Analysis of Autonomous Many-Body Particle Models from Geometric Perspective and Its Applications

Abstract

AbstractBy introducing geometrical perspectives such as tropical geometry and discrete Morse theory, which have made remarkable progress, we will discuss analytical methods and the development of basic models for autonomous many-body particle interaction systems. In particular, the Burgers Cellular Automaton, which is considered to be the basic traffic flow model, is analyzed by introducing critical cells of discrete Morse theory. An extension to a quantum walk model that takes into account the internal states of particles is also proposed. Finally, future prospects for the application of the geometric perspective to pedestrian flow models are discussed.