Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations

Abstract

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 to 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-KPZ universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations, kinetic roughening, and the noise-induced pushed-pulled transition, which is predicted and observed for the first time. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

17 pages, 6 figures

References in corpus (5)

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Cited by in corpus (8)

• Front propagation into unstable states
• Effects of Fluctuations on Propagating Fronts
• Intrinsic noise-induced phase transitions: beyond the noise interpretation
• A collective coordinate framework to study the dynamics of travelling waves in stochastic partial differential equations
• Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts
• Sharp-Interface Limit of a Fluctuating Phase-Field Model
• Field Theory of Propagating Reaction-Diffusion Fronts
• FKPP fronts in quenched random media