arXiv subjects

V. I. Ratushnaya

Publications and source records attributed to V. I. Ratushnaya.

4 recordsLinked to original sources

arXiv2006

Collective Behavior of Self Propelling Particles with Kinematic Constraints; The relation between the discrete and the continuous description

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.

physics.flu-dyn↗

arXiv2006

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.

physics.flu-dyn↗

arXiv2005

Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider 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. 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.

physics.flu-dyn↗

arXiv2004

Collective behavior in the system of self propelling particles with nonholonomic constraints

We consider the dynamics of systems of self propelling particles with nonholonomic constraints. A continuum model for a discrete algorithm used in works by T. Vicsek et al. is proposed. For a case of planar geometry the finite flocking behavior is obtained. The circulation of the velocity field is found not to be conserved as a consequence of the nonholomicity. The stability of ordered motion with respect to noise is discussed. An analogy with the kinetics of charges in superconductors is noted.

physics.class-ph↗