Collective Motion of Inelastic Particles between Two Oscillating Walls

TL;DR

This paper investigates the collective behavior of inelastic particles between oscillating walls, revealing phase transitions and energy dynamics through theoretical analysis and molecular dynamics simulations.

Contribution

It introduces a novel analytical approach treating the particle system as a pseudo-particle, explaining critical filling fractions and phase changes in vibrated granular media.

Findings

Critical filling fraction decreases with vibration amplitude

System transitions to a solid-like phase at critical points

Resonant solutions explain energy stability

Abstract

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a solid-like phase with particles clustered in their compact form. Molecular dynamics simulations of the system show that the critical filling fraction is a decreasing function of vibration amplitude independent of vibration frequency, which is consistent with previous experimental results. This study considers the entire group of particles as a giant pseudo-particle with an effective size and an effective coefficient of restitution. The N-particles system is then analytically treated as a one-particle problem. The critical filling fraction's dependence on vibration amplitude can be explained as a necessary condition for a stable resonant solution. The fluctuation to the system's mean flow energy is also studied to show the relation between the granular temperature and the system phase.