Random Packings of Frictionless Particles

O’Hern, Corey S.; Langer, Stephen A.; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1103/physrevlett.88.075507

Cited by 610 publications

(1,069 citation statements)

References 23 publications

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“…In both cases ∆Z goes to zero at jamming: ∆Z ∼ √ ∆φ [5,20,21]. A recent experiment aimed at testing this scaling, albeit in a system with friction, can be found in [22].…”

Section: Isostaticity and Marginally Connected Solidsmentioning

confidence: 99%

The jamming scenario—an introduction and outlook

Liu

Nagel

Saarloos

et al. 2011

Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

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119

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Abstract. The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the paper is devoted to an overview of the findings for model systems of frictionless spheres, focussing on the excess of low-frequency modes as the jamming point is approached. Particular attention is paid to a discussion of the cross-over frequency and length scales that govern this approach. We then discuss the effects of particle asphericity and static friction, the applicability to bubble models for wet foams in which the friction is dynamic, the dynamical arrest in colloids, and the implications for molecular glasses.

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“…In both cases ∆Z goes to zero at jamming: ∆Z ∼ √ ∆φ [5,20,21]. A recent experiment aimed at testing this scaling, albeit in a system with friction, can be found in [22].…”

Section: Isostaticity and Marginally Connected Solidsmentioning

confidence: 99%

The jamming scenario—an introduction and outlook

Liu

Nagel

Saarloos

et al. 2011

Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

Self Cite

119

View full text Add to dashboard Cite

show abstract

“…This model has been wellstudied and it is significantly different from our experimental system with respect to friction, gravity, and the fixed boundaries. We generate mechanically-stable packings via a standard conjugate-gradient method [40]. We then perform simulations for a fixed packing fraction and volume, and we analyze 20 mechanically-stable packings at each packing fraction φ.…”

Section: B Frictionless Simulationsmentioning

confidence: 99%

Extraction of force-chain network architecture in granular materials using community detection

et al. 2015

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Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.

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“…In Ref. [65] the authors showed that the presence of non-self-averaging alters the force distribution function P (F ), which we now consider. In foams and granular materials, P (F ) is measured as a distribution of interparticle normal forces [66,67].…”

Section: Average Force and Instantaneous Force Distribution Functmentioning

confidence: 99%

Dynamical Heterogeneity and Jamming in Glass-Forming Liquids

Lacevic

Glotzer

2004

J. Phys. Chem. B

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The relationship between spatially heterogeneous dynamics (SHD) and jamming is studied in a glass-forming binary Lennard-Jones system via molecular dynamics simulations. It has been suggested by O'Hern et al. [1] that the probability distribution of interparticle forces P (F ) develops a peak at the glass transition temperature Tg, and that the large force inhomogeneities, responsible for structural arrest in granular materials, are related to dynamical heterogeneities in supercooled liquids that form glasses. It has been further suggested that "force chains" present in granular materials may exist in supercooled liquids, and may provide an order parameter for the glass transition. Our goal is to investigate the extent to which the forces experienced by particles in a glass-forming liquid are related to SHD, and compare these forces to those observed in granular materials and other glass-forming systems. Our results are summarized as follows. We find no peak in P (F ) at any temperature in our system, even below Tg. We also find that particles that have been localized for a long time are less likely to experience high relative force and that mobile particles experience higher relative forces at shorter time scales, indicating a correlation between pairwise forces and particle mobility. We construct force chains based on the magnitude of pairwise forces. We find that force chains constructed in this manner are composed of both localized and mobile particles, therefore there is no one-to-one correspondence between force chains as defined here and locally mobile or immobile regions of the liquid. We also find that force chains do not play the same role as force chains in granular materials, but may indicate a difference in the evolution of the local environment of particles with different mobility. We also discuss a possible relationship between force chains found here and the development of string-like motion found in other glass-forming liquids [2,3].

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Random Packings of Frictionless Particles

Cited by 610 publications

References 23 publications

The jamming scenario—an introduction and outlook

The jamming scenario—an introduction and outlook

Extraction of force-chain network architecture in granular materials using community detection

Dynamical Heterogeneity and Jamming in Glass-Forming Liquids

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