Flame front propagation III: Random Noise and Pole-Dynamics in Unstable Front Propagation (new version)

Details Flame front propagation III: Random Noise and Pole-Dynamics in Unstable Front Propagation (new version) Flame front propagation III: Random Noise and Pole-Dynamics in Unstable Front Propagation (new version)

2003-02-11

arxiv.org/abs/nlin/0302021v2

Nonlinear Sciences

Pattern Formation and Solitons

12 pages 29 figures

Scientific paper

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with random initial conditions and perturbations. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulations that lead to scaling laws for the velocity and acceleration of the front as a function of the system size and the level of noise, and analytic arguments that explain these results in terms of the noisy pole dynamics.terms of the dynamics of singularities in the complex plane, yielding detailed understanding of the physics of the eigenfunctions and eigenvalues.

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