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.

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

References in corpus (1)

• A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles

Cited by in corpus (14)

• A High Robustness and Low Cost Model for Cascading Failures
• DNA bubble dynamics as a quantum Coulomb problem
• Fearless versus Fearful Speculative Financial Bubbles
• First-passage and first-exit times of a Bessel-like stochastic process
• The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
• Market bubbles and crashes
• Dynamics of DNA-breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem
• Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis
• Diffusion in a logarithmic potential: scaling and selection in the approach to equilibrium
• Damped finite-time-singularity driven by noise
• Patterns in the Kardar-Parisi-Zhang equation
• Diagnosis and Prediction of Tipping Points in Financial Markets: Crashes and Rebounds
• Finite-time blowup of a Brownian particle in a repulsive potential
• Population dynamics with nonlinear delayed carrying capacity