Pattern propagation in nonlinear dissipative systems |
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Authors: | E. Ben-Jacob H. Brand G. Dee L. Kramer J.S. Langer |
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Affiliation: | 1. Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA |
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Abstract: | We discuss the problem of pattern selection in situations where a stable, nonuniform state of a nonlinear dissipative system propagates into an initially unstable, homogeneous region. Our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known; and we point out that these known properties are consistent with a marginal-stability hypothesis that has been suggested in the theory of dendritic crystal growth. We then describe a more general interpretation of the marginal-stability hypothesis and, finally, present numerical evidence for its validity from three different pattern-forming models. |
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