Related papers: Circle radius distributions determine random close…
We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
To what extent can particulate random media be characterised using direct wave backscattering from a single receiver/source? Here, in a two dimensional setting, we show using a machine learning approach that both the particle radius and…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
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…
Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long history of research, the conditions under…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
We review results about the density of typical lattices in $R^n.$ They state that such density is of the order of $2^{-n}.$ We then obtain similar results for random packings in $R^n$: after taking suitably a fraction $\nu$ of a typical…
Granular packing structures of cohesive micro-sized particles with different sizes and size distributions, including mono-sized, uniform and Gaussian distribution, are investigated by using two different history dependent contact models…
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…
We have studied using the KLUN sample of 5171 spiral galaxies having Tully-Fisher distance moduli, the average radial space distribution of galaxies out to a distance of about 200 Mpc (for H_0=50 km/s/Mpc). One motivation came from the…
We measure the number Omega(phi) of mechanically stable states of volume fraction phi of a granular assembly under gravity. The granular entropy S(phi) = log Omega(phi) vanishes both at high density, at phi = phi_rcp, and a low density, at…
Motivated by problems in high-dimensional statistics such as mixture modeling for classification and clustering, we consider the behavior of radial densities as the dimension increases. We establish a form of concentration of measure, and…
Granular materials often segregate under mechanical agitation, which differs from the expectation of mixing. It is well known that a bidisperse mixture of granular materials in a partially filled rotating cylinder exhibits alternating bands…
In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length…
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings,…
We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are…
We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
In the usual segregation scenario for stable inclined chute flows of bidisperse mixtures of fine and coarse spherical particles, coarse particles rise toward the free surface, forming a coarse-rich region atop the flowing pile. Beyond a…