Y. Hobiki et al., SPECTRAL CHARACTERISTICS IN RESONATORS WITH FRACTAL BOUNDARIES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(2), 1996, pp. 1997-2004
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.