Nodal domain distribution of rectangular drums
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We consider the sequence of nodal counts for eigenfunctions of the Laplace-Beltrami operator in two dimensional domains. It was conjectured recently that this sequence stores some information pertaining to the geometry of the domain, and we show explicitly that this is the case for the family of rectangular domains with Dirichlet boundary conditions.
3 pages, 2 figures, presented in National Conference on Nonlinear Systems and Dynamics (Feb. 24-26, 2005), Aligarh Muslim University, India
3 pages, 2 figures, presented in National Conference on Nonlinear Systems and Dynamics (Feb. 24-26, 2005), Aligarh Muslim University, India