Is Random Close Packing of Spheres Well Defined?

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 ...

Disordered jammed packings under confinement have received considerably less attention than their \textit{bulk} counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes, and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E {\bf 82}, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic wit...

The maximally random jammed (MRJ) state is the most random configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors $S(\mathbf{k})$ tend to zero as the wavenumber $|\mathbf{k}|$ tends to zero. Here, we show that generating high-quality strictly jammed states for space dimensions ...

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings a...

We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using volume fluctuation analysis and graph theoretical methods. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter. At the mesoscopic level the entropy vanishes at ...

We propose an interpretation of the random close packing of granular materials as a phase transition, and discuss the possibility of experimental verification.

Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the densest packings; Crystallographers and chemists have been fascinated by the lattice packings for centuries as well. On the other hand, physicists, geologists, material scientists and engineers have been challenged by the mysterious random packi...

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in 2d using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2d and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability $P(\phi)$ for obtaining a collectively jammed state at a particular pa...

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network's clustering occurring at the packing fractions (fraction of volume occupied by the spheres respect to the total volume, $\rho$) corresponding to the so called Random Loo...

We present an analytical derivation of the volume fractions for random close packing (RCP) in both $d=3$ and $d=2$, based on the same methodology. Using suitably modified nearest neigbhour statistics for hard spheres, we obtain $\phi_{\mathrm{RCP}}=0.65896$ in $d=3$ and $\phi_{\mathrm{RCP}}=0.88648$ in $d=2$. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This order-...