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Homogenization and Anomalous Diffusion

4:00 pm Thursday, January 22, 2015
Gautam Iyer (Carnegie Mellon University)

Homogenization is a well known technique used to approximate the macroscopic behaviour of a material with microscopic impurities. While this originally arose in the study of composite materials, it has applications to various other fields, and I will focus on a few results motivated by fluid dynamics. One well known result in this direction is that of GI Taylor concerning fluid flows in pipes. Unfortunately the length scales involved in typical oil pipelines are not too short this result to apply. I will conclude by describing joint work with A. Novikov concerning cellular flows (i.e. strong array of opposing vortices) and a conjecture on the effective behaviour in a regime outside that of standard homogenization results.

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