Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session W39: Focus Session: Jamming II: Packing and Force Networks 
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Sponsoring Units: GSNP Chair: Gregg Lois, Yale University Room: Morial Convention Center 231 
Thursday, March 13, 2008 2:30PM  2:42PM 
W39.00001: A phase diagram for jammed matter reveals the nature of the random loose and random close packing of spheres Ping Wang, Chaoming Song, Hernan A. Makse We employ statistical mechanics of jammed matter to demonstrate the phase diagram of all available jammed configurations of frictional and frictionless granular packings. This provides a statistical definition of RLP and RCP, predicts their density values in close agreement with simulations, and establishes the concomitant equations of state relating observables such as the coordination number, $z$, entropy, $S$, and volume fraction, $\phi$. We show that the RCP state is not a unique point in the phase space but extends along a line of zero compactivity, a temperaturelike variable, predicted to be at a constant $\Phi_{RCP} = 0.634$, but with different $z$. The lowest density of RLP appears as a line of infinite compactivity parameterized by $z$, ending at the minimum possible density theoretically predicted to be $\Phi_{RLP} = 0.543$. The nature of the disorder of the packings is statistically characterized by the entropy which is shown to be larger in the random loose case than in the random close case. [Preview Abstract] 
Thursday, March 13, 2008 2:42PM  2:54PM 
W39.00002: Random loose packing of rough spheres Greg Farrell, Michael Martini, Narayanan Menon We report experiments in which random loose packings of spheres are created by sequential deposition of monodisperse (3.18$\pm$0.05mm) PMMA beads of high sphericity in a fluid. The deposition speed is controlled by varying the relative densities of the spheres and the fluid, as well as by varying fluid viscosity. As in the work of Onoda and Liniger, we find that the volume fraction of the sediment asymptotically approaches a lower limit as we approach neutral buoyancy. However, we find that deposition in increasingly viscous fluids has the same effect. We also study the effect on the packing of controlled chemical roughening of the surface of the spheres. The volume fractions attained can be significantly lower than the oftenquoted volume fraction of 0.555 for random loose packing. Thus there is no unique volume fraction for the random loose packing of spheres; the measured volume fraction, even in the limit of slow deposition dynamics is determined by particle surface properties. [Preview Abstract] 
Thursday, March 13, 2008 2:54PM  3:06PM 
W39.00003: Tunable Random Packings Geoffroy Lumay, Nicolas Vandewalle We present an experimental protocol that allows one to tune the packing fraction $\eta$ of a random pile of ferromagnetic spheres from a value close to the lower limit of random loose packing $\eta_{RLP} \simeq 0.56$ to the upper limit of random close packing $\eta_{RCP} \simeq 0.64$. This broad range of packing fraction values are obtained under normal gravity in air, by adjusting a magnetic cohesion between the grains during the formation of the pile. Attractive and repulsive magnetic interactions are found to deeply affect the internal structure and the stability of sphere packing. After the formation of the pile, the induced cohesion is decreased continuously along a linear decreasing ramp. The controlled collapse of the pile is found to generate various and reproducible values of the random packing fraction $\eta$. (see New Journal of Physics 9 406 (2007)). [Preview Abstract] 
Thursday, March 13, 2008 3:06PM  3:18PM 
W39.00004: Analysis of Configurational Entropy in Jammed Granular Matter Christopher Briscoe, Ping Wang, Chaoming Song, Hernan Makse Energy fluctuations in jammed granular matter are negligible and cannot control the statistical mechanics. It is of interest to explore volume fluctuations in an effort to describe the statistical mechanics of jammed matter, originally proposed by Edwards. Current studies have introduced the concept of a theoretical phase diagram for jammed matter, providing plausible statistical explanations for the RCP and RLP states, along with intermediate jammed states, as a function of coordination number, z, friction coefficient $\mu$, and volume fraction, $\phi$. Entropy can be derived from this theoretical framework by means of a Hamiltonian, with energy and temperature replaced by volume, W, and compactivity, X, where X is an analogue of temperature. Our present efforts are to calculate the Shannon entropy of jammed granular packings along various paths of the phase diagram, resulting in an extensive entropy density, and X, as a function of $\phi$, providing a new equation of state for jammed granular matter. [Preview Abstract] 
Thursday, March 13, 2008 3:18PM  3:30PM 
