Mixing and Un-mixing by Incompressible Flows

2014/07/15 by Yao Yao, Yao, Yao, Andrej Zlatoš +1 · 6 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Markov Chains and Monte Carlo Methods #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1407.4163

Abstract

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(|logε|^1+ν_p), with ν_p=0 for p

Cited by

• Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows
• Introduction to the theory of mixing for incompressible flows
• Quantitative dependence of the Pierrehumbert flow's mixing rate on the amplitude
• Cellular flow control design for mixing based on the least action principle
• Superexponential dissipation enhancement on \mathbbT^d
• Exponentially mixing flows with slow enhanced dissipation

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