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Thermodynamic Formalism Of The Harmonic Measure Of Diffusion Limited Aggregates: Phase Transition And Converged, Mogens H. Jensen, Anders Levermann, Joachim Mathiesen, Benny Davidovitch, Itamar Procaccia
Thermodynamic Formalism Of The Harmonic Measure Of Diffusion Limited Aggregates: Phase Transition And Converged, Mogens H. Jensen, Anders Levermann, Joachim Mathiesen, Benny Davidovitch, Itamar Procaccia
Benny Davidovitch
No abstract provided.
Laplacian Growth And Diffusion Limited Aggregation: Different Universality Classes, Felipe Barra, Benny Davidovitch, Anders Leverman, Itamar Procaccia
Laplacian Growth And Diffusion Limited Aggregation: Different Universality Classes, Felipe Barra, Benny Davidovitch, Anders Leverman, Itamar Procaccia
Benny Davidovitch
It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a oneparameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value is higher than the dimension of diffusion limited aggregates, showing that the two problems belong to two different universality classes.