W39.00005: Jamming of Frictional Spheres Abdullah Cakir, Leonardo Silbert Packings of monodisperse, frictional spheres are studied for a wide range in particle friction coefficient on approach to the jamming transition  the point where the packing loses mechanical stability. In particular, we focus on dynamical properties through the study of the vibrational normal modes. The dynamical matrix includes terms that take into account the rotational degrees of freedom due to noncentral forces in the presence of friction. The influence of friction on the normal mode frequencies and particle polarization vectors are examined. Distinct from frictionless systems, for finite friction, the normal modes now allow for particle rotations. [Preview Abstract] 
Thursday, March 13, 2008 3:30PM  3:42PM 
W39.00006: Hard Discs on the Hyperbolic Plane Carl Modes, Randall Kamien We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space. [Preview Abstract] 
Thursday, March 13, 2008 3:42PM  3:54PM 
W39.00007: Random subcubes as a toy model for constraint satisfaction problems Thierry Mora, Lenka Zdeborova abstractMany hard combinatorial problems, such as Random Satisfiability, have been shown to reproduce some salient properties of glassy materials. In particular, it has been proved that the configurational landscapes of the hardest problems are made of many disconnected ergodic components, leading to rich phase diagrams. Here we present an exactly solvable randomsubcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random satisfiability and coloring problems, and undergoes the same phase transitions. Distance properties, and their relation to ergodicity, are studied. The model can also be generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics. [Preview Abstract] 
Thursday, March 13, 2008 3:54PM  4:06PM 
W39.00008: Random Packing of Platonic Solids Taber Hersum, MartinD. Lacasse, Hubert King While a large amount of literature has been devoted to the packing of spheres, very little is known about the packing of regular polyhedra, such as platonic solids. This presentation will describe numerical work on the packing of model systems in which monodisperse tetrahedra, cubes, dodecahedra, and icosahedra are randomly packed. [Preview Abstract] 
Thursday, March 13, 2008 4:06PM  4:18PM 
W39.00009: Experiments on Random Packings of Tetrahedrons Alexander Jaoshvili, Paul Chaikin We have performed experiments related to the random packing of tetrahedral. The main experiments are MRI scans of tetrahedral dice from which we determine their positions and orientations. We have done a direct analysis of the dice packing. The dice differ from mathematical tetrahedral in having slightly rounded vertices and edges. We have performed a best fit to each die to a perfect tetrahedral and then relaxed the packing to reduce the resulting overlaps. Analyzed data for the dice, the relaxed tetrahedra and simulations include the packing density, the orientational and spatial correlation functions, the average coordination number as well as the distribution of point to face, edge to edge and edge to face contacts. We also study the boundary effects from the walls and the distribution of constraints per particle. Our measurements indicate that random packed tetrahedral have a very small spatial or orientational correlation length. They are more random, that is with smaller and shorter range correlations than what has been found for spheres, or ellipsoids. [Preview Abstract] 
Thursday, March 13, 2008 4:18PM  4:30PM 
W39.00010: Local pressure distributions in the force network ensemble for granular media Brian Tighe We present an analytic calculation of the probability distribution of pressure on individual grains in a static granular packing. We maximize entropy within an ensemble of all possible force networks on a fixed contact network, which incorporates force balance on each grain. Similar to energy in the microcanonical ensemble, the average pressure in each configuration is fixed. Subject to this global constraint alone, entropy maximization would yield a pressure distribution with an exponential tail. We demonstrate that, as a direct consequence of local force balance, there exists an additional global conserved quantity. Maximizing entropy while also respecting this new conserved quantity, we find a pressure distribution that, in frictionless packings, grows as a power law for small pressures and decays with a Gaussian tail. The form of the distribution is confirmed by numerics. As we increase the coefficient of friction, the tail approaches an exponential. [Preview Abstract] 
Thursday, March 13, 2008 4:30PM  4:42PM 
