École Nationale Supérieure de
Techniques Avancées

Abstract

When two bodies collide, their speeds can change and they can lose some mat- ter. Many equations can describe this phenomenon, such as the Fokker-Planck one for example. To know the evolution of a population of bodies undergoing collisions, one has to know what happens when two bodies collide, but it is also necessary to know the frequency at which the bodies collide. The aim of this internship was then to built a model giving the probability for a body to collide with another depending on its volume. The study led in this document is focusing on bodies moving freely, being submitted to no other forces than the ones resulting from elastic collisions. Two main approaches are developed here : a practical one, with the help of C and Python algorithms and a more theoretical one. To gradually arrive to a solution, the problem is first studied with the bodies being able to move only in one direction of space, then two and finally three. Those two approaches led to the elaboration of an empiric formula giving the pro- bability for a body to collide with another when moving in one direction of space and to a theoretical formula giving the probability for a body to collide with another when moving in any directions of space. Keywords : Collision Probability, Elastic Collision, Collective abrasion