Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session H8: Focus Session: Jamming in Glasses, Grains, and Gels I |
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Sponsoring Units: GSNP Chair: Andrea Liu, University of Pennsylvania Room: Baltimore Convention Center 314 |
Tuesday, March 14, 2006 11:15AM - 11:27AM |
H8.00001: Random-Packing Dynamics in Dense Granular Flow Martin Z. Bazant, Chris H. Rycroft, Kenneth Kamrin The jamming transition of disordered hard spheres has attracted much recent attention, but how do slightly less dense random packings flow? Here, we propose a simple mechanism based on diffusing ``spots'' of free volume, which cause correlated displacements of neighboring particles. A multiscale algorithm, alternating between coarse-grained spot dynamics and microscopic particle relaxation, can produce realistic flowing packings, and yet is also convenient for mathematical analysis of mean flow and diffusion. We apply the model to granular drainage from a silo and fit three basic parameters (spot size, volume, and diffusivity) to brute-force simulations by the discrete-element method. For a wide silo, we find that the spot simulations can largely reproduce the dynamics of 100,000 frictional, visco- elastic spheres in the DEM simulations, while running over 100 times faster, although a general model for the spot dynamics in different geometries is still lacking. This may come from a stochastic reformulation of Mohr-Coulomb plasticity, where spots undergo random walks along slip planes. [Preview Abstract] |
Tuesday, March 14, 2006 11:27AM - 11:39AM |
H8.00002: Contact Numbers in 2D Granular Systems Matthias Sperl, Trushant Majmudar, Robert Behringer There exists a critical density below which a granular system is no longer mechanically stable. Above this threshold, the particles form stable contacts with each other, while below there are no permanent contacts. We introduce a method to determine the number of contacts per particle with high accuracy: Using stress induced birefringence to identify contact points, the critical density can be identified with an uncertainty of 0.5\%. For a binary mixture of frictional disks we find a discontinuous transition in the number of contacts per particle from zero to a value around 2.5; the transition point is located at an area fraction of 0.845. For higher densities, the increase in the contact number is compatible with a square-root law; however, different exponents close to 0.5 cannot be ruled out yet. At the same transition point, the average force in the system increases linearly with density. [Preview Abstract] |
Tuesday, March 14, 2006 11:39AM - 11:51AM |
H8.00003: A hydrodynamic view on elasticity Ana\"el Lema\^{\i}tre, Laurentiu Pasol, Xavier Chateau Considerable attention was drawn in the recent years on the non-affine displacement fields that accompany elastic deformation of non-crystalline materials. These non-affine displacements bring order unity corrections to the sound speed and Lam\'e constants that would be estimated using the traditional Born-Huang approximation. Bearing on standard homogenization tools and a compatibility theorem, we provide a simple analytical framework to write exact expressions for the elastic constants. We show that, in the thermodynamic limit, exact microscopic expressions reduce to integrals over the pair correlation function. We next show that the corrective terms may be further reduced to a simple integral involving the Green function of the disordered packing. This brings hope to be able to devise systematic procedures to estimate the real elastic constants of amorphous solids. [Preview Abstract] |
Tuesday, March 14, 2006 11:51AM - 12:27PM |
H8.00004: Non-affine elasticity in jammed systems Invited Speaker: Symmetry dictates that perfect crystals should deform homogeneously, or \emph {affinely}, under external load, and computing the elastic moduli from the underlying interaction potential is then straightforward. For disordered materials no such simple procedure exists, and recent numerical works have demonstrated that non-affine corrections can dramatically reduce the naive expectation for the shear modulus in a broad class of disordered systems and may control rigidity loss in the zero pressure limit in purely repulsive systems, i.e. the unjamming transition (c.f. [O'Hern et. al. PRE 68, 011306 (2003)]). We present numerical results and an analytical framework for the study of these non-affine corrections to the elastic response of disordered packings. [Preview Abstract] |
Tuesday, March 14, 2006 12:27PM - 12:39PM |
