On-lattice Vicsek model in confined geometries

TL;DR

This paper introduces an efficient on-lattice implementation of the Vicsek model with reflective boundaries, analyzing its behavior in confined geometries and revealing boundary-induced phenomena like swarm trapping and rotational states.

Contribution

The paper presents a novel on-lattice version of the Vicsek model and characterizes its behavior in confined geometries with reflective boundaries, expanding the model's applicability.

Findings

Boundary alignment causes swarms to move along channels.

Edges act as traps, causing discontinuous noise dependence.

Ordered rotational states emerge in disk geometries.

Abstract

The Vicsek model (Vicsek et al. 1995) is a very popular minimalist model to study active matter with a number of applications to biological systems at different length scales. With its off-lattice implementation and periodic boundary conditions, it aims at the analysis of bulk behaviour of a limited number of particles. We introduce an efficient on-lattice implementation with finite particle volume and analyse its behaviour for three different geometries with reflective boundary conditions. For sufficiently fine lattices, the model behaviour does not differ between off-lattice and on-lattice implementation. The reflective boundary conditions introduce an alignment of the particles with the boundary for low levels of noise. Numerical sensitivity analysis of the swarming behaviour results in a detailed characterisation of the on-lattice Vicsek model for confined geometries with reflective boundary conditions. In a channel geometry, the boundary alignment causes swarms to move along the channel. In a box, the edges act as swarm traps and the trapping shows a discontinuous noise dependence. In a disk geometry, an ordered rotational state arises. This state is well described by a novel order parameter. Our works provides a foundation for future studies of Vicsek-like models with discretized space.