title: Power laws and stretched exponentials in a noisy finite-time-singularity model.
abstract: 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.
authors.affiliation: Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark. fogedby@ifa.au.dk
authors.forename: Hans C
authors.initials: HC
authors.lastname: Fogedby
authors.forename: Vakhtang
authors.initials: V
authors.lastname: Poutkaradze