Critical Scaling in Linear Response of Frictionless Granular Packings near Jamming

Ellenbroek, Wouter G.; Somfai, Ellák; Hecke, Martin van; Saarloos, Wim van

doi:10.1103/physrevlett.97.258001

Cited by 219 publications

(366 citation statements)

References 26 publications

(65 reference statements)

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“…In line with the arguments given above, it has been found that near the jamming point, one needs to coarse grain over the scale ℓ * to see elastic response emerge [26,27]: as one approaches the jamming point, one has to coarse grain over larger and larger lengths, diverging as ℓ * ∼ 1/∆Z. That elasticity emerges in granular media on long enough scales is also implicitly confirmed by the data of Fig.…”

Section: Behavior or Elastic Constants Near Jammingsupporting

confidence: 68%

“…1.7, which summarizes data for B and G for packings of two-dimensional discs interacting with Hertzian forces [26,27]. The bulk modulus B is clearly seen to scale as p 1/3 [5], which as we argued above is the scaling of the average bond strength for this force law.…”

Section: Behavior or Elastic Constants Near Jammingmentioning

confidence: 94%

“…Another difficulty lies in the fact that the floppy modes which form the basis for the behavior up to scale ℓ * are very disordered so that a weak, elastic-like distortion of such modes is difficult to detect. Nevertheless, it has been discovered that the cross-over length is easily discernable by eye in the response to a point force or to inflation of a local particle [26,27], as Fig. 1.5 illustrates.…”

Section: 23mentioning

confidence: 99%

“…A detailed analysis shows that this range grows proportionally to the length scale ℓ * . From Ellenbroek et al [26,27].…”

Section: 23mentioning

confidence: 99%

“…Squares refer to data obtained from response to a local point force, diamonds to data obtained from a global deformation. After [26,27].…”

Section: Microscopic Criterion For Stability Under Compressionmentioning

confidence: 99%

See 4 more Smart Citations

The jamming scenario—an introduction and outlook

Liu

Nagel

Saarloos

et al. 2011

Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

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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Section: Behavior or Elastic Constants Near Jammingsupporting

confidence: 68%

Section: Behavior or Elastic Constants Near Jammingmentioning

confidence: 94%

Section: 23mentioning

confidence: 99%

“…A detailed analysis shows that this range grows proportionally to the length scale ℓ * . From Ellenbroek et al [26,27].…”

Section: 23mentioning

confidence: 99%

“…Squares refer to data obtained from response to a local point force, diamonds to data obtained from a global deformation. After [26,27].…”

Section: Microscopic Criterion For Stability Under Compressionmentioning

confidence: 99%

See 3 more Smart Citations

The jamming scenario—an introduction and outlook

Liu

Nagel

Saarloos

et al. 2011

Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

119

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Elasticity of Soft Particles and Colloids near the Jamming Threshold

Wyart

2011

Microgel Suspensions

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Assemblies of purely repulsive and frictionless particles, display very curious elastic properties near the jamming transition where the overlap between particles vanish. Although such systems do not contain the long and cross-linked polymeric chains characterizing a rubber, they behave macroscopically in a similar way: the shear modulus G can become negligible in comparison with the bulk modulus B, as observed in emulsions 1 . Numerics 1,2 have established a scaling relationship between the ratio of elastic moduli and the compression in systems of athermal compressed elastic particles. After reviewing recent theoretical results on the microscopic structure of such packings (in particular the coordination number z, the average number of contact per particle) I will propose an explanation for these observations, and explain why the arguments apply both to soft athermal particles and to colloids where elasticity has an entropic nature.

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Jamming in attractive granular media

Lois

Bławzdziewicz

O’Hern

2007

Proc Appl Math and Mech

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The jamming transition is studied numerically in systems of particles with attraction. Unlike the purely repulsive case where a single transition separates the jammed from unjammed phase, the presence of even an infinitesimal amount of attraction yields two distinct transitions: connectivity and rigidity percolation. We measure critical exponents of these two percolation transitions and find that they are different than the corresponding lattice values.Granular materials are collections of macroscopic particles (grains) that are too large to exhibit Brownian motion and dissipate energy when grains interact. Some common examples include sand, rice, powders, and coins. Under dry conditions, and for grains of sufficient mass, interactions between grains are purely repulsive. If the grains are wet (or it is humid) liquid bridges can form between grains in contact and produce an attractive force. Additionally, if the grain mass is small enough, Van der Waals forces become relevant and include an attractive component.Jamming is related to the mechanical response of the system and occurs when the material first becomes rigid. For granular materials with purely repulsive interactions, the jamming transition has been studied extensively in simulations [1,2] and experiments [3]. It occurs at a well defined solid fraction φ J , the stress tensor exhibits power law scalings in (φ − φ J ), and there is a length scale that diverges. The order parameter of the transition is the number of grains in the rigid cluster, and for repulsive granular media the jamming transition at φ J is discontinuous in the order parameter.We carry out numerical simulations to explore the jamming transition in attractive granular media. While it has been argued that the inclusion of attraction will simply induce an effective stress and qualitatively alter the features of the jamming transition, we find important qualitative changes, as well as a second transition. Instead of the single discontinuous transition observed in repulsive systems, attractive systems exhibit two continuous transitions-connectivity percolation and rigidity percolation. These transitions separate three mechanical states: a nonpercolated liquid-like state, a percolated but unjammed state, and a jammed state. Simulations are conducted with between 16 and 1024 grains interacting via the central force given bywhere r is the distance between grains, σ is the distance between the interacting grains at contact, and C is the minimum force. We have considered both monodisperse and bidisperse distributions of σ. While this force law in Equation 1 is discontinuous at r = σ, our main results are not altered when we consider force laws that continuously go to zero over a finite range when r > σ. In the simplest numerical protocol, the system is compressed slowly by increasing the diameter of the grains. Energy is dissipated in each simulation step by quenching to the nearest energy minimum. Both two-dimensional and three-dimensional systems are considered. Connectivity percolation is stud...

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Critical Scaling in Linear Response of Frictionless Granular Packings near Jamming

Cited by 219 publications

References 26 publications

The jamming scenario—an introduction and outlook

The jamming scenario—an introduction and outlook

Elasticity of Soft Particles and Colloids near the Jamming Threshold

Jamming in attractive granular media

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