Related papers: Hard spheres dynamics: weak vs hard collisions
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…
Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different…
The simplicity of hard spheres as a model system is deceptive. Although the particles interact solely through volume exclusion, that nevertheless suffices for a wealth of static and dynamical phenomena to emerge, making the model an…
We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation…
We present a model for the motion of hard spherical particles on a two dimensional surface. The model includes both the interaction between the particles via collisions, as well as the interaction of the particles with the substrate. We…
Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential…
Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation.…
The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium molecular dynamics simulations and direct simulation Monte Carlo. In the molecular dynamics simulations Lees-Edwards boundary conditions are used to…
Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even…
We characterize a system of hard spheres with a simple collision rule that breaks time reversal symmetry, but conserves energy. The collisions lead to an a-chiral, isotropic, and homogeneous stationary state, whose properties are determined…
A set of hard spheres with tangential inelastic collision is found to reproduce observations of real and numerical granular matter. After time is scaled so as to cancel energy dissipation due to inelastic collisions out, inelastically…
When granular systems are modeled by frictionless hard spheres, particle-particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the…
While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…
The effects of purely elastic collisions on the dynamics of heavy inertial particles is investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of inter-particle separations and relative…
Consider a microscopic system of $N$ hard spheres that are initially independent (modulo the exclusion condition on particle positions) and identically distributed in $\mathbb{R}^3$. When the number $N$ of particles goes to infinity and the…
Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and…
We examine the dynamics of hard spheres and discs at high packing fractions in two and three dimensions, modeling the simplest systems exhibiting a glass transition. As it is well known, cooperativity and dynamic heterogeneity arise as…
The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent…
The finite size effect of electron and nucleus is accounted for in the model of atom. Due to their hard sphere repulsion the energy of the 1s orbital decreases and the corrections amount up to 8% in Uranium. Several models for boundary…
A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low density…