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| For a given map or flow, possibly time-dependent, we consider the problem of how to apply local perturbations to either optimally enhance or mitigate mixing. We develop an extremely flexible modelling approach, based on the Perron-Frobenius operator or transfer operator, posing this problem in the language of convex optimisation, and efficiently solving it with standard convex optimisation techniques.
The perturbations applied satisfy physical constraints, such as preservation of the invariant measure of the dynamics (e.g., for incompressible fluid flow, the perturbations preserve volume), and a variety of other natural constraints can also be easily enforced.
We can ask the optimiser to perturb so as to achieve complete mixing as quickly as possible by targeting the equilibrium distribution, or alternatively, we can specify a target non-equilibrium distribution; the latter may be of interest if one is trying to contain e.g. pollutants in a safe region. |
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