Rare events for low energy domain in bouncing ball model

TL;DR

This paper investigates the probability distribution of rare multiple collisions in a chaotic bouncing ball model, revealing a scale-invariant power law behavior in the low energy domain.

Contribution

It demonstrates that the distribution of successive collisions follows a power law that remains invariant under changes in control parameters in the bouncing ball model.

Findings

Probability distribution follows a power law.

Distribution is scale-invariant with respect to control parameters.

Rare successive collisions are characterized by this power law.

Abstract

The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control parameters. The model considers the dynamics of a bouncing ball particle colliding elastically with two rigid walls. One is fixed, and the other one moves periodically in time. The dynamics is described by a two-dimensional mapping for the variables velocity of the particle and phase of the moving wall. For a specific combination of velocity and phase, the particle may experience a type of rare collision named successive collisions. We show that a power law describes the probability distribution of the multiple impacts and is scaling invariant to the control parameter.