Hydrodynamic model for the system of self propelling particles with conservative kinematic constraints; two dimensional stationary solutions

Ratushnaya, V. I. and Kulinskii, V. L. and Zvelindovsky, Andrei and Bedeaux, D. (2006) Hydrodynamic model for the system of self propelling particles with conservative kinematic constraints; two dimensional stationary solutions. Physica A: Statistical Mechanics and its Applications, 366 . pp. 107-114. ISSN 0378-4371

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Hydrodynamic model for the system of self propelling particles with conservative kinematic constraints; two dimensional stationary solutions

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Abstract

In a first paper we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. Phys. Rev. Lett. 75 (1995) 1226. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional. © 2005 Elsevier B.V. All rights reserved.

Keywords:Algorithms, Kinematics, Kinetic energy, Mathematical models, Velocity measurement, Vortex flow, Discrete algorithm, Finite-flocking behavior, Self-propelling particles, Continuum mechanics
Subjects:F Physical Sciences > F390 Physics not elsewhere classified
Divisions:College of Science > School of Mathematics and Physics
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ID Code:14976
Deposited On:23 Sep 2014 10:05

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