Collective Dynamics of Interacting Particles in Unsteady Flows

Collective Dynamics of Interacting Particles in Unsteady Flows

We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid, and find analytic single-peaked traveling sol...

Collective dynamics of interacting particles

Flocking, swarming, aggregation there is a multitude of actual real-life phenomena that from the mathematical point of view can be interpreted as one of these concepts. The mathematical description of collective dynamics of self-propelled agents with nonlocal interaction originates from one of the basic equations of kinetic theory – Vlasov’s equation from 1938. Recently it was noted that such m...

Collective Behaviors in Two-Dimensional Systems of Interacting Particles

Collective dynamics of interacting molecular motors.

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Mor...

Study of dynamics in unsteady flows using Koopman mode decomposition

The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study bifurcations of the lid-driven flow in a two-dimensional square cavity based on rigorous theorems related to the spectrum of the Koopman operator. We adopt a new computational algorithm, which is capable of detecting t...