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

Abstract

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 $v_f=-r{v}_i$, 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 $P(x,v)$.

15 pages + 5 figures

References in corpus (3)

• Steady state velocity distributions of an oscillated granular gas
• Randomly accelerated particle in a box: mean absorption time for partially absorbing and inelastic boundaries
• Equilibrium of a confined, randomly-accelerated, inelastic particle: Is there inelastic collapse?

Cited by in corpus (5)

• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• First-passage and extreme-value statistics of a particle subject to a constant force plus a random force
• A statistical physics viewpoint on the dynamics of the bouncing ball
• Finite-time blowup of a Brownian particle in a repulsive potential
• Collective Motion of Inelastic Particles between Two Oscillating Walls