BYU

Abstract by Stewart McGinnis

Personal Infomation


Presenter's Name

Stewart McGinnis

Co-Presenters

None

Degree Level

Masters

Co-Authors

Ben Webb

Abstract Infomation


Department

Mathematics

Faculty Advisor

Ben Webb

Title

Multiparticle Dynamics in a Lattice Gas System

Abstract

We consider a deterministic dynamical system of particles traveling along the bonds of the triangular lattice. When a particle arrives at a lattice site it is scattered either to the left or right depending on whether the lattice site is oriented to either the left or right, respectively. After scattering a particle the scatterer switches orientation. As a result there is an interplay between the configuration of scatterers, i.e. the medium the particle travels through, and the particle's trajectory. Under the given rule, it is known that a single particle will propagate through the lattice. We  extend the system to include multiple particles, and describe the rich resulting dynamics. The addition of multiple particles gives rise to periodic structures and tangles in which at least two particles have an infinite number of indirect interactions via the medium. We prove time-invertibility of the dynamics, and provide a number of necessary conditions for aperiodicity and unboundedness of a given initial configuration.