On pinned billiard balls and foldings
Jayadev S. Athreya, Krzysztof Burdzy, Mauricio Duarte

TL;DR
This paper analyzes systems of fixed-position balls with pseudo-velocities, providing explicit bounds on the maximum number of collisions, and explores foldings as a mathematical analogy for paper folding along creases.
Contribution
It introduces bounds on the number of pseudo-collisions in pinned ball systems and connects these to the mathematical concept of foldings.
Findings
Derived explicit upper bounds for pseudo-collisions in n pinned balls in d dimensions.
Established a link between pseudo-collision systems and foldings.
Provided a mathematical framework for analyzing collision sequences in fixed-position systems.
Abstract
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times of collisions for different pairs of pinned balls are chosen in an exogenous way. We give an explicit upper bound for the maximum number of pseudo-collisions for a system of pinned balls in a -dimensional space, in terms of , and the locations of ball centers. As a first step, we study foldings, i.e., mappings that formalize the idea of folding a piece of paper along a crease.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Materials and Mechanics · Mathematics and Applications · Mathematical Dynamics and Fractals
