January 23, 2023
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in $d=3$ dimensions, and thus obtain an estimate of the random close packing (RCP) volume fraction, $\phi_{\textrm{RCP}}$, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations, using both our own and results reported in previous works, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity, using three different particle size distributions, namely the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions, when using as reference our own simulations and results from the literature. In particular, we find $\phi_{\textrm{RCP}}$ to increase monotonically with the relative standard deviation, $s_{\sigma}$, of the distribution, and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for $\phi_{\textrm{RCP}}$ that quantitatively captures a distribution-independent regime for $s_{\sigma} < 0.5$. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.
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February 14, 2014
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January 6, 2011
We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density $\phi$ as low as 0.6. This is well below the value of 0.64 associated with the maximally random jammed state and entirely unrelated to the ill-defined ``random loose packing'' state density. Specifically, collectively jammed packings are generated with a very narrow d...
January 29, 2010
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how ...
August 16, 2006
We present the first study of disordered jammed hard-sphere packings in four-, five- and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions $d=4$, 5 and 6 to be $\phi_{MRJ} \simeq 0.46$, 0.31 and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form $\phi_{MRJ}= c_1/2^d+(c_2 d)/2^d$, where ...
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March 24, 2009
We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the system gets arrested into a glass state as the relaxation time exceeds the compression speed. Further compression yields a jammed configuration that can be regarded as the infinite pressure configuration of that glass state. Consequently, we...
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August 15, 2008
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications spanning from the mathematician's pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack ...
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