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Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion

Ben Arous, Gérard and Owhadi, Houman (2003) Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion. Communications on Pure and Applied Mathematics, 56 (1). pp. 80-113. ISSN 0010-3640. https://resolver.caltech.edu/CaltechAUTHORS:20160224-121708361

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Abstract

We show that the effective diffusivity matrix D(V^n) for the heat operator ∂_t − (Δ/2 − ∇V^n∇) in a periodic potential V^n = Σ^n_(k=0)U_k(x/R_k) obtained as a superposition of Hölder-continuous periodic potentials U_k (of period T^d:= ℝ^d/ℤ^d, d ∈ ℕ^*, U_k(0) = 0) decays exponentially fast with the number of scales when the scale ratios R_(k+1)/R_k are bounded above and below. From this we deduce the anomalous slow behavior for a Brownian motion in a potential obtained as a superposition of an infinite number of scales, dy_t = dω_t − ∇V^∞(yt)dt.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/cpa.10053DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/cpa.10053/abstractPublisherArticle
http://arxiv.org/abs/math/0105258arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2002 Wiley Periodicals, Inc. Received December 2001. Article first published online: 29 Oct 2002. The authors would like to thank Alain-Sol Sznitman, Stefano Olla, and Alano Ancona [2] for stimulating discussions.
Issue or Number:1
Record Number:CaltechAUTHORS:20160224-121708361
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160224-121708361
Official Citation:Ben Arous, G. and Owhadi, H. (2003), Multiscale homogenization with bounded ratios and anomalous slow diffusion. Comm. Pure Appl. Math., 56: 80–113. doi: 10.1002/cpa.10053
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64736
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 21:06
Last Modified:03 Oct 2019 09:40

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