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Langevin approach to a chemical wave front: Selection of the propagation velocity in the presence of internal noise

par Lemarchand, Annie;Lesne, Annick;Mareschal, Michel
Référence Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 51, 5, page (4457-4465)
Publication Publié, 1995

Article révisé par les pairs

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Résumé :

The reaction-diffusion equation associated with the Fisher chemical model A+B→2A admits wave-front solutions by replacing an unstable stationary state with a stable one. The deterministic analysis concludes that their propagation velocity is not prescribed by the dynamics. For a large class of initial conditions the velocity which is spontaneously selected is equal to the minimum allowed velocity vmin, as predicted by the marginal stability criterion. In order to test the relevance of this deterministic description we investigate the macroscopic consequences, on the velocity and the width of the front, of the intrinsic stochasticity due to the underlying microscopic dynamics. We solve numerically the Langevin equations, deduced analytically from the master equation within a system size expansion procedure. We show that the mean profile associated with the stochastic solution propagates faster than the deterministic solution at a velocity up to 25% greater than vmin.