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28 March 2024
 
  » arxiv » cond-mat/9909225

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Two-finger selection theory in the Saffman-Taylor problem
F.X. Magdaleno ; J. Casademunt ;
Date 15 Sep 1999
Subject Statistical Mechanics; Materials Science; Chaotic Dynamics; Pattern Formation and Solitons | cond-mat.stat-mech chao-dyn cond-mat.mtrl-sci nlin.CD nlin.PS patt-sol
AbstractWe find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two it unequal m fingers advancing with the same velocity but with different relative widths $lambda_1$ and $lambda_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $lambda = lambda_1 + lambda_2$ and of the relative individual finger width $p=lambda_1/lambda_2$ are selected out of a two-parameter continuous degeneracy. They scale as $lambda-1/2 sim d_0^{2/3}$ and $|p-1/2| sim d_0^{1/3}$. The selected values of $lambda$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given.
Source arXiv, cond-mat/9909225
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