Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session V39: Focus Session: Jamming I: Theory |
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Sponsoring Units: GSNP Chair: Wouter Ellenbroek, University of Pennsylvania Room: Morial Convention Center 231 |
Thursday, March 13, 2008 11:15AM - 11:27AM |
V39.00001: Anisotropic power-laws in sheared amorphous solids Craig Maloney, Mark Robbins The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Spatial correlations in the strain field are highly anisotropic and show apparent power-law behavior with a dramatic angular dependence of the effective scaling exponent. The strongest correlations are for wavevectors roughly perpendicular to the line of maximum resolved shear stress with systematic deviations from this which can be understood in terms of a Mohr-Coulomb effect. These results shed light on the nature of the so-called Jamming transition, supporting the notion that the dense steady flowing state is effectively critical in the slow-driving limit, and provide important, testable predictions for experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, etc., which can directly access the particle displacements. [Preview Abstract] |
Thursday, March 13, 2008 11:27AM - 11:39AM |
V39.00002: Apparent critical scaling for a steady-state sheared glass Thomas Haxton, Andrea Liu We conducted simulations of a two-dimensional model glass at nonzero temperature under steady-state shear, and calculated the shear stress and shear viscosity as a function of temperature, shear rate and density. Over a dynamic range of two to three decades, we find excellent collapse of the data using critical scaling of the shear viscosity as a function of the distance from the jamming surface in the parameter space spanned by temperature, shear stress, and density. The shear viscosity can be rescaled to collapse onto a master function of the rescaled stress, where the scale factors are powers of the displacement in parameter space from the critical jamming surface. The master function separates into two branches, a high-temperature or low-density branch that approaches a finite rescaled viscosity at low stress, and a low-temperature or high-density branch that appears to diverge at a finite value of the rescaled stress. These results are consistent with those of Olsson and Teitel[1], who found scaling collapse near the zero-temperature, zero shear-stress jamming transition. We compare our results to mode-coupling calculations of sheared systems. [1] P. Olsson and S. Teitel, Phys. Rev. Lett. 99, 178001 (2007). [Preview Abstract] |
Thursday, March 13, 2008 11:39AM - 11:51AM |
V39.00003: Predicting the Viscosity of a Supercooled Liquid Xi Lin We present an atomistic description of the viscosity of a supercooled liquid capturing the highly non-Arrhenius temperature variation for which no previous calculation has been given. A temperature dependent activation energy for structural relaxation is derived by mapping the potential energy surface and extracting saddle-point configurations and associated atomic coordinates. This essential information is combined with the temperature variation of an effective local energy minimum (inherent structure) to describe shear relaxation by thermal activation. For a binary Lennard-Jones model the calculated viscosity shows a characteristic crossover from strong (Arrhenius) to fragile (highly non-Arrhenius) behavior upon appreciable undercooling, followed by a second crossover from fragile back to strong behavior on approaching the glass transition temperature, both features we believe to be generic. Analysis of atomic displacements associated with barrier crossing in the fragile regime suggests a scenario of correlated motions along a chain of particles as the underlying mechanism for slow viscous relaxation in glassy states. [Preview Abstract] |
Thursday, March 13, 2008 11:51AM - 12:27PM |
V39.00004: Jamming in systems with attraction Invited Speaker: Many materials jam. As density increases or temperature decreases, structural relaxation becomes sluggish and the system approaches mechanical equilibrium without spatial ordering. The concept of a universal jamming transition and the conjecture that the mechanical response at zero temperature is linked to slow dynamics at non-zero temperature has inspired research in a variety of glassy materials such as colloidal suspensions, emulsions, granular media and foams. While most recent theoretical and simulation studies of the jamming transition have focused on systems with purely repulsive interactions, many materials also possess attractive forces. I will present our recent numerical results on the jamming transition in particulate systems with attractive interactions. At zero temperature, instead of the single discontinuous jamming transition observed in purely repulsive systems, attractive systems exhibit two second-order transitions---connectivity and rigidity percolation---which belong to different universality classes than their lattice counterparts. This observation also holds for low temperature before diffusion and activation/bond-breaking become relevant. At higher temperatures, the universality class of the jamming transition can depend on the age of the system. Finally, I will discuss a proposed phase diagram for gelation and rigidification in the temperature- density plane. [Preview Abstract] |
