A lower bound for the number of elastic collisions

Abstract

We prove by example that the number of elastic collisions of $n$ balls of equal mass and equal size in $d$-dimensional space can be greater than $n^3/27$ for $n\ge 3$ and $d\ge 2$. The previously known lower bound was of order $n^2$.

arXiv comment35 pages, 7 figures

References in corpus (1)

• On pinned billiard balls and foldings

Cited by in corpus (5)

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• Hard spheres dynamics: weak vs hard collisions
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• An improved upper bound on the number of billiard ball collisions
• Counting Collisions in an $N$-Billiard System Using Angles Between Collision Subspaces