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

Ana Laura Boscolo¹, Valdir Barbosa da Silva Junior¹, Luiz Antonio Barreiro¹

¹Institute of Geosciences and Exact Sciences, Physics Department, São Paulo State University (Unesp), CEP 13506-900, Rio Claro, São Paulo, Brazil.

Physical Review. E

|May 18, 2023

Summary

This summary is machine-generated.

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Thermodynamics of a time-dependent and dissipative oval billiard: A heat transfer and billiard approach.

Physical review. E·2017

See all related articles

Investigating a bouncing ball on uneven surfaces reveals that surface undulations introduce random horizontal forces. This leads to behaviors resembling Brownian motion, including normal and superdiffusion on the x-axis.

Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

The motion of bouncing objects is typically studied on planar surfaces.
Understanding the dynamics of bouncing systems on complex terrains is crucial for various applications.
Surface irregularities can introduce complex behaviors not observed in idealized models.

Purpose of the Study:

To investigate the dynamics of a bouncing ball on a nonplanar surface.
To analyze the impact of surface undulation on the ball's motion.
To characterize the resulting horizontal force and particle distribution.

Main Methods:

Theoretical analysis of a bouncing ball model on a nonplanar surface.
Investigation of the horizontal component of the impact force.

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Analysis of the particle's horizontal distribution and diffusion characteristics.

Formulation of a scaling hypothesis for the probability density function.

Main Results:

Surface undulation introduces a random horizontal component to the impact force.
The horizontal distribution of the bouncing ball exhibits characteristics of Brownian motion.
Both normal and superdiffusion are observed along the x-axis.
A scaling hypothesis is proposed for the probability density's functional form.

Conclusions:

Nonplanar surfaces significantly alter the dynamics of bouncing objects.
The random horizontal forces lead to diffusive behaviors in the particle's trajectory.
The findings provide insights into complex particle dynamics and statistical mechanics.