Finite-time-singularity with noise and damping
Hans C. Fogedby
Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark and NORDITA, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
The combined influence of linear damping and noise on a dynamical finite-time-singularity model is considered for a single degree of freedom. The noise resolves the finite-time-singularity and replaces it by a first-passagetime 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 first-passage-time distribution shows 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 damping prevails. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.
Braz. J. Phys. vol.33 no.3 São Paulo Sept. 2003. Open Access Article.