VIBRATIONS OF STRONGLY IRREGULAR OR FRACTAL RESONATORS

It is shown on a specific example that fractal boundary conditions dra stically alter the properties of wave excitations in space. The low-fr equency part of the vibration spectrum of a finite-range fractal drum is computed using an analogy between the Helmoltz equation and the dif fusion equation. The irregularity of the frontier is found to influenc e strongly the density of states at low frequency. The fractal perimet er generates a specific screening effect. Very near the frontier, the decrease of the wave form is related directly to the behavior of the h armonic measure, The possibility of localization of the vibrations is qualitatively discussed and we show that localized modes may exist at low frequencies if the geometrical structures possess narrow paths. Po ssible application of these results to the interpretation of thermal p roperties of binary glasses is briefly discussed.