On-lattice Vicsek model in confined geometries

Andreas Kuhn; Sabine C. Fischer

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arXiv · 2105.08792

On-lattice Vicsek model in confined geometries

Andreas Kuhn·Sabine C. Fischer

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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.

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Andreas Kuhn, Sabine C. Fischer. 2021-05-18. On-lattice Vicsek model in confined geometries. https://arxiv.org/abs/2105.08792

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