Mixing in low rate flows

Rate of chaotic mixing in localized flows

Flows, Random Perturbations and Rate of Mixing

A new approach to the study of the rate of mixing in Anosov flows, recently proposed by N. Chernov, is simplified and generalized to the higher dimensional case. CONTENT 0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p. 2 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Institute for Mathematical Physics Flows, Random Perturbations and Rate of Mixing Flows, Random Perturbations and Rate of Mixing

A new approach to the study of the rate of mixing in Anosov ows, recently proposed by N. Chernov, is simpliied and generalized to the higher dimensional case.

Mixing and Un-mixing by Incompressible Flows

We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint ‖∇u(·, t)‖p ≤ 1 we show that any function can be mixed to scale ε in time O(| log ε|1+νp), with νp = 0 for p < 3+ √ 5 2 and νp ≤ 13 for p ≥ 3+ √ 5 2 . Known lower bounds show that this rate is optima...

Clustering by mixing flows.

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain...