arXiv subjects

Stanislav N. Kotsev

Publications and source records attributed to Stanislav N. Kotsev.

3 recordsLinked to original sources

arXiv2006

Equilibrium statistics of an inelastically bouncing ball, subject to gravity and a random force

We consider a particle moving on the half line $x>0$ and subject to a constant force in the $-x$ direction plus a delta-correlated random force. At $x=0$ the particle is reflected inelastically. The velocities just after and before reflection satisfy $v_f=-rv_i$, where $r$ is the coefficient of restitution. This simple model is of interest in connection with studies of driven granular matter in a gravitational field. With an exact analytical approach and simulations we study the steady state distribution function $P(x,v)$.

cond-mat.stat-mech↗

arXiv2005

Randomly accelerated particle in a box: mean absorption time for partially absorbing and inelastic boundaries

Consider a particle which is randomly accelerated by Gaussian white noise on the line segment $0<x<1$ and is absorbed as soon as it reaches $x=0$ or $x=1$. The mean absorption time $T(x,v)$, where $x$ and $v$ denote the initial position and velocity, was calculated exactly by Masoliver and Porrà in 1995. We consider a more general boundary condition. On arriving at either boundary, the particle is absorbed with probability $1-p$ and reflected with probability $p$. The reflections are inelastic, with coefficient of restitution $r$. With exact analytical and numerical methods and simulations, we study the mean absorption time as a function of $p$ and $r$.

cond-mat.stat-mech↗

arXiv2004

Equilibrium of a confined, randomly-accelerated, inelastic particle: Is there inelastic collapse?

We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0<x<1. The reflections of the particle from the boundaries at x=0 and 1 are inelastic, with coefficient of restitution r. We have solved the Fokker-Planck equation satisfied by the equilibrium distribution function P(x,v) with a combination of exact analytical and numerical methods. Throughout the interval 0<r<1, P(x,v) remains extended, as opposed to collapsed. The particle is not localized at the boundary. However, for r<0.163 the equilibrium boundary collision rate is infinite, as predicted by Cornell et al., and all moments of the velocity just after reflection from the boundary vanish.

cond-mat.stat-mech↗