Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 53: Statistical physics (general) II
DY 53.1: Talk
Friday, March 28, 2003, 11:30–11:45, G\"OR/229
Bi-Laplacian growth patterns in disordered media — •Anders Levermann1,2 und Itamar Procaccia1 — 1Weizmann Institute of Science, Rehovot, Israel — 2Potsdam Institute for Climate Impact Research, Potsdam, Germany
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a pre-requisite to describing the fracture of elastic material is the solution of the bi-Laplace- rather than the Laplace-equation. We offer a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps. The resulting patterns can be conveniently analysed using this analytically-given map from its exterior to the exterior of the unit circle. As an example we determine the fractal dimension of the patterns through the scaling of the first Laurent coefficient of the map with the cluster size. [1] A. Levermann and I. Procaccia,”Bi-Laplacian Growth Patterns in Disordered Media", Phys. Rev. Lett. 89, (2002), 234501. www.weizmann.ac.il/chemphys/anders/