SPECTRAL CHARACTERISTICS IN RESONATORS WITH FRACTAL BOUNDARIES

Vibrations of drums with self-similar (fractal) boundaries are investi gated in terms of large-scale simulations, for elucidating the charact eristics of their spectral densities of states. It is found that the i ntegrated density of states Delta I(omega) is proportional to omega(Df ) (D-f the fractal dimension of the boundary) in the frequency regime higher than a characteristic frequency omega(c) with oscillating but s mall amplitude. The frequency omega(c) is related to the length scale characterizing the fractal boundary. We show that there exist edge mod es localized near the fractal boundary under the stress-free boundary condition (Neumann condition), which vibrate at both ends of the drum with antiphase.