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تسجيل مستخدم جديدOn-lattice Vicsek model in confined geometries
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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 the periodic boundary conditions, it aims at the analysis of bulk behaviour of a limited number of particles. To expand the applicability of the model to further biological systems, we introduce an on-lattice implementation 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 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. These results provide the basis for applications of the Vicsek model to biological questions involving large particle numbers in confined environments.
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