Clustering transition in a system of particles self-consistently driven by a shear flow

Details Clustering transition in a system of particles self-consistently driven by a shear flow Clustering transition in a system of particles self-consistently driven by a shear flow

2004-09-13

arxiv.org/abs/nlin/0409028v1

Physical Review E 70, 066205 (2004)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 2 figures. To appear in PRE

Scientific paper

10.1103/PhysRevE.70.066205

We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists in that the effective velocity of every particle is given by the average of the external flow velocities felt by the particles located at a distance less than a typical radius, $R$. Numerical analysis reveals the existence of a transition to clustering depending on the parameters of the external flow and on $R$. A continuum description in terms of the number density of particles is derived, and a linear stability analysis of the density equation is performed in order to characterize the transitions observed in the model of interacting particles.

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