Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas

Fuente: arXiv
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Autori principali: Armstrong, Scott, Vicol, Vlad
Natura: Preprint
Pubblicazione: 2025
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author Armstrong, Scott
Vicol, Vlad
author_facet Armstrong, Scott
Vicol, Vlad
contents Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent result, in which 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. Our main contribution is to propose an analytical framework in which to study anomalous diffusion via a backward cascade of renormalized eddy viscosities.
format Preprint
id arxiv_https___arxiv_org_abs_2503_11744
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas
Armstrong, Scott
Vicol, Vlad
Analysis of PDEs
Mathematical Physics
Fluid Dynamics
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent result, in which 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. Our main contribution is to propose an analytical framework in which to study anomalous diffusion via a backward cascade of renormalized eddy viscosities.
title Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas
topic Analysis of PDEs
Mathematical Physics
Fluid Dynamics
url https://arxiv.org/abs/2503.11744