/54001}, Key = {fds245505} } @article{fds245509, Author = {Behringer, RP and Bi, D and Zhang, J and Chakraborty, B}, Title = {Sheared Granular Materials near Jamming}, Journal = {Proceedings of the 8th European Solid Mechanics Society}, Year = {2012}, Key = {fds245509} } @article{fds245510, Author = {Tordesillas, A and Walker, DM and Froyland, G and Zhang, J and Behringer, RP}, Title = {Transition Dynamics of Frictional Granular Clusters}, Journal = {Phys, Rev, E}, Volume = {86}, Number = {1 Pt 1}, Pages = {011306}, Year = {2012}, url = {http://www.ncbi.nlm.nih.gov/pubmed/23005410}, Abstract = {Force chains, the primary load-bearing structures in dense granular materials, rearrange in response to applied stresses and strains. These self-organized grain columns rely on contacts from weakly stressed grains for lateral support to maintain and find new stable states. However, the dynamics associated with the regulation of the topology of contacts and strong versus weak forces through such contacts remains unclear. This study of local self-organization of frictional particles in a deforming dense granular material exploits a transition matrix to quantify preferred conformations and the most likely conformational transitions. It reveals that favored cluster conformations reside in distinct stability states, reminiscent of "magic numbers" for molecular clusters. To support axial loads, force chains typically reside in more stable states of the stability landscape, preferring stabilizing trusslike, three-cycle contact triangular topologies with neighboring grains. The most likely conformational transitions during force chain failure by buckling correspond to rearrangements among, or loss of, contacts which break the three-cycle topology.}, Doi = {10.1103/PhysRevE.86.011306}, Key = {fds245510} } @article{fds245511, Author = {Kondic, L and Fang, X and Losert, W and O'Hern, CS and Behringer, RP}, Title = {Microstructure evolution during impact on granular matter}, Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics}, Volume = {85}, Number = {1}, Year = {2012}, ISSN = {1539-3755}, url = {http://dx.doi.org/10.1103/PhysRevE.85.011305}, Abstract = {We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself. © 2012 American Physical Society.}, Doi = {10.1103/PhysRevE.85.011305}, Key = {fds245511} } @article{fds245512, Author = {Clark, AH and Mort, P and Behringer, RP}, Title = {Coarse graining for an impeller-driven mixer system}, Journal = {Granular Matter}, Volume = {14}, Number = {2}, Pages = {283-288}, Year = {2012}, ISSN = {1434-5021}, url = {http://dx.doi.org/10.1007/s10035-011-0306-z}, Abstract = {We apply a coarse graining approach developed by Isaac Goldhirsch to data acquired from a model of an impeller-driven mixer system. The experiment uses a bidisperse system of photoelastic particles in a quasi-2D system to determine local mass and momentum densities, velocities, granular temperatures, size concentration, and pressure. Raw data consist of high speed video images obtained with polarizers (to obtain particle-scale force data) and without polarizers (to obtain particle positions). We coarse grain the experimental data using a Gaussian coarse graining function, φ, of variable width, w. © Springer-Verlag 2012.}, Doi = {10.1007/s10035-011-0306-z}, Key = {fds245512} } @article{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}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811860}, Key = {fds245428} } @article{fds245429, Author = {Ren, J and Dijksman, J and Behringer, RP}, Title = {Homogeneity and Packing Structure of a 2D Sheared Granular System}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {527-530}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200127&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811984}, Key = {fds245429} } @article{fds245430, Author = {Farhadi, S and Behringer, RP and Zhu, AZ}, Title = {Slow Dynamics for Elliptical Particles Under Continuous Shear And Cyclic Compression}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {879-882}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200215&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4812072}, Key = {fds245430} } @article{fds245431, Author = {Clark, AH and Kondic, L and Behringer, RP}, Title = {Granular Impact Dynamics: Fluctuations at Short Time-Scales}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {445-448}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200106&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811963}, Key = {fds245431} } @article{fds245432, Author = {Dijksman, JA and Zheng, H and Behringer, RP}, Title = {Imaging Soft Sphere Packings in a Novel Triaxial Shear Setup}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {457-460}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200109&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811966}, Key = {fds245432} } @article{fds245433, Author = {Sepulveda, N and Behringer, RP}, Title = {Measuring Creep and Stick-Slip Behavior in 2-Dimensional Photoelastic Granular Medium}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {469-+}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200112&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811969}, Key = {fds245433} } @article{fds245434, Author = {Zheng, H and Dijksman, JA and Behringer, RP}, Title = {Novel Experimental Apparatus for Granular Experiments on Basal Friction}, Journal = {AIP Conference Proceedings}, Volume = {1542}, Pages = {465-468}, Year = {2013}, ISSN = {0094-243X}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321003200111&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Doi = {10.1063/1.4811968}, Key = {fds245434} } @article{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 J-point has little to say about real system? What about granular media? Such a-thermal, frictional, systems are a-priori even further away from the idealized case of thermal soft spheres. In the past ten years, we have systematically investigated horizontally shaken grains in the vicinity of the Jamming transition. We discuss the above issue in the light of very recent experimental results. First, we demonstrate that the contact network exhibits a remarkable dynamics, with strong heterogeneities, which are maximum at a packing fraction phi star, distinct and smaller than the packing fraction phi dagger, where the average number of contact per particle starts to increase. The two cross-overs converge at point J in the zero mechanical excitation limit. Second, a careful analysis of the dynamics on time scales ranging from a minute fraction of the vibration cycle to several thousands of cycles allows us to map the behaviors of this shaken granular system onto those observed for thermal soft spheres and demonstrate that some light of the J-point street-lamp indeed reaches the granular universe.}, Doi = {10.1039/C3SM51231B}, Key = {fds303626} } @article{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}, Abstract = {This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable method retains all the advantages of discrete element method (DEM) simulations and does not require the use of costly finite element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels up to the experimental maximum limit of 13\%. Comparisons with traditional non-deformable spheres approach are provided, as well as with alternative models for interactions between multiple contacts. The success of our model compared to these alternatives demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.}, Key = {fds303621} } @article{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}, Abstract = {This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable MC-DEM method retains all the advantages of discrete-element method simulations and does not require the use of costly finite-element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels of the packing up to the experimental maximum limit of 13%. Comparisons with classic simulations using the nondeformable spheres approach, as well as with alternative models for interactions between multiple contacts, are provided. The success of our model, compared to these alternatives, demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.}, Doi = {10.1103/PhysRevE.91.032201}, Key = {fds245415} } @article{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 kind of experiment involved adding a uniform load to the top of the column, and then determining the collapse properties. A third experiment involved testing stability to tipping of the piles. We find a stability diagram relating the pile height, h, vs. pile diameter, delta, where the stable and unstable regimes are separated by a boundary that is roughly a power-law in h vs. delta with an exponent that is less than one. Increasing friction and vibration both tend to stabilize piles, while increasing particle size can destabilize the system under certain conditions.}, Doi = {10.1007/s10035-016-0606-4}, Key = {fds303615} } @article{fds303617, Author = {Tang, J and Behringer, RP}, Title = {Orientation, flow, and clogging in a two-dimensional hopper: Ellipses vs. disks}, Journal = {EPL (Europhysics Letters)}, Volume = {114}, Number = {3}, Pages = {34002-34002}, Year = {2016}, Month = {May}, ISSN = {0295-5075}, url = {http://hdl.handle.net/10161/10941 Duke open access}, Abstract = {Two-dimensional (2D) hopper flow of disks has been extensively studied. Here, we investigate hopper flow of ellipses with aspect ratio $\alpha = 2$, and we contrast that behavior to the flow of disks. We use a quasi-2D hopper containing photoelastic particles to obtain stress/force information. We simultaneously measure the particle motion and stress. We determine several properties, including discharge rates, jamming probabilities, and the number of particles in clogging arches. For both particle types, the size of the opening, $D$, relative to the size of particles, $\ell$ is an important dimensionless measure. The orientation of the ellipses plays an important role in flow rheology and clogging. The alignment of contacting ellipses enhances the probability of forming stable arches. This study offers insight for applications involving the flow of granular materials consisting of ellipsoidal shapes, and possibly other non-spherical shapes.}, Doi = {10.1209/0295-5075/114/34002}, Key = {fds303617} } @article{fds322474, Author = {Tordesillas, A and Pucilowski, S and Lin, Q and Peters, JF and Behringer, RP}, Title = {Granular vortices: Identification, characterization and conditions for the localization of deformation}, Journal = {Journal of the Mechanics and Physics of Solids}, Volume = {90}, Pages = {215-241}, Year = {2016}, Month = {May}, url = {http://dx.doi.org/10.1016/j.jmps.2016.02.032}, Doi = {10.1016/j.jmps.2016.02.032}, Key = {fds322474} } @article{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{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} }