Knudsen's law and random billiards in irrational triangles

TL;DR

This paper proves Knudsen's law for particles in a two-dimensional irrational triangular billiard with random perturbations, demonstrating ergodic and exact dynamics through a skew-type deterministic model.

Contribution

It introduces a novel approach to analyze irrational triangular billiards with randomness, establishing ergodicity and exactness of the system.

Findings

Proves Knudsen's law in irrational triangle billiards

Shows the system's dynamics are ergodic and exact

Uses a skew-type deterministic representation

Abstract

We prove Knudsen's law for a gas of particles bouncing freely in a two dimensional pipeline with serrated walls consisting of irrational triangles. Dynamics are randomly perturbed and the corresponding random map studied under a skew-type deterministic representation which is shown to be ergodic and exact.