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Bi-Laplacian Growth Patterns in Disordered Media | | Anders Levermann
; Itamar Procaccia
; | | Date: |
21 Aug 2002 | | Subject: | Statistical Mechanics; Materials Science; Pattern Formation and Solitons | cond-mat.stat-mech cond-mat.mtrl-sci nlin.PS | | Abstract: | 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. In this Letter we close this gap, offering a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps. | | Source: | arXiv, cond-mat/0208403 | | Other source: | [GID 1059418] pmid12485011 | | Services: | Forum | Review | PDF | Favorites | |
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