Pinned Balls, Foldings and Particle Collisions

Abstract

In the foldings part, we estimated the convergence rate for the folding model on the unit sphere in R^n. This is a toy model for the coupling approach to the convergence rate in densely packed pinned billiard balls on a torus. In the particle collisions part, we gave the asymptotic formula for the collision location of two sample particles with fixed initial locations and velocities distributed according to the microcanonical ensemble formula.