Interfacial velocity corrections due to multiplicative noise

@article{Pechenik1999InterfacialVC,
title={Interfacial velocity corrections due to multiplicative noise},
author={Leonid Pechenik and Herbert Levine},
journal={Physical Review E},
year={1999},
volume={59},
pages={3893-3900}
}
• Published 2 November 1998
• Mathematics, Physics
• Physical Review E
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability (MS) approach for propagation into an unstable state. Because the front velocity is controlled by the leading edge which perforce has low density, it is interesting to study the role that finite particle number fluctuations have on this picture. Here, we use the well-known mapping of discrete Markov processes to stochastic differential equations and focus on the…

Figures from this paper

Effect of Microscopic Noise on Front Propagation E
• 2001
We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the linearly marginal stability
Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2013
Here, the theory is formulated as an effective Hamiltonian mechanics which operates with the density field and the conjugate "momentum" field and proves that the most probable density field history of an unusually slow front represents a traveling front solution of the Hamilton equations.
Effect of noise on front propagation in reaction-diffusion equations of KPP type
• Mathematics, Physics
• 2009
AbstractWe consider reaction-diffusion equations of KPP type in one spatial dimension, perturbed by a Fisher-Wright white noise, under the assumption of uniqueness in distribution. Examples include
Effect of Microscopic Noise on Front Propagation
• Physics
• 2001
We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the “linearly marginal stability case.”
Dynamical aspects of a moving front model of mean-field type
We focus on the discrete-time stochastic model studied by E. Brunet and B. Derrida in 2004: a fixed number $N$ of particles evolve on the real line according to a branching/selection mechanism. The
Kardar–Parisi–Zhang universality class for the critical dynamics of reaction–diffusion fronts
• Physics, Mathematics
• 2019
We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov
Macroscopic response to microscopic intrinsic noise in three-dimensional Fisher fronts.
• Physics, Medicine
Physical review letters
• 2014
There is no weak-noise regime for Fisher fronts, even for realistic numbers of particles in macroscopic systems, according to the Fisher equation subject to stochastic internal noise.
Front Propagation Dynamics with Exponentially-Distributed Hopping
• Physics
• 2005
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as
On the maximal noise for stochastic and QCD travelling waves
Abstract Using the relation of a set of nonlinear Langevin equations to reaction–diffusion processes, we note the existence of a maximal strength of the noise for the stochastic travelling wave
Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.
• Physics, Medicine
Physical review letters
• 2005
A new class of fronts in finite particle-number reaction-diffusion systems corresponding to propagating up a reaction-rate gradient is introduced and analytic expressions for the front velocity dependence on bulk particle density are derived.

References

SHOWING 1-10 OF 23 REFERENCES
Stochastic Processes in Physics and Chemistry
N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical
Stochastic processes in physics and chemistry
• Physics
• 1981
Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master
Physique
Approche lagrangienne et relativité restreinte – Licence 3 année UNIVERSITE PARIS DIDEROT Résumé du programme : Première partie : approche lagrangienne et mécanique analytique • Introduction :
J. Stat. Phys
• J. Stat. Phys
• 1998
Phys. Rev. E
• Phys. Rev. E
• 1998
em Physica A
• em Physica A
• 1998
Phys. Rev. E
• Phys. Rev. E
• 1997
Phys. Rev. Lett
• Phys. Rev. Lett
• 1996
Phys. Rev. E
• Phys. Rev. E
• 1995
Phys. Rev. Lett
• Phys. Rev. Lett
• 1995