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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. doi:10.1002/cpa.10053.

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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.

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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.
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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
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 21:06
Last Modified:10 Nov 2021 23:34

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