Multiscale Homogenization with Bounded Ratios and Anomalous Slow Diffusion

Gérard Ben Arous, Houman Owhadi

Research output: Contribution to journalArticle

Abstract

We show that the effective diffusivity matrix D(Vn) for the heat operator ∂t - (Δ/2 - ∇Vn∇) in a periodic potential Vn = ∑k=0 n U k(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period double-struck Td:= ℝd/ℤd, d ∈ N*, Uk (0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk 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, dyt = dωt - ∇V(yt)dt.

Original languageEnglish (US)
Pages (from-to)80-113
Number of pages34
JournalCommunications on Pure and Applied Mathematics
Volume56
Issue number1
DOIs
StatePublished - Jan 2003

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Brownian movement
Homogenization
Anomalous
Periodic Potential
Superposition
Diffusivity
Brownian motion
Deduce
Heat
Decay
Operator
Hot Temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Multiscale Homogenization with Bounded Ratios and Anomalous Slow Diffusion. / Arous, Gérard Ben; Owhadi, Houman.

In: Communications on Pure and Applied Mathematics, Vol. 56, No. 1, 01.2003, p. 80-113.

Research output: Contribution to journalArticle

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