Thursday, March 13, 2008 12:27PM - 12:39PM |
V39.00005: Is there a connection between structure and heterogeneous dynamics in supercooled liquids? William Krekelberg, Venkat Ganesan, Thomas Truskett Structurally arrested (jammed or glassy) states are often prepared from supercooled fluids, though there a number of open questions regarding how that process occurs. One involves explaining why modest increases in structural order accompany the pronounced slowing of liquid-state dynamics near structural arrest. Another involves understanding why self-diffusion in deeply supercooled fluids occurs much faster than would be predicted from knowledge of the viscosity and the Stokes-Einstein relation. Single-particle displacements become heterogeneous near the glass transition, but corresponding structural heterogeneities have been difficult to identify. Collectively, these observations call into question the general prospect of understanding and predicting dynamical behavior of liquids based on structural information. In this talk, we present simulation data on several model systems that show that the dynamics of supercooled liquids can be quantitatively correlated to structure in a simple way. Specifically, we show that the breakdown of the Stokes-Einstein relationship reflects simple and distinct couplings between structure, viscosity, and diffusivity in the supercooled fluid. We also demonstrate how heterogeneous dynamics correlate with dynamically heterogeneous structure. [Preview Abstract] |
Thursday, March 13, 2008 12:39PM - 12:51PM |
V39.00006: An effective field theory for soft granular matter Silke Henkes, Corey O'Hern, Bulbul Chakraborty Work on packings of soft spheres (PRE \textbf{68}, 011306 (2003)) has demonstrated the existence of a jamming transition and has highlighted the need for a general statistical framework to describe granular packings. We have shown that a statistical ensemble, based on conservation properties of the global stress tensor, is consistent with simulated packings of frictionless disks (PRL \textbf{99}, 038002 (2007)). We construct an effective field theory based on this ensemble, in the spirit of an earlier attempt (PRL \textbf{95}, 198002 (2005)). The field theory is constructed by synthesizing results from simulations into one functional form for the effective free energy. We will describe ongoing efforts to derive this form by combining scaling ideas with microscopic properties of the packings. [Preview Abstract] |
Thursday, March 13, 2008 12:51PM - 1:03PM |
V39.00007: Jamming and correlated percolation on energetically-evolved graphs Shiliyang Xu, Jennifer Schwarz Numerical simulations suggest that the zero-temperature jamming transition in repulsive soft spheres has an unusual mixed second-order/first-order character whose exponents appear to be in the same universality class as mean-field $k$-core percolation. In $k$-core percolation model, every occupied site must have at least $k$ occupied neighbors. The $k$-core analogy of jamming is similar to the kinetically constrained analogy of the glass transition where the geometric constraint of $k=d+1$ contacts needed for local mechanical stability drives the transition. We now introduce energetics explicitly into the analogy by investigating $k$-core percolation on a graph where edges are dynamically evolved with the goal of minimizing an xy-model-type interaction between a node and each of its neighbors. The xy-model-type interaction captures the angular arrangements of jammed configurations at the onset of jamming. Moreover, the graph dynamics captures nonequilibrium aspects of jamming that cannot be captured by static approaches such as a version of rigidity percolation with repulsive forces only. [Preview Abstract] |
Thursday, March 13, 2008 1:03PM - 1:15PM |
V39.00008: A ``Hamiltonian'' for Jammed Granular Matter Chaoming Song, Ping Wang, Hernan A. Makse We introduce a ``Hamiltonian''-like function, called the volume function, to describe the microstates of jammed matter such as granular materials and emulsions from a geometrical point of view. We present a theory of volume fluctuations and derive the volume function defined in terms of the available free volume of the particles in the jammed systems. At the microscopic level the volume function provides an analytical formula for the calculation of the Voronoi volume associated with a single particle in terms of field variables. We then coarse-grain the volume function over a scale of a few particle diameters and provide a mesoscopic volume function which is now solely a function of the coordination number. We predict an exponential tail in the distribution of volumes in general agreement with experiments. Our analysis allows the calculation of macroscopic obervables using the statistical mechanics of jammed states when it is supplemented by the condition of mechanical equilibrium of jamming. [Preview Abstract] |
Thursday, March 13, 2008 1:15PM - 1:27PM |
