Analysis Seminar

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Anomalous diffusion by fractal homogenization

Speaker: Scott Armstrong, Courant Institute

Location: Warren Weaver Hall 1302

Date: Thursday, September 21, 2023, 11 a.m.

Synopsis:

We construct a class of incompressible vector fields that have many of the properties observed in a fully turbulent velocity field, and for which the associated scalar advection-diffusion equation generically displays anomalous diffusion. We also propose an analytical framework in which to study anomalous diffusion, via a backward cascade of renormalized eddy viscosities. Our proof is by "fractal" homogenization, that is, we perform a cascade of homogenization across arbitrarily many length scales. This talk is based on joint work with Vlad Vicol.