Anomalous dimensions and the renormalization group in a nonlinear diffusion process

Nigel Goldenfeld, Olivier Martin, Y. Oono, Fong Liu

Research output: Contribution to journalArticle

Abstract

We present a renormalization-group (RG) approach to the nonlinear diffusion process tu=D x2u, with D=1/2 for x2u>0 and D=(1+)/2 for x2u<0, which describes the pressure during the filtration of an elastic fluid in an elastoplastic porous medium. Our approach recovers Barenblatts long-time result that, for a localized initial pressure distribution, u(x,t)t-(+1/2)f(x/ t), where f is a scaling function and =(2e)1/2+O(2) is an anomalous dimension, which we compute perturbatively using the RG. This is the first application of the RG to a nonlinear partial differential equation in the absence of noise.

Original languageEnglish (US)
Pages (from-to)1361-1364
Number of pages4
JournalPhysical review letters
Volume64
Issue number12
DOIs
StatePublished - Jan 1 1990

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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