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