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We find the self-similar scaling behavior xt^3/5, yt^2/5 for the arms which form in radial Hele-Shaw flow with anisotropic surface energy, where x is the longitudinal and y is the transverse coordinate of each primary finger. We first obseve this by direct numerical simulation using a boundary-integral method. Then we analytically derive the scaling law and the full asymptotic shape, by combining a simple boundary-layer analysis with previous results on velocity selection.
Almgren et al. (Mon,) studied this question.
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