Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session Y7: The Statistical Properties of Forces in Jammed Granular Matter |
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Sponsoring Units: GSNP DCMP Chair: Wim van Saarloos, Leiden University Room: 407 |
Friday, March 20, 2009 8:00AM - 8:36AM |
Y7.00001: Statistical Mechanics of Jammed Matter Invited Speaker: Bob Behringer Jammed systems consist of large numbers of macroscopic particles. As such, they are inherently statistical in nature. However, in general, key assumptions of ordinary statistical mechanics need not apply. For instance, energy does not flow in a meaningful way from a thermal bath to such systems. And energy need not be conserved. However, experiments and simulations have shown that there are well defined distributions for such important properties as forces, contact numbers, etc. And new theoretical constructions have been proposed, starting with Edwards et al. The present symposium highlights recent developments for the statistics of jammed matter. This talk reviews the overall field, and highlights recent work in granular systems[1]. Brian Tighe[2] will describe new results from a force ensemble approach proposed recently by Snoeijer et al. Silke Henkes will describe a different force-based ensemble approach that yields a generalized partition function[3]. Eric Corwin will describe state-of-the-art experiments on dense emulsions[4]. And Matthias Schr\"{o}ter will present novel experiments on fluidized suspensions that address the issue of jamming and glassy behavior[5]. So, do we have a complete description of jammed matter? Not yet, but these talks, as well as other exciting developments in the field, show that there has been enormous progress, towards that end. \\[4pt] [1] T. S. Majmudar et al., Nature {\bf 435}, 1079 (2005); Phys. Rev. Lett. {\bf 98} 058001 (2007). \\[0pt] [2] B. P. Tighe, A. R. T. van Eerd, and T. J. H. Vlugt , Phys. Rev. Lett. 100, 238001 (2008). \\[0pt] [3] S. Henkes, C. O'Hern and B. Chakrabory, Phys. Rev. Lett. 99, 038002 (2007). \\[0pt] [4] J. Bruji\'{c} et al., Phys. Rev. Lett. 98, 248001 (2007). \\[0pt] [5] M. Schr\"{o}oter, D. I. Goldman, and H. L. Swinney, Phys. Rev. E 71, 030301(R) (2005). [Preview Abstract] |
Friday, March 20, 2009 8:36AM - 9:12AM |
Y7.00002: A statistical mechanics framework for static granular matter Invited Speaker: Silke Henkes It is still an open question if the formalism of equilibrium statistical mechanics can be extended to athermal granular media. A number of authors have used a maximum entropy approach with a flat measure in configuration space to derive the equivalent of the canonical ensemble for the total volume or for the boundary forces as conserved quantities. We have generalized the force-based ensemble to the full force-moment tensor, and allow for the effects of a measure that is not flat. At the isostatic point, this formalism allows us to compute the force distribution exactly, and we obtain an exponential if we choose a flat measure. We use this result as a baseline to investigate the effects of the measure, and we also study the link to a recently proposed ensemble which incorporates an additional stress-based conserved quantity. At a coarse-grained level, the jamming transition can be studied within this framework by postulating a field-theoretical model for the density of states. We construct a minimal model based on symmetry arguments and a positivity constraint for the pressure, which incorporates force and torque balance through the Airy stress function. Unlike in continuum elasticity, the material constants crucially depend on the imposed boundary stresses. The model predicts that the jamming transition is characterized by a vanishing phase space available to the system as the pressure goes to zero. We are able to calculate correlation functions for the components of the stress tensor and compare them to simulation results. [Preview Abstract] |
Friday, March 20, 2009 9:12AM - 9:48AM |
Y7.00003: Confocal measurements of emulsions leading to a statistical model for frictionless, polydisperse packings Invited Speaker: Eric I. Corwin We use confocal microscopy to image a frictionless, polydisperse emulsion in 3D. Using a deconvolution technique we determine the position and radius of every droplet. This information allows us to calculate the network of nearest neighbors and the local packing fraction around each droplet. Additionally, we exploit an enhanced fluorescence at the points of droplet contacts to determine the contact network. Based on our observations we build a simple statistical model in which the complexity of the global packing is distilled into a local stochastic process. We show that, locally, the packing problem may be reduced to the random assembly of nearest neighbors, followed by a random choice of contacts among them. Our model is based on only two parameters, the available solid angle around each particle and the ratio of contacts to neighbors, which are both directly obtained from experiments. We find that this ``granocentric'' view captures the essential properties of the polydisperse emulsion packing, ranging from the microscopic distributions of nearest neighbours and contacts to local density fluctuations and all the way to the global packing density. This model suggests a general principle of organization for random packing. [Preview Abstract] |
Friday, March 20, 2009 9:48AM - 10:24AM |
Y7.00004: Statistics of force networks Invited Speaker: Brian Tighe We study the statistics of contact forces in the force network ensemble, a minimal model of jammed granular media that emphasizes the role of vector force balance. We show that the force probability distribution can be calculated analytically by way of an analogy to equilibrium ensemble methods. In two dimensions the large force tail decays asymptotically as a Gaussian, distinct from earlier predictions, due to the existence of a conserved quantity related to the presence of local vector force balance. We confirm our predictions with highly accurate statistical sampling -- we sample the force distribution over more than 40 decades -- permitting unambiguous confrontation of theory with numerics. We show how the conserved quantity arises naturally within the context of any constant stress ensemble. [Preview Abstract] |
Friday, March 20, 2009 10:24AM - 11:00AM |
Y7.00005: Measuring the configurational temperature of granular media Invited Speaker: Matthias Schr\"{o}ter Twenty years ago Edwards and Oakeshott suggested developing a statistical mechanics of static granular media based on the idea that the logarithm of the number of mechanically stable states of a specific sample constitutes the relevant entropy [1]. From this entropy then, a configurational temperature, named compactivity, could be derived. However, in the absence of an appropriate thermometer to measure compactivity, the question if it is indeed a relevant state variable remained untested. Only recently it was shown that the steady state volume fluctuations of a periodically driven sample can be used to measure the compactivity of a granular sample including its dependence on volume fraction and surface friction of the particles [2]. This opens up the possibility of studying questions like the existence of a zeroth law of granular thermodynamics or the relationship between compactivity and other forms of granular temperature. \newline [1] Edwards and Oakeshott, Physica A {\bf 157}, 1080 (1989). \newline [2] M. Schr\"{o}ter, D. Goldman, and H. L. Swinney Phys. Rev. E {\bf 71}, 030301(R) (2005) [Preview Abstract] |
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