Vibrations of fractals: dynamic scaling, correlation functions and inelastic light scattering

Abstract

Earlier work on the vibrations of fractals is extended and a firmer formal basis is constructed which should help in comparing detailed dynamic scaling assumptions to simulations and experiments. We show how the strong scattering assumption: that the vibrations of random fractals should be characterized by a single unique length scale which combines the roles of a wavelength, a scattering length and a localization length, can be checked. We relate the dynamical density-density correlation functions to the averaged strain of the fractal mass distribution. We show how scaling assumptions for the frequency dependence of this strain averaged over the whole vibrating region and also at scales small compared to the characteristic frequency length-scale, can be tested. We also analyze the inelastic scattering of light from the vibrations of the fractal in detail - mainly emphasizing the dipole-induced-dipole scattering mechanism - and relate the predictions to the strains and to the same scaling assumptions made for the correlation functions. This should provide additional cross-checks on these assumptions. © 1993.