RANDOM NOISE AND POLE DYNAMICS IN UNSTABLE FRONT PROPAGATION

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansio n in the complex plane is employed to address the interaction of the u nstable growth process with random initial conditions and perturbation s. We argue that the effect of random noise is immense and that it can never be neglected in sufficiently large systems. We present simulati ons 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 an alytic arguments that explain these results in terms of the noisy pole dynamics.