Flip motion of solitary wave in an Ising-type Vicsek model

TL;DR

This paper introduces an Ising-type Vicsek model for collective motion, demonstrating solitary wave behavior and sudden direction changes in one- and two-dimensional particle systems, with numerical and mean-field analysis.

Contribution

It presents a novel Ising-type Vicsek model capturing flip motion of solitary waves and extends it from 1D to 2D, analyzing direction reversal phenomena.

Findings

Solitary waves appear in the model similar to previous models.

The average reversal time of the wave's direction is characterized.

Flip motion of bandlike solitons observed in 2D model.

Abstract

An Ising-type Vicsek model is proposed for collective motion and sudden direction change in a population of self-propelled particles. Particles move on a linear lattice with velocity +1 or -1 in the one-dimensional model. The probability of the velocity of a particle at the next step is determined by the number difference of the right- and left- moving particles at the present lattice site and its nearest-neighboring sites. A solitary wave appears also in our model similarly to previous models. In some parameter range, the moving direction of the solitary wave sometimes changes rather suddenly, which is like the sudden change of moving direction of a flock of birds. We study the average reversal time of traveling direction numerically and compare the results with a mean-field theory. The one-dimensional model is generalized to a two-dimensional model. Flip motion of a bandlike soliton is observed in the two-dimensional model.