منابع مشابه
Eigenfrequencies of Fractal Drums Eigenfrequencies of Fractal Drums
A method for the computation of eigenfrequencies and eigenmodes of fractal drums is presented. The approach involves first mapping the unit disk to a polygon approximating the fractal and then solving a weighted eigenvalue problem on the unit disk by a spectral collocation method. The numerical computation of the complicated conformal mapping was made feasible by the use of the fast multipole m...
متن کاملThe Distribution of Eigenfrequencies of Anisotropic Fractal Drums
Motivated by some aspects of boundary value problems for partial differential equations, several authors have recently been concerned with the study of function spaces on and of fractals. We refer mainly to the papers by A. Jonsson and H. Wallin [7–10] and to the book [16] where complete references to this topic are given. Let Ω be a bounded domain in 2# having C ¢ boundary ¦Ω and let 0! d A ! ...
متن کاملPeriodic orbit theory in fractal drums
The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity ∆3(L), which is a measure for the correlations between the eigenvalues, decreases to quite small values (as compared to systems with only small boundary roughness), thereby approaching the behavior of chaotic systems. The periodic orbit results are in goo...
متن کاملLocalizations in Fractal Drums: An Experimental Study
The low-frequency eigenmodes of a fractal drum are studied through experimental observation of the acoustical resonances of a fractal-shaped liquid crystal film. The resonance frequencies agree with the numerical predictions for the Laplacian eigenvalues in the fractal domain with Dirichlet boundary conditions. The amplitude distribution of the modes is detected by scanning the excitation posit...
متن کاملEigenmodes of Isospectral Drums
Recently it was proved that there exist nonisometric planar regions that have identical Laplace spectra. That is, one cannot “hear the shape of a drum.” The simplest isospectral regions known are bounded by polygons with reentrant corners. While the isospectrality can be proven mathematically, analytical techniques are unable to produce the eigenvalues themselves. Furthermore, standard numerica...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.11.015