Laplacian growth of parallel needles: A Fokker-Planck equation approach - art. no. 041401

Using a conformal transformation to set up the iterative nonlinear equation s, We Study analytically the kinetics of growth of parallel needles. We est ablish a discrete Fokker-Planck equation for the probability of finding at time t a given distribution of needle lengths. In the linear regime, it sho ws a short-wavelength Laplacian instability which we investigate in detail. From the crossover of the solutions to the nonlinear regime, we deduce ana lytically the general scale invariance of the two-dimensional models.