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Collective behavior of self-propelling particles with kinematic constraints: The relation between the discrete and the continuous description

Author

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  • Ratushnaya, V.I.
  • Bedeaux, D.
  • Kulinskii, V.L.
  • Zvelindovsky, A.V.

Abstract

In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we derive the continuous hydrodynamic model from the discrete description. The similarities and differences between the resulting model and the hydrodynamic model postulated in our previous papers are discussed. The results clarify the assumptions used to obtain a continuous description.

Suggested Citation

  • Ratushnaya, V.I. & Bedeaux, D. & Kulinskii, V.L. & Zvelindovsky, A.V., 2007. "Collective behavior of self-propelling particles with kinematic constraints: The relation between the discrete and the continuous description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 39-46.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:39-46
    DOI: 10.1016/j.physa.2007.03.045
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    Citations

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    Cited by:

    1. Chepizhko, A.A. & Kulinskii, V.L., 2010. "On the relation between Vicsek and Kuramoto models of spontaneous synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5347-5352.
    2. García Cantú Ros, A. & Antonopoulos, Ch.G. & Basios, V., 2011. "Emergence of coherent motion in aggregates of motile coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 574-586.

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    Keywords

    Self-propelling particles;

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