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Negative velocity fluctuations of pulled reaction fronts
Baruch Meerson1, Pavel V Sasorov
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
Summary
Shot noise causes reaction front fluctuations. A new WKB theory reveals the probability of fronts moving slower than deterministic models, and how noise can arrest or reverse front motion.
Area of Science:
- Statistical Physics
- Chemical Kinetics
- Reaction-Diffusion Systems
Background:
- Reaction fronts propagating into unstable states are subject to fluctuations due to inherent randomness (shot noise).
- Understanding these fluctuations is crucial for predicting the behavior of systems ranging from biological pattern formation to chemical reactors.
Purpose of the Study:
- To investigate the probability of reaction front motion significantly deviating from deterministic predictions.
- To explore the potential for noise to temporarily halt or even reverse the direction of front propagation.
Main Methods:
- Development of a Wentzel-Kramers-Brillouin (WKB) theory tailored for reaction fronts with many particles.
- Application of the WKB theory to analyze the microscopic model A⇄2A and random walk processes.
Main Results:
- The WKB theory quantifies the probability of a reaction front moving slower than its deterministic counterpart due to shot noise.
- The study demonstrates that noise can indeed arrest front motion and, under certain conditions, induce backward propagation.
Conclusions:
- Shot noise plays a significant role in modulating reaction front dynamics, leading to potentially counterintuitive behaviors.
- The developed WKB theory provides a powerful analytical tool for understanding noise-induced phenomena in reaction-diffusion systems.
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