Biomedical subjects

A. A. Vasiliev

Publications and source records attributed to A. A. Vasiliev.

4 recordsLinked to original sources

PubMed2002

Transport in a slowly perturbed convective cell flow.

We study transport properties in a simple model of two-dimensional roll convection under a slow periodic (period of order 1/ varepsilon >>1) perturbation. The problem is considered in terms of conservation of the adiabatic invariant. It is shown that the adiabatic invariant is well conserved in the system. It results in almost regular dynamics on large time scales (of order approximately varepsilon (-3) ln varepsilon ) and hence, fast transport. We study both generic systems and an example having some symmetry. (c) 2002 American Institute of Physics.

Journal Article↗

PubMed1996

Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow.

The steady incompressible flow in a unit sphere introduced by Bajer and Moffatt [J. Fluid Mech. 212, 337 (1990)] is discussed. The velocity field of this flow differs by a small perturbation from an integrable field whose streamlines are almost all closed. The unperturbed flow has two stationary saddle points (poles of the sphere) and a two-dimensional separatrix passing through them. The entire interior of the unit sphere becomes the domain of streamline chaos for an arbitrarily small perturbation. This phenomenon is explained by the nonconservation of a certain adiabatic invariant that undergoes a jump when a streamline crosses a small neighborhood of the separatrix of the unperturbed flow. An asymptotic formula is obtained for the jump in the adiabatic invariant. The accumulation of such jumps in the course of repeated crossings of the separatrix results in the complete breaking of adiabatic invariance and streamline chaos. (c) 1996 American Institute of Physics.

Journal Article↗

PubMed1996

Adiabatic chaos in a two-dimensional mapping.

A close to identity symplectic mapping describing the dynamics of a charged particle in the field of an infinitely wide packet of electrostatic waves is studied. A region of chaotic dynamics, whose width is large for an arbitrarily small deviation of the mapping from the identity, exists on the phase cylinder. This is explained by the quasirandom change occurring in an adiabatic invariant of the problem when the phase trajectory crosses a resonance curve. An asymptotic formula is derived for the jump in the adiabatic invariant. The width of the chaos region and the density of the set of invariant curves near the boundary of the chaos region are estimated. (c) 1996 American Institute of Physics.

Journal Article↗

PubMed1994

Regular and chaotic transport of impurities in steady flows.

This paper considers the properties of the transport of impurity particles in steady fluid flows and describes the principal modes of particle motion. An impurity consisting of particles with a lower density than that of the medium is localized at stationary points of the flow, whereas a heavy impurity can perform a spatially unbounded motion. The conditions for the transition from the bounded motion of a heavy impurity to the long-range transport mode, which occurs as a result of a loss of the stability of the heteroclinic trajectory, are obtained for a model two-dimensional flow having an eddy-cell structure. A mode is found in which a particle, after being transported over a long distance, is trapped forever within the confines of one cell. The transition from regular to chaotic particle transport is analyzed. The question of the effect of a small noise (for example, molecular diffusion) on the character of the motion of a heavy impurity is investigated. It is shown that this effect is important at high viscosity and leads to a transition from bounded motion of the impurity particle to diffusion-type chaotic motion. (c) 1994 American Institute of Physics.

Journal Article↗