Random particle packing with large particle size variations using reduced-dimension algorithms

In this thesis I present most of the results obtained during my PhD, where I worked on different subjects regarding jamming in systems of frictionless spheres. In particular, I focused on microscopic properties of jammed packings, such as the distribution of contact forces and interparticle gaps, as well as the single particle dynamics that occur near the jamming point. Several of these results have already been presented in Refs. [1,2], but here I include a more detailed ana...

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why the isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to nonspherical particles. We...

We analyze the large scale structure and fluctuations of jammed packings of size disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small wavevectors, the compressibility displays an anomalous linear dependence at low wavectors and vanishes when q -> 0. We show that such behavior occurs because jammed packings of size disperse spheres have no bulk fluctuations of the volume fra...

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically-augmented surface area rather than the volume of the window. The structure factor shows an unusual non-analytic linear dependence near the origin, $S(k)\sim|k|$. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-la...

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that conform to a given pair correlation function g(r). Such a study is required to observe the basic constraints of non-negativity for g(r) as well as for its structure factor S(k). The hard sphere case receives special attention, to help identify w...

We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination numbers between the species, and (ii) the dependence of the coordination numbers with the concentration of species; quantities that are calculated analytically. The model predicts the density of random close packing and random loose packing o...

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 ...

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...

The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of neighbors define channels, which are relevant for the concept of caging. The analysis of the channel size distribution is shown to be very useful in distinguishing between gaseous, liquid, partially and fully crystallized, and glassy (random) jamme...

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