Fingered growth in channel geometry: a Loewner-equation approach.
نویسندگان
چکیده
A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. Following Carleson and Makarov [L. Carleson and N. Makarov, J. Anal. Math. 87, 103 (2002)], the evolution of the fingers is studied with use of the deterministic Loewner equation. The method is then extended to study the growth in a linear channel with reflecting sidewalls. One- and two-finger solutions are found and analyzed. It turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.
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ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 77 4 Pt 1 شماره
صفحات -
تاریخ انتشار 2008