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arXiv · physics/9902023

Collective Motion

A. Czirok·T. Vicsek
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Abstract

With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In these models particles interact with their neighbors by turning towards the local average direction of motion. In the limit of vanishing velocities this behavior results in a dynamics analogous to some Monte Carlo realization of equilibrium ferromagnets. However, numerical simulations indicate the existence of new types of phase transitions which are not present in the corresponding ferromagnets. In particular, here we demonstrate both numerically and analytically that even in certain one dimensional self-propelled particle systems an ordered phase exists for finite noise levels.

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A. Czirok, T. Vicsek. 1999-02-09. Collective Motion. https://doi.org/10.1007/bfb0105013

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