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Full-Text Articles in Physics
Ripening Of Porous Media, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Ripening Of Porous Media, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Benny Davidovitch
We address the surface tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points – surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane, and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between open and closed system dynamics, pointing out the unlikelihood that CMC surfaces are ever realized in these systems on any time scale.
Iterated Conformal Dynamics And Laplacian Growth, Felipe Barra, Benny Davidovitch, Itamar Procaccia
Iterated Conformal Dynamics And Laplacian Growth, Felipe Barra, Benny Davidovitch, Itamar Procaccia
Benny Davidovitch
The method of iterated conformal maps for the study of diffusion limited aggregates (DLA) is generalized to the study of Laplacian growth patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportional to the gradient of the Laplacian field. We introduce a two-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth. The ultraviolet putative finite-time singularities are regularized here by a minimal tip size, equivalently for all the models in …