Related Experiment Video
Updated: May 4, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Ergodicity of the generalized lemon billiards
Jingyu Chen1, Luke Mohr2, Hong-Kun Zhang2
1Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-2302, USA.
Abstract:
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Related Concept Videos
Conservation of Linear Momentum for a System of Particles
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
Geometric Sequences
The Squeeze Theorem
Laws of Logarithms II
Poisson's And Laplace's Equation
Indeterminate Forms and L’Hôpital’s Rule

