Long time, large scale properties of the noisy driven-diffusion equation

J. Ravi Prakash, J. P. Bouchaud, S. F. Edwards

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Abstract

We study the driven-diffusion equation, describing the dynamics of density fluctuations δρ(qq, t) in powders or traffic flows. We have performed quite detailed numerical simulations of this equation in one dimension, focusing in particular on the scaling behaviour of the correlation function 〈δρ(qq, t)δρ(0, 0)〉. One of our motivations was to assess the validity of various theoretical approaches, such as Renormalization Group and different self consistent truncation schemes, to these nonlinear dynamical equations. Although all of them are seen to predict correctly the scaling exponents, only one of them (where the non-exponential nature of the relaxation is taken into account) is able to reproduce satisfactorily the value of the numerical prefactors. Several other interesting issues, such as the noise spectrum of the output current, or the statistics of distance between jams (showing a transition between a 'laminar' regime for small noise to a 'jammed' regime for higher noise) are also investigated.

Original languageEnglish
Pages (from-to)67-85
Number of pages19
JournalProceedings of The Royal Society of London A: Mathematical and Physical Sciences
Volume446
Issue number1926
Publication statusPublished - 8 Jul 1994
Externally publishedYes

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