Power laws and stretched exponentials in a noisy finite-time-singularity model

Details Power laws and stretched exponentials in a noisy finite-time-singularity model Power laws and stretched exponentials in a noisy finite-time-singularity model

2002-04-10

arxiv.org/abs/cond-mat/0204221v3

Physics

Condensed Matter

Statistical Mechanics

10 pages revtex file, including 4 postscript-figures. References added and a few typos corrected

Scientific paper

10.1103/PhysRevE.66.021103

We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or absorbing state distribution with a peak at the singularity and a long time tail exhibiting power law or stretched exponential behavior. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.

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