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Deceleration of one-dimensional mixing by discontinuous mappings

Lookup NU author(s): Dr Hannah Kreczak

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Abstract

We present a computational study of a simple one-dimensional map with dynamics composed of stretching, permutations of equally sized cells, and diffusion. We observe that the combination of the aforementioned dynamics results in eigenmodes with long-time exponential decay rates. The decay rate of the eigenmodes is shown to be dependent on the choice of permutation and changes nonmonotonically with the diffusion coefficient for many of the permutations. The global mixing rate of the map M in the limit of vanishing diffusivity approximates well the decay rates of the eigenmodes for small diffusivity, however this global mixing rate does not bound the rates for all values of the diffusion coefficient. This counterintuitively predicts a deceleration in the asymptotic mixing rate with an increasing diffusivity rate. The implications of the results on finite time mixing are discussed.


Publication metadata

Author(s): Kreczak H, Sturman R, Wilson MCT

Publication type: Article

Publication status: Published

Journal: Physical Review E

Year: 2017

Volume: 96

Issue: 5

Print publication date: 27/11/2017

Online publication date: 27/11/2017

Acceptance date: 17/08/2017

ISSN (print): 2470-0045

ISSN (electronic): 2470-0053

Publisher: American Physical Society

URL: https://doi.org/10.1103/PhysRevE.96.053112

DOI: 10.1103/PhysRevE.96.053112


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