H8.00005: Effects of Nonaffinity on Jammed Materials Daniel Vernon, Andrea J. Liu, Tom Lubensky If an amorphous solid such as a jammed particle system is subjected to an external stress, the induced displacements of internal particles are necessarily nonaffine. Using numerical minimization procedures, we investigate the response to stress of a disordered packing of purely repulsive spheres. We calculate the correlations of the nonaffine part of the displacements of individual particles just above the jamming threshold (point J)\footnote{C.S.~O'Hern, L.E.~Sibert, A.J.~Liu, and S.R.~Nagel, Phys.\ Rev.\ E {\bf 68}, 011306 (2003)}. We find that these correlations are consistent with those predicted by a continuum theory and verified numerically in simple model random elastic systems\footnote{ B.~DiDonna and T.C.~ Lubensky, Phys.Rev.\ E (to be published)}. [Preview Abstract] |
Tuesday, March 14, 2006 12:39PM - 12:51PM |
H8.00006: Compactivity measurements for a bidimensional granular Frederic Lechenault, Frederic Dacruz, Olivier Dauchot, Eric Bertin We investigate experimentally the statistical properties of the free volumes inside a bidimensional granular packing. Having in mind the more general issue of the measure of intensive thermodynamical parameters in out-of-equilibrium systems, we propose an experimental procedure to access the compactivity of the packing from the free volume distributions over clusters of grains, varying the size of the cluster. Our main result is that the logarithm of the probability to find a given free volume in a cluster scales in a nonextensive way. The compactivity of the packing is then extracted from the corresponding scaling function for two different kinds of grains, and two levels of compaction. [Preview Abstract] |
Tuesday, March 14, 2006 12:51PM - 1:03PM |
H8.00007: How does friction affect the distribution of mechanically stable disk packings? Erik Brown, Guo-Jie Gao, Jerzy Blawzdziewicz, Corey O'Hern In recent work ({\it Physical Review E} {\bf 71} (2005) 061306), we generated nearly all of the mechanically stable packings in small systems composed of up to $20$ bidisperse frictionless disks that interact via normal forces. Complete enumeration allowed us to decompose the probability distribution $P(\phi)$, for obtaining a mechanically stable state at packing fraction $\phi$ into algorithm-dependent and independent contributions, $\beta(\phi)$ and $\rho(\phi)$. $\rho(\phi)$ is the probability density to obtain a distinct mechanically stable packing at $\phi$, while $\beta(\phi)$ is the frequency with which each distinct state occurs. In the present study, we add frictional interactions between grains that vanish when the particles are rest. We will compare distributions of mechanically stable packings in systems with and without friction. In particular, we will comment on whether a well-defined random loose-packed state exists in 2D. [Preview Abstract] |
Tuesday, March 14, 2006 1:03PM - 1:15PM |
H8.00008: Jamming as a critical phenomenon: A field theoretical approach Silke Henkes, Bulbul Chakraborty The proposed jamming diagram (Nature \textbf{396}, 21 (1998)) features a special point, termed point J, along the packing fraction axis where the jamming transition is sharp. Recent simulation work (PRE \textbf{68}, 011306 (2003)) has shown that point J has some features of a critical point. To model the jamming transition along the packing fraction axis, a field theory of frictionless, zero-temperature grain packings in two dimensions has been constructed (PRL \textbf{95}, 198002 (2005)). A mean-field theory involving two order parameters, $\langle \phi \rangle$, the average force per contact, and $\langle z \rangle$, the deviation of the average contact number from its isostatic value, predicts a transition from a jammed to an unjammed phase. The transition is of mixed order with a jump in $\langle \phi \rangle$ and divergent fluctuations. Current work focuses on application of this formalism to simulation data. This allows for the study of spatial fluctuations of $\phi$ and attempts are made to relate these to the concept of force chains. The $\phi$-field emerges as an excellent tool for data analysis and allows quantification of the structures seen in granular packings. Work supported by NSF-DMR 0403997. [Preview Abstract] |
Tuesday, March 14, 2006 1:15PM - 1:27PM |
H8.00009: Emergence of a critical scale in jamming of frictional grains Ellak Somfai, Martin van Hecke, Wouter Ellenbroek, Wim van Saarloos We probe the characteristic scale of two-dimensional frictional granular media close to the jamming transition by studying their vibrational properties as function of the applied pressure $P$ and friction coefficient $\mu$. The density of vibrational states exhibits a crossover from a plateau at frequencies $\omega > \omega^*(P,\mu)$ to a linear growth for $\omega < \omega^*(P,\mu)$. Both for large and for zero friction, this characteristic frequency $\omega^*$ vanishes when $P$ is lowered towards zero. For moderate friction, however, $\omega^*$ saturates at a finite value for $P\downarrow0$. We show that $\omega^*$ is proportional with $\Delta z$, the excess number of contacts per grains relative to the minimally allowed, isostatic value, and that only for zero and infinitely large friction, systems at the jamming threshold have $\Delta z \rightarrow 0$ and hence are critical. [Preview Abstract] |
