کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1898096 1534070 2007 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Growth processes related to the dispersionless Lax equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Growth processes related to the dispersionless Lax equations
چکیده انگلیسی

This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy, we interpret them as evolution equations for conformal maps in the plane. This provides a unified approach to evolution of smooth domains (such as Laplacian growth) and growth of slits. We show that the Löwner differential equation for a parametric family of conformal maps of slit domains arises as a consistency condition for reductions of the dispersionless Toda hierarchy. It is also demonstrated how the both types of growth processes can be simulated by the large NN limit of the Dyson gas picture for the model of normal random matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 235, Issues 1–2, November 2007, Pages 101–108
نویسندگان
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