Wind-tree model for billiard motion from a signal processing viewpoint

TL;DR

This paper reinterprets the wind-tree billiard model using signal processing techniques, specifically a 3-state hidden Markov model, offering a novel perspective on the dynamics of particle trajectories.

Contribution

It introduces a signal processing approach to analyze the wind-tree model, contrasting with traditional algebraic topology and ergodic theory methods.

Findings

Trajectory behavior modeled by a 3-state hidden Markov model

Provides new insights into long-term dynamics of the system

Bridges billiard dynamics with signal processing techniques

Abstract

In the Ehrenfest wind tree model, a point particle moves on the plane and collides with randomly placed fixed square obstacles under the usual law of geometric optics. The particle represents the wind and the squares are the trees. We examine the periodic version of the model. Previous authors analyze the dynamical properties of the model using techniques from algebraic topology or ergodic theory. In contrast to these works, we adopt a signal processing viewpoint. We describe the phenomenon of the long-term trajectories by using a 3-state hidden Markov model.