Tuesday, March 14, 2006 1:27PM - 1:39PM |
H8.00010: Granular dynamics in compaction and stress relaxation Ping Wang, Jasna Brujic, Chaoming Song, David Johnson, Olivier Sindt, Hernan Makse Elastic and dissipative properties of granular assemblies under uniaxial compression are studied both experimentally and by numerical simulations. Following a novel compaction procedure at varying oscillatory pressures, the stress response to a step- strain reveals an exponential relaxation followed by a slow logarithmic decay. Simulations indicate that the latter arises from the coupling between damping and collective grain motion predominantly through sliding. We characterize an analogous ``glass transition'' for packed grains, below which the system shows aging in time-dependent sliding correlation functions. [Preview Abstract] |
Tuesday, March 14, 2006 1:39PM - 1:51PM |
H8.00011: Jamming in Quasi-One Dimensional Systems Prasanta Pal, Corey O'Hern We study the dynamics of hard rods undergoing Brownian motion in narrow channels. Our system is in the shape of a ``figure-8'' and composed of a horizontal and a vertical channel that intersect. In our preliminary studies, we allow the particles to switch at the ends of the channels, but not at the intersection. We calculate the mean-square displacement (msd), the residence time that a particle spends in the intersection, and other important dynamical quantities as a function of the density of rods and system size. In contrast to purely one-dimensional systems, we find that the figure-8 system jams (i.e. the msd possesses a plateau at long times) above a characteristic density that increases with system size. In addition, we have studied the effects of a biasing field on the dynamics and find that the jamming transition is pushed to much lower densities than at zero field. We also compare our results to those found in model glass-forming liquids in two and three dimensions. [Preview Abstract] |
Tuesday, March 14, 2006 1:51PM - 2:03PM |
H8.00012: Voronoi Volumes in Dense Granular Flow Chris H. Rycroft, Martin Z. Bazant The concept of free volume in amorphous materials has a long history, including void-based theories of viscous flow (Eyring 1936), the glass transition (Turnbull and Cohen 1957), and granular drainage (Mullins 1972), although it has become clear that particle displacements are highly correlated and not mediated by single-particle voids. Recently, we have shown that dense random packings can be made to flow cooperatively at nearly uniform density by diffusing ``spots'' of influence and find good agreement with discrete-element (DEM) simulations of frictional spheres in the case of granular drainage. Spots are presumed to carry a slight excess of interstitial volume, but verifying this would require tracking changes in local volume fraction of only a few percent. In flowing random packings, this is a significant computational challenge, which we address here by computing the evolving Voronoi tesselation with an efficient new algorithm. We study the distribution of local Voronoi volumes in simulations of granular drainage using the spot model and DEM and observe some intriguing differences. The Voronoi volume also provides a sensitive measure of whether a given region is ``liquid-like'' of ``solid-like'' in dense granular flow. [Preview Abstract] |
Tuesday, March 14, 2006 2:03PM - 2:15PM |
H8.00013: Correlated Dynamics in Dense Granular Flow Shubha Tewari, Allison Ferguson, Bulbul Chakraborty We report on studies of dense, gravity-driven granular flow via simulations of two-dimensional, inelastic, bidisperse hard disks in a vertical tube geometry. We analyze the flow in terms of coarse-grained velocity and stress fields. We find that as the flow rate decreases towards jamming, there is an increase in the timescale over which stress autocorrelations decay. While the spatial correlations of the stress do not increase significantly, there is a marked increase in the spatial correlation of the velocity, which is indicative of an increasing length scale that approaches the system size as the flow rate decreases. We further analyze the flow in terms of two different four-point correlation functions of the stress and the velocity analogous to those used to characterize dynamical heterogeneities in supercooled liquids. These allow us to extract a dynamical length scale as well as a relaxation time for this system. [Preview Abstract] |
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