Y. Hobiki et al., SPECTRAL DISTRIBUTION OF DRUMS WITH FRACTAL PERIMETERS - THE WEYL-BERRY-LAPIDUS CONJECTURE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(2), 1995, pp. 1310-1312
The Weyl-Berry-Lapidus conjecture on vibrational spectra of drums with
fractal perimeters (fractal drums) is examined in terms of large-scal
e numerical simulations. The integrated densities of states of fractal
drums with the perimeter of the Koch curve are computed by employing
a powerful numerical method. It is confirmed that the Weyl-Berry-Lapid
us conjecture holds in the frequency regime higher than a crossover fr
equency omega(c) related to the length scale characterizing the fracta
l boundary.