W39.00011: Using MR Elastography to Image Force Chains in a QuasiStatic Granular Assembly L. Sanfratello, S.A. Altobelli, R.P. Behringer, E. Fukushima Questions about the internal structure of dense granular assemblies remain unanswered for lack of 3D experimental data. It is known from 2D observations and from the boundaries of 3D systems that nonuniform stresses are present on container boundaries as well as at the bottom of granular piles. These forces are seen in 2D to be distributed by force chains, where most of the stress is transmitted through a small number of chains with much of the assembly transmitting little or none of the force. However, force chains have yet to be fully visualized in 3D. We propose a variation of magnetic resonance elastography (MRE) to image 3D force chains within a densely packed granular assembly. MRE is an MRI technique whereby small periodic displacements within an elastic material can be measured. Multiple bipolar motion encoding gradients incorporated into a typical pulse sequence, and applied at the frequency of mechanical oscillations, are used to detect the displacements. We have verified our MRE technique using a gel (PermaGel). We now extend this method to image force chains within a 3D granular assembly of particles under stress, on top of which is superimposed a smallamplitude vibration. It is our hypothesis that significant coherent displacements will be found only along force chains while most particles will move randomly. Experimental results will be presented. [Preview Abstract] 

W39.00012: ABSTRACT WITHDRAWN 
Thursday, March 13, 2008 4:54PM  5:06PM 
W39.00013: Contact Percolation in Dense Granular Flow Fuping Zhou, Deniz Ertas Steadystate rheology of spheres are studied in the dense flow regime with threedimensional molecular dynamics simulations in two different geometries: Simple shear flow and gravitydriven chute flow. The same set of constitutive equations, which are only a function of the local dimensionless strain rate, $I$, are found to characterize bulk macroscopic observables such as density, internal Coulomb coefficient and scaled velocity fluctuations in both cases. A transition has been identified at a finite (nonuniversal) value of $I=I_{c}$, corresponding to the percolation transition of the instantaneous contact network. For $I \quad < \quad I_{c}$, an infinite contact network spans the system. The flow dilates and the internal Coulomb coefficient increases with increasing $I$. For $I > \quad I_{c}$, the instantaneous contact network is broken into finite clusters. The system dilates further with increasing $I$ while the internal Coulomb coefficient becomes independent of $I$, resulting in a maximum tilt angle for steady chute flow. Scaled velocity fluctuations exhibit powerlaw dependence on $I$ on both sides of $I_{c}$, with a minimum at the transition. The transition is distinct from the ``jamming'' transition at $I$ = 0 associated with the \textit{rigidity} percolation of the contact network. [Preview Abstract] 
Thursday, March 13, 2008 5:06PM  5:18PM 
W39.00014: Dynamics of the Granular Jamming Transition. Mahesh Bandi, Andras Libal, Michael Rivera, Robert Ecke We experimentally study the force fluctuations felt by a probe disk as it is dragged through a twodimensional bidisperse system of randomly packed photoelastic disks. The fluctuations are studied as a function of packing fraction where the system goes from an unjammed to a jammed state with increasing packing fraction. As the system approaches the Jamming Point, the fluctuations are expected to diverge and become increasingly intermittent. We will present preliminary results of the force fluctuations felt by the probe disk as measured by a force transducer and compare them with visual data as obtained from the forcechains formed by the photoelastic disks. [Preview Abstract] 
Thursday, March 13, 2008 5:18PM  5:30PM 
W39.00015: StickSlip and Granular Force Networks Robert Behringer, Peidong Yu We describe friction/failure experiments for a granular system consisting of photoelastic particles. The goal of the experiments is to provide a microscopic understanding of stickslip friction for an object that is pulled across a granular material. The granular material consists of a photoelastic disks (bidisperse distribution) that are confined to a vertically oriented channel. A slider that is rough at the grain scale is pulled across the upper surface of the material. The pulling is accomplished by a screwdriven platform that is connected to the slider by a spring. Photoelastic image data are acquired by a camera and light source that move with the platform. Nonperiodic stickslip occurs for the regime of parameters studied here. During a stick event, force builds up in a strong network of force chains in the granular material. When one or more of the chains break, a slip event occurs. Energy changes from these events are powerlaw distributed. Analysis of failure points and slip events yields the effective friction coefficients, which are broadly scattered. An alternative description involves modeling the force chain network as a collection of springs. Failure of one spring can lead to a cascade and hence the broad distribution of energy losses. [Preview Abstract] 
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