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Updated: Aug 6, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Fluctuation-induced instabilities in front propagation up a comoving reaction gradient in two dimensions
C Scott Wylie1, Herbert Levine, David A Kessler
1Center for Theoretical Biological Physics, University of California-San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0319, USA. cwylie@physics.ucsd.edu
Summary
Fluctuations destabilize reaction-diffusion fronts in narrow channels, altering their velocity. A density cutoff partially explains these stochastic effects, showing fluctuations are essential.
Area of Science:
- Physics
- Chemical Engineering
- Mathematical Biology
Background:
- Reaction-diffusion systems model phenomena from population dynamics to chemical reactions.
- Understanding front propagation in confined geometries is crucial for various scientific applications.
- Deterministic models often overlook the impact of random fluctuations.
Purpose of the Study:
- To investigate the behavior of two-dimensional (2D) fronts in reaction-diffusion systems with a moving reaction rate gradient.
- To compare the stability and velocity of planar fronts in deterministic versus stochastic systems within a 2D rectangular channel.
- To explore the role of fluctuations and a density cutoff in altering front dynamics.
Main Methods:
- Analysis of deterministic mean-field equations for planar front stability.
- Investigation of stochastic reaction-diffusion systems in finite-width channels.
- Development and application of a density cutoff model to approximate stochastic effects.
Main Results:
- Planar solutions are stable in the deterministic 2D rectangular channel.
- Stochastic fronts become unstable beyond a critical channel width.
- Stochastic front velocity depends on channel width, unlike deterministic fronts.
- A density cutoff partially captures these fluctuation-induced effects.
Conclusions:
- Fluctuations fundamentally alter reaction-diffusion front behavior in confined systems.
- Channel width is a critical parameter influencing front stability and dynamics.
- The density cutoff model offers insights into the impact of stochasticity.
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