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Fisher waves in the strong noise limit
Oskar Hallatschek1, K S Korolev
1Max Planck Research Group for Biological Physics and Evolutionary Dynamics, Max Planck Institute for Dynamics & Self-Organization (MPIDS), Göttingen, Germany. ohallats@gmail.com
Physical Review Letters
|October 2, 2009
Summary
Strong number fluctuations significantly alter traveling waves in reaction-diffusion systems, revealing unexpected dynamics and front structures unlike typical approximations. This research highlights novel behaviors in particle density-dependent wave speeds and front evolution.
Area of Science:
- Physics
- Applied Mathematics
- Chemical Engineering
Background:
- Reaction-diffusion systems are crucial for modeling phenomena like population dynamics and chemical reactions.
- Deterministic and weak-noise approximations are commonly used but may fail under strong fluctuations.
- Understanding the impact of noise is essential for accurate modeling.
Purpose of the Study:
- To investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system.
- To compare findings with commonly used deterministic and weak-noise approximations.
- To analyze wave velocity and front profile dynamics under strong noise conditions.
Main Methods:
- Numerical computation of wave velocity in one and two spatial dimensions.
- Analysis of traveling wave profiles and their evolution.
- Investigation of particle density dependence on wave speed.
Main Results:
- Wave velocity exhibits a linear dependence on particle density in 1D and a square-root dependence in 2D.
- Observed wave fronts are composed of rugged kinks, not smooth sigmoidal profiles.
- Kink dynamics (diffusion, annihilation, branching) lead to power-law tails in front size distributions.
Conclusions:
- Strong number fluctuations lead to distinct traveling wave behaviors not captured by standard approximations.
- The observed kink dynamics and power-law distributions represent a significant departure from continuous wave theories.
- This study provides new insights into noise-driven phenomena in reaction-diffusion systems.
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