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Article overview
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Dispersion in rectangular networks: effective diffusivity and large-deviation rate function | Alexandra Tzella
; Jacques Vanneste
; | Date: |
3 Oct 2015 | Abstract: | We investigate the dispersion of a passive scalar released in a fluid flowing
within a rectangular, Manhattan-style network. We use large-deviation theory to
approximate the scalar concentration as it evolves under the combined action of
advection and diffusion and derive an expression for the rate function that
controls the form of the concentration at large times $t$. For moderately large
distances $O(t^{1/2})$ from the centre of mass, this form reduces to a Gaussian
parameterised by a (tensorial) effective diffusivity given in closed form.
Further away, at distances $O(t)$, a more complex form reveals the strong
imprint of the network geometry. Our theoretical predictions are verified
against Monte Carlo simulations of Brownian particles. | Source: | arXiv, 1510.0784 | Services: | Forum | Review | PDF | Favorites |
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