Elegance of Disordered Granular Packings: A Validation of Edward’s Hypothesis

Metzger, Philip T.; Donahue, Carly M.

doi:10.1103/physrevlett.94.148001

Cited by 26 publications

(26 citation statements)

References 33 publications

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“…A convenient way to study and characterize force networks is by means of the probability distribution of contact forces, P (f ). This has been the topic of many experimental [11][12][13][14][15][16], theoretical [17][18][19][20][21][22] and computer simulation studies [23][24][25][26][27].…”

Section: Acknowledgmentmentioning

confidence: 99%

Numerical study of the force network ensemble

Eerd¹,

Tighe²,

Vlugt³

2009

Molecular Simulation

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Section: Acknowledgmentmentioning

confidence: 99%

Numerical study of the force network ensemble

Eerd¹,

Tighe²,

Vlugt³

2009

Molecular Simulation

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“…Imposing these constraints poses difficult challenges [34,[62][63][64]. While the force and torque balance are equality constraints and are therefore straightforward to implement, the positivity of forces and the static friction law are both inequality constraints that are notoriously difficult to implement.…”

Section: Statistical Mechanics Of Jammed Statesmentioning

confidence: 99%

The Statistical Physics of Athermal Materials

Henkes

Daniels

et al. 2015

Annu. Rev. Condens. Matter Phys.

138

140

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At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

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“…The question whether a statistical mechanics approach can correctly describe granular systems has sparkled an intense debate in the scientific community in recent years [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Such a statistical mechanics theory of granular matter must be able to connect the observable behavior of large aggregates with the structural and dynamical properties of the grains constituting these systems.…”

Section: Introductionmentioning

confidence: 99%

Emergence of Gamma distributions in granular materials and packing models

2008

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We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such a distribution is the equivalent of the MaxwellBoltzmann's distribution in the kinetic theory of gasses. The comparison with a very extensive set of experimental and simulation data for packings of monosized spherical grains, reveals a remarkably good quantitative agreement with the theoretical predictions for the density fluctuations both at the grain level and at the global system level. Such agreement is robust over a broad range of packing fractions and it is observed in several distinct systems prepared by using different methods. The equilibrium distributions are characterized by only one parameter (k) which is a quantity very sensitive to changes in the structural organization. The thermodynamical equivalent of k and its relation with the 'granular temperature' are also discussed.

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Elegance of Disordered Granular Packings: A Validation of Edward’s Hypothesis

Cited by 26 publications

References 33 publications

Numerical study of the force network ensemble

Numerical study of the force network ensemble

The Statistical Physics of Athermal Materials

Emergence of Gamma distributions in granular materials and packing models

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