Noise, Fractal Growth, and Exact Integrability in Nonequilibrium Pattern Formation

  • Mark B. Mineev-Weinstein
Part of the Institute for Nonlinear Science book series (INLS)


An informal review on a pedestrian level about integrability in dissipative nonequilibrium systems, describing pattern formation and exhibiting a noise-driven fractal growth, and particularly about remarkable properties of the nonlinear Laplacian growth equation (LGE), is performed. Main results concerning nonper-turbative properties of the LGE, which are signatures of exact integrability, are presented and discussed. Computing experiments exhibiting a large (potentially infinite) number of conservation laws in diffusion-limited aggregation fractal growth are discussed. Recent extensions of the LGE, intriguing connections with different branches of physics and mathematics, and various applications are outlined.


Fractal Growth Exact Integrability Schwarz Function Truncate Fourier Series Laplacian Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag New York, Inc. 1996

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  • Mark B. Mineev-Weinstein

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