Damped finite-time-singularity driven by noise

Details Damped finite-time-singularity driven by noise Damped finite-time-singularity driven by noise

2003-05-27

arxiv.org/abs/cond-mat/0305630v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 eps-figures, revtex4 file

Scientific paper

10.1103/PhysRevE.68.051105

We consider the combined influence of linear damping and noise on a 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. The damping introduces a characteristic cross-over time. In the early time regime the probability distribution and first-passage-time distribution show a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the behavior is controlled by the damping. 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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