Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise.

https://arxiv.org/pdf/cond-mat/0003416.pdf

Is random close packing of spheres well defined

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1405&context=physastro_pubs

Random and cooperative sequential adsorption

When a can containing one large ball and a number of smaller ones is shaken, the large ball rises to the top, even when the larger ball is more dense than the others. Similarly, a mixture of different sized particles will segregate by size when shaken. An adaptation of the Monte Carlo method is used to study this size segregation. The results show the local, geometric mechanism by which the segregation is produced. Segregation by size is to be distinguished from the more obvious sifting process which occurs when tiny grains filter down through the interstices between large particles.

Why the Brazil nuts are on top: Size segregation of particulate matter by shaking

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity. \textcopyright{} 1996 The American Physical Society.

/pdf/model-for-collisions-in-granular-gases-30o51d5xir.pdf

Model for collisions in granular gases

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ∼ L α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no e...

Heat transport in low-dimensional systems

A new computer simulation of random packing of spheres is applied to two- and three-dimensional problems with a uni-directional gravitational force.

Random Packing of Equal and Unequal Spheres in Two and Three Dimensions

Independent heat reservoirs are postulated to interact with the atoms in a harmonic system as a substitute for real nonharmonic forces. The temperature of each reservoir is determined by the condition that it exchange no energy with the system in the steady state. An explicit solution for the covariance matrix is obtained for the case of the linear chain. The thermal conductivity is finite and inversely proportional to the coupling to the reservoirs.

Simulation of Nonharmonic Interactions in a Crystal by Self-Consistent Reservoirs

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Random Packing of Equal and Unequal Spheres in Two and Three Dimensions

Simulation of Nonharmonic Interactions in a Crystal by Self-Consistent Reservoirs