Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Q2: Jamming |
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Sponsoring Units: DCMP GSNP Chair: Wouter Ellenbroek, University of Pennsylvania Room: Oregon Ballroom 202 |
Wednesday, March 17, 2010 11:15AM - 11:51AM |
Q2.00001: Rigidity and Excitations in Jammed Solids Invited Speaker: Jamming particles together can produce a rigid structure. As the geometrical constraints between particles become important, a fluid can lose its ability to flow. The jamming transition, at least at zero temperature for spheres, is sharp and has properties associated with both first and second order transitions. We have studied the properties of solids created by jamming. We find that they are unusual and provide a new way of thinking about disordered systems generally. I will give an overview of the properties of these systems, concentrating on the anharmonic as well as the anharmonic properties of the normal-mode excitations. [Preview Abstract] |
Wednesday, March 17, 2010 11:51AM - 12:27PM |
Q2.00002: Jamming transition as probed by quasi-static shear simulations Invited Speaker: This contribution deals with flow properties of amorphous colloidal or granular materials close to their jamming threshold. There is by now ample evidence that the (athermal) jamming transition (``point J'') can be thought of as a critical phenomenon with a divergent length-scale. While much effort has been put into characterizing the critical properties of the arrested solid state, only little is known about the actual physical mechanisms that lead to this arrest when coming from the flowing side. We try to fill this gap by studying the particle dynamics in the flowing state. We show how the motion of single particles is connected to the growth of dynamical heterogeneities. Approaching point J from below we find a diverging dynamical susceptibility. The associated particle mobilities show signs of strong spatial correlations, with patterns involving string- and loop-like excitations as well as compact regions of active particles. As a result we can develop an intuitive and appealing picture that describes flow in terms of a ``liquid of temporarily rigid clusters''. This picture of how flow is realized below point J contrasts well with the traditional view of plastic flow in ``soft-glassy'' materials, where flow is described by the failure of localized defects embedded in an elastic solid. We argue that this latter behavior is observed in the yield-stress flow regime above point J. [Preview Abstract] |
Wednesday, March 17, 2010 12:27PM - 1:03PM |
Q2.00003: Random close packing of polydisperse jammed emulsions Invited Speaker: Packing problems are everywhere, ranging from oil extraction through porous rocks to grain storage in silos and the compaction of pharmaceutical powders into tablets. At a given density, particulate systems pack into a mechanically stable and amorphous jammed state. Theoretical frameworks have proposed a connection between this jammed state and the glass transition, a thermodynamics of jamming, as well as geometric modeling of random packings. Nevertheless, a simple underlying mechanism for the random assembly of athermal particles, analogous to crystalline ordering, remains unknown. Here we use 3D measurements of polydisperse packings of emulsion droplets to build a simple statistical model in which the complexity of the global packing is distilled into a local stochastic process. From the perspective of a single particle the packing problem is reduced to the random formation of nearest neighbors, followed by a choice of contacts among them. The two key parameters in the model, the available space around a particle and the ratio of contacts to neighbors, are directly obtained from experiments. Remarkably, we demonstrate that this ``granocentric'' view captures the properties of the polydisperse emulsion packing, ranging from the microscopic distributions of nearest neighbors and contacts to local density fluctuations and all the way to the global packing density. Further applications to monodisperse and bidisperse systems quantitatively agree with previously measured trends in global density. This model therefore reveals a general principle of organization for random packing and lays the foundations for a theory of jammed matter. [Preview Abstract] |
Wednesday, March 17, 2010 1:03PM - 1:39PM |
Q2.00004: Jamming of Ellipsoids: Abundance of Zero-Frequency Modes and What to Do With Them Invited Speaker: As spheres are distorted into ellipsoids of revolution, their aspect ratio, $\epsilon$ departs from the symmetric value, $\epsilon = 1$. At the jamming transition, the average number of contacts per particle, $Z(\epsilon)$, increases {\em continuously} from the isostatic value for spheres, $Z_{\rm iso}(\epsilon = 1)=6$, as $|\epsilon - 1|$ is increased. This leads to an apparent paradox: as soon as $\epsilon$ departs from unity, the number of contacts is considerably less than that needed for stability according to the Maxwell rigidity criterion: $Z_{\rm iso}(\epsilon \neq 1)=10$. There are therefore many unconstrained and nontrivial rotational degrees of freedom that give rise to new features in the vibrational spectrum: zero-frequency modes are gradually mobilized into a new rotational band as $|\epsilon - 1|$ is increased. For small $|\epsilon - 1|$, this rotational band is separated by a gap from the translational band found for simple spheres. Like many singular points, the spherical jamming transition controls a broader class of behavior but in an unusual and nontrivial way. At larger distortions, the two bands merge producing vibrations with a mixed character. Here I present detailed studies of the evolution of the spectrum and the implications for the mechanical properties of these packings [1]. [1] Z. Zeravcic, N. Xu, A. J. Liu, S. R. Nagel and W. van Saarloos, {\em Europhys. Lett.} 87, 26001 (2009). [Preview Abstract] |
Wednesday, March 17, 2010 1:39PM - 2:15PM |
Q2.00005: Elasticity and response in nearly isostatic periodic lattices Invited Speaker: The emergence of rigidity, especially when complicated by disorder, is a subtle phenomenon that occurs in a wide variety of systems. Isostatic lattices, such as the $d$-dimensional hypercubic lattice and the $2d$ kagome lattice with nearest neighbor springs, in which the number of contacts $z$ per particle in $d$-dimensions is equal to $z_c=2d$, provide simple models, which inform us about systems like jammed solids, glasses, colloidal suspensions, and foams, for the analytic study of general features of the onset of rigidity. Isostatic lattices are marginally stable and may exhibit a non-extensive number of zero modes that can be removed by the addition of bond-bending forces, negative pressure, or additional springs. We use the coherent potential approximation (CPA) to study the onset of rigidity induced by randomly adding next-nearest-neighbor ($NNN$) bonds to the square and kagome lattices, and we relate the results to the random packings of frictionless spheres at point J. We identify a characteristic frequency scale $\omega^*$ and length scale $l^*$ and show that within the CPA they scale, respectively, as $\Delta z$ and $\Delta z^{-1}$ where $\Delta z = z - z_c$. This result, which replicates results near jamming, is a result of strongly nonaffine elastic response at small $\Delta z$. We find that the frequency-dependent effective $NNN$ spring constant $\kappa$ obeys a scaling relation $\kappa ( \omega)/\kappa (0) = f(\omega/\omega*)$, where $\kappa ( 0 ) \sim (\Delta z)^2$. In the square lattice the shear modulus $G(\omega)$ is equal to $\kappa ( \omega)$, whereas in the kagome lattice, the shear modulus $G_0$ at $\Delta z = 0$ is finite and proportional to the spring constant of nearest-neighbor bonds, and $G(\omega) -G_0 \sim \kappa ( \omega)$, Finally, we show that the CPA exhibits strong phonon scattering for $\omega >\omega^*$ indicating a Ioffe-Regel limit for heat transport. This work was supported by NSF DMR 0804900. [Preview Abstract] |
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