Description
This interdisciplinary project focuses on improving the lower bound for the number of collisions of a finite system of n-balls in d-dimensional space. This is an open problem in mathematics whose solution might also be applicable to modeling collisions between particles in liquids and gases. However, our study goes beyond traditional 3-dimensional models known from physics. We developed software that computes all possible collisions between a system of balls with given initial positions and velocities, including collisions in positive and negative time. Building on the computation of collisions, we analyze various configurations of balls and their velocities in order to find configurations that produced more collisions than others. My research yielded a minimum of 8 collisions for a system of 4 balls in 3-dimensional space, a configuration which has never been published before.
Bounds on The Number of Elastic Collisions in D-Dimensional Space
This interdisciplinary project focuses on improving the lower bound for the number of collisions of a finite system of n-balls in d-dimensional space. This is an open problem in mathematics whose solution might also be applicable to modeling collisions between particles in liquids and gases. However, our study goes beyond traditional 3-dimensional models known from physics. We developed software that computes all possible collisions between a system of balls with given initial positions and velocities, including collisions in positive and negative time. Building on the computation of collisions, we analyze various configurations of balls and their velocities in order to find configurations that produced more collisions than others. My research yielded a minimum of 8 collisions for a system of 4 balls in 3-dimensional space, a configuration which has never been published before.