Kinematic reduction of reaction-diffusion fronts with multiplicative noise: derivation of stochastic sharp-interface equations.
Rocco, A, Ramírez-Piscina, L and Casademunt, J (2002) Kinematic reduction of reaction-diffusion fronts with multiplicative noise: derivation of stochastic sharp-interface equations. Phys Rev E Stat Nonlin Soft Matter Phys, 65. ISSN 1539-3755
Rocco02_PRE56116.pdf - Published Version
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We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.
|Divisions :||Faculty of Health and Medical Sciences > Microbial and Cellular Sciences|
|Date :||May 2002|
|Identification Number :||10.1103/PhysRevE.65.056116|
|Additional Information :||Copyright 2002 The American Physical Society.|
|Depositing User :||Symplectic Elements|
|Date Deposited :||24 May 2012 12:04|
|Last Modified :||09 Jun 2014 13:37|
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