The existence of a static lengthscale that grows in accordance with the dramatic slowing down observed at the glass transition is a subject of intense interest. Due to limitations on the relaxation times reachable by standard molecular dynamics techniques (i.e. a range of about 4-5 orders of magnitude) it was until now impossible to demonstrate a significant enough increase in any proposed length scale. In this Letter we explore the typical scale at unprecedented lower temperatures. A swap Monte Carlo approach allows us to reach a lengthscale growth by more than 500%. We conclude by discussing the relationship between the observed lengthscale and various models of the relaxation time, proposing that the associated increase in relaxation time approaches experimental values.
The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, daunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.
Emergent interparticle interactions in thermal amorphous solidsGendelman, O.; Lerner, E.; Pollack, Y.G.; Procaccia, I.; Rainone, C.; Riechers, B. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Amorphous media at finite temperatures, be them liquids, colloids, or glasses, are made of interacting particles that move chaotically due to thermal energy, continuously colliding and scattering off each other. When the average configuration in these systems relaxes only at long times, one can introduce effective interactions that keep the mean positions in mechanical equilibrium. We introduce a framework to determine the effective force laws that define an effective Hessian that can be employed to discuss stability properties and the density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these experience zero forces when not in contact and infinite forces when they touch. Close to jamming we recapture the effective interactions that at temperature T depend on the gap h between spheres as T /h [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006)]. For hard spheres at lower densities or for systems whose binary bare interactions are longer ranged (at any density), the emergent force laws include ternary, quaternary, and generally higher-order many-body terms, leading to a temperature-dependent effective Hessian.
The determination of the normal and tangential forces between frictional disks from visual data was considered insoluble for three main reasons: (i) the tangential forces that accumulate at contacts are history-dependent and were believed not to be obtainable from a visual [1], (ii) the number of mechanical constraints, i.e the vanishing of the net force and the torque on each disk, is much smaller than the number of inter-disk normal and tangential forces, and the problem is thus under-determined. (iii) In many realistic granular systems (sand, metallic disks etc.) the compression is so small that the change in the distances between centers of mass cannot be measured accurately. In the context of an array of disks of diameters σ i , one can determine the positions of the center of mass r i relatively easily. But if the disks are highly incompressible, it is not possible to determined accurately the difference between the nominal distance σ i + σ j and the actual distance |r i −r j |. In Ref.[2] it was shown that given the directions of the vectors connecting the centers of masses of the disks (but not the actual distances between the center of mass) and the external forces on the disks, all the normal and tangential forces can be determined exactly provided the normal forces are linear.
In very recent work the mean field theory of the jamming transition in infinite-dimensional hard sphere models was presented. Surprisingly, this theory predicts quantitatively the numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement is nongeneric: only for hard sphere models does it happen that sufficiently close to the jamming density (at any temperature) the effective interactions are binary, in agreement with mean field theory, justifying the truncation of many-body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in many-body effective interactions that are not mean field at any density, making the d=∞ results not applicable.
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