On Nonlinear Diffusion with Multiplicative Noise

Details On Nonlinear Diffusion with Multiplicative Noise On Nonlinear Diffusion with Multiplicative Noise

1997-02-25

arxiv.org/abs/cond-mat/9702217v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, LaTeX, text and figures also available at http://matisse.ucsd.edu/~hwa

Scientific paper

10.1209/epl/i1998-00123-2

Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall. Two different universality classes, corresponding to the cases of an ``upper'' and a ``lower'' wall, are identified and their critical properties are characterized. While the lower wall problem can be understood by applying the knowledge of linear diffusion with multiplicative noise, the upper wall problem exhibits an anomaly due to nontrivial dynamics in the vicinity of the wall. Broad power-law distribution is obtained throughout the bound phase.

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