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Abstract
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a largedeviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t≫1. This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O(t) and thus much beyond the O(t^{1/2}) range where a standard Gaussian approximation holds. A byproduct of the approach is a closedform expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the largedeviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.
Original language  English 

Article number  114501 
Number of pages  7 
Journal  Physical Review Letters 
Volume  117 
Issue number  11 
Early online date  7 Sep 2016 
DOIs  
Publication status  Published  9 Sep 2016 
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Dive into the research topics of 'Dispersion in Rectangular Networks: Effective Diffusivity and LargeDeviation Rate Function'. Together they form a unique fingerprint.Projects
 1 Finished

Passive scalars in complex fluid flows: variability and extreme events
1/10/11 → 30/11/14
Project: Research
Datasets

Scattering of inertial waves by random flows
Danioux, E. (Creator), Edinburgh DataShare, 1 Feb 2016
DOI: 10.7488/ds/1332, http://arxiv.org/abs/1510.00784
Dataset
Profiles

Jacques Vanneste
 School of Mathematics  Personal Chair in Fluid Dynamics
Person: Academic: Research Active