Front Stability in Mean Field Models of Diffusion Limited Growth

Details Front Stability in Mean Field Models of Diffusion Limited Growth Front Stability in Mean Field Models of Diffusion Limited Growth

1995-07-18

arxiv.org/abs/patt-sol/9507004v1

Nonlinear Sciences

Pattern Formation and Solitons

26 pp. revtex, 7 uuencoded ps figures. submitted to PRE

Scientific paper

10.1103/PhysRevE.53.861

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.

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