Emergent dynamic structures and statistical law in spherical lattice gas automata

TL;DR

This paper explores how spherical lattice gas automata exhibit unique dynamic structures and statistical behaviors due to curvature, revealing non-equilibrium phenomena and equilibrium distributions on curved surfaces.

Contribution

It introduces a spherical lattice gas automaton model that uncovers curvature-driven structures and links their statistical behavior to a generalized random walk.

Findings

Emergent bubble and vortex structures due to geometric frustration.

System reaches equilibrium with Maxwell-Boltzmann speed distribution.

Mapping to a random walk explains statistical regularities.

Abstract

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several non-equilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven non-equilibrium physics.