Normal and anomalous diffusion in a bouncing ball over an irregular surface

TL;DR

This paper investigates the dynamics of a bouncing ball on an irregular surface, revealing how surface undulations induce random impact forces leading to Brownian-like horizontal motion, including normal and superdiffusion behaviors.

Contribution

It introduces a scaling hypothesis for the probability density function and characterizes the diffusion regimes caused by surface irregularities.

Findings

Surface undulation induces a random horizontal impact component.

Horizontal motion exhibits normal and superdiffusion.

A scaling hypothesis describes the probability density function.

Abstract

The problem of a bouncing ball on a non-planar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in the horizontal distribution of the particle. On the x-axis, normal and super diffusion are observed. For the probability density's functional form, a scaling hypothesis is presented.