V39.00009: Vacancy localization in the square dimer model Mark Bowick, Jeremie Bouttier, Emmanuel Guitter, Monwhea Jeng We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. The motion of a vacancy induced by dimer slidings is analyzed including the size distribution of the domain accessible to the vacancy and the probability for a vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. In a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} $. The resultant weak localization of vacancies still allows for unbounded diffusion with a diffusion exponent related to that of diffusion on spanning trees. [Preview Abstract] |
Thursday, March 13, 2008 1:27PM - 1:39PM |
V39.00010: Velocity fluctuations in dense granular flows John Drozd, Colin Denniston We use simulations to investigate velocity fluctuations in dry granular flow. Our system is comprised of mono- and poly-disperse sets of spherical grains falling down a vertical chute under the influence of gravity. We find three different classes of velocity distributions depending on factors such as the local density. The class of the velocity distribution depends on whether the grains are in a free-fall, fluid or glassy state. The analytic form of the distributions match those that have been found by other authors in fairly diverse systems. Here, we have all three present in a single system in steady-state. Power-law tails that match recent experiments are also found but in a transition area suggesting they may be an artifact of crossover from one class of velocity distribution to another. By studying both fast and slow flowing systems, we find that the velocity fluctuations are related to collision times by a scaling with the glass transition temperature. We measure collision time distributions along the height of the chute and find that the collision time distributions evolve from exponential tails into power-laws. This suggests that the particles may be forming clusters as they approach the glass state which may correspond to a second order dynamical phase transition. [Preview Abstract] |
Thursday, March 13, 2008 1:39PM - 1:51PM |
V39.00011: Energy Transport of Jammed Systems Ning Xu, Vincenzo Vitelli, Matthieu Wyart, Andrea Liu, Sidney Nagel We performed computer simulations to calculate the thermal diffusivity of vibrational modes in jammed sphere packings near the jamming transition (Point J). The diffusivity $d(\omega)$ is low for all modes, including those at low frequency $\omega$, and appears to be finite in the zero frequency limit. In ordinary solids, by contrast, $d(\omega)$ diverges at low frequencies due to long wavelength plane waves. The low- frequency modes near Point J are very different from plane waves: they are quasi-localized with large anharmonic corrections. Thus, these modes, which can be viewed as harmonic precursors to two-level systems, are poor conductors of energy. [Preview Abstract] |
Thursday, March 13, 2008 1:51PM - 2:03PM |
V39.00012: Testing ergodicity in dense granular systems Guo-Jie Gao, Jerzy Blawzdziewicz, Corey O'Hern The Edwards' entropy formalism provides a statistical mechanical framework for describing dense granular systems. Experiments on vibrated granular columns and numerical simulations of quasi- static shear flow of dense granular systems have provided indirect evidence that the Edwards' theory may accurately describe certain aspects of these systems. However, a fundamental assumption of the Edwards' description---that all mechanically stable (MS) granular packings at a given packing fraction and externally imposed stress are equally accessible---has not been explicitly tested. We investigate this assumption by generating all mechanically stable hard disk packings in small bidisperse systems using a protocol where we successively compress or decompress the system followed by energy minimization. We then apply quasi-static shear flow at zero pressure to these MS packings and record the MS packings that occur during the shear flow. We generate a complete library of the allowed MS packings at each value of shear strain and determine the frequency with which each MS packing occurs. We find that the MS packings do not occur with equal probability at any value of shear strain. In fact, in small systems we find that the evolution becomes periodic with a period that grows with system-size. Our studies show that ergodicity can be improved by either adding random fluctuations to the system or increasing the system size. [Preview Abstract] |
Thursday, March 13, 2008 2:03PM - 2:15PM |
V39.00013: Anomalously Slow Dynamics in the Manhattan Model Prasanta Pal, Corey O'Hern We study the Brownian dynamics of hard rods in a Manhattan-like traffic grid, in which a series of narrow horizontal and vertical channels intersect at right angles and particles are forbidden from turning at the intersections. We measure the mean-square displacement (msd) as a function of packing fraction $\phi$ and determine the $\phi_g$ at which dynamical arrest occurs as a function of system size, number of intersections, and topology of the grid. We observe that structural relaxation occurs via a complex out-of-equilibrium process in which particles occupy locally dense regions of the grid and then undergo a first passage process. We compare our results for the msd and $\phi_g$ to that found in model glass-forming liquids in two and three dimensions. [Preview Abstract] |
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