Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts

Abstract

The position of an invasion front, propagating into an unstable state, fluctuates because of the shot noise coming from the discreteness of reacting particles and stochastic character of the reactions and diffusion. A recent macroscopic theory [Meerson and Sasorov, Phys. Rev. E 84, 030101(R) (2011)] yields the probability of observing, during a long time, an unusually slow front. The theory is formulated as an effective classical Hamiltonian field theory which operates with the density field and the conjugate "momentum" field. Further, the theory assumes that the most probable density field history of an unusually slow front represents, up to small corrections, a traveling front solution of the Hamilton equations. Here we verify this assumption by solving the Hamilton equations numerically for models belonging to the directed percolation universality class.

6 pages

References in corpus (7)

• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Void formation in diffusive lattice gases
• Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts

Cited by in corpus (14)

• WKB theory of large deviations in stochastic populations
• Survival of a static target in a gas of diffusing particles with exclusion
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• An exactly solvable travelling wave equation in the Fisher-KPP class
• Large deviations for the branching Brownian motion in presence of selection or coalescence
• The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles
• Enhancement of large fluctuations to extinction in adaptive networks
• Large order fluctuations, switching, and control in complex networks
• Irreversible Reactions and Diffusive Escape: Stationary Properties
• Persistent fluctuations of the swarm size of Brownian bees
• Velocity fluctuations of stochastic reaction fronts propagating into an unstable state: strongly pushed fronts
• Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian Bees
• Negative large deviations of the front velocity of $N$-particle branching Brownian motion
• Emergent population dynamics of random walkers with cooperative reproduction and spatial selection