Europhys. Lett.
Volume 71, Number 2, July 2005
Page(s) 207 - 213
Section General
Published online 17 June 2005
Europhys. Lett., 71 (2), pp. 207-213 (2005)
DOI: 10.1209/epl/i2005-10086-2

Hydrodynamic model for a system of self-propelling particles with conservative kinematic constraints

V. L. Kulinskii1, V. I. Ratushnaya2, A. V. Zvelindovsky3 and D. Bedeaux2

1  Department for Theoretical Physics, Odessa National University Dvoryanskaya 2, 65026 Odessa, Ukraine
2  Colloid and Interface Science group, LIC, Leiden University P.O. Box 9502, 2300 RA Leiden, The Netherlands
3  Centre for Materials Science, Department of Physics, Astronomy & Mathematics University of Central Lancashire - Preston PR1 2HE, UK

received 7 February 2005; accepted in final form 26 May 2005
published online 17 June 2005

We consider the dynamics of systems of self-propelling particles with kinematic constraints on the velocities. A continuum model for a discrete algorithm used in works by Vicsek et al. is proposed. For a case of planar geometry, finite-flocking behavior is obtained. The circulation of the velocity field is found not to be conserved. The stability of ordered motion with respect to noise is discussed.

05.65.+b - Self-organized systems.
47.32.-y - Rotational flow and vorticity.
87.10.+e - General theory and mathematical aspects.

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