An improved upper bound on the number of billiard ball collisions

Abstract

We give a new upper bound $K_{+}$ on the number of totally elastic collisions of $n$ hard spheres with equal radii and equal masses in $R^d$. Our bound satisfies $\log K_{+}\le c(d)n\log n$.

arXiv admin note: text overlap with arXiv:1804.04650

References in corpus (3)

• Examples of exponentially many collisions in a hard ball system
• A lower bound for the number of elastic collisions
• Hard spheres dynamics: weak vs hard collisions