Laplacian growth as one-dimensional turbulence
Abstract
A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The first few Fourier components of the mapping define the web, an envelope of the cluster. The web is used to study the transition and the dynamics of large-scale features of the cluster characterized by evolution from macro- to micro-scales. Also, we derive scaling laws for the cluster size.
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