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Power laws and stretched exponentials in a noisy finite-time-singularity model
Hans C Fogedby1, Vakhtang Poutkaradze
1Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark. fogedby@ifa.au.dk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
White noise prevents finite-time singularities in dynamical models by creating a first-passage-time distribution. This finding has implications for nanohydrodynamics, material physics, and biophysics.
Area of Science:
- Physics
- Dynamical Systems
- Statistical Mechanics
Background:
- Finite-time singularities pose challenges in modeling dynamical systems.
- Understanding noise effects is crucial in various scientific fields.
Purpose of the Study:
- To investigate the influence of white noise on a generic dynamical finite-time-singularity model.
- To characterize the resulting behavior and its potential applications.
Main Methods:
- Analysis of a single-degree-of-freedom dynamical model.
- Introduction of white noise perturbation.
- Examination of the system's response and emergent distributions.
Main Results:
- White noise resolves finite-time singularities.
- A first-passage-time or absorbing state distribution emerges.
- The distribution exhibits a peak at the singularity and a power-law or stretched exponential tail.
Conclusions:
- White noise can regularize singular behavior in dynamical systems.
- The findings are relevant to nanohydrodynamics, material physics, and biophysics.
- This work provides insights into noise-induced transitions and phenomena.