材料期刊网

The vibrational densities of states for a deterministic self-affine aggregate and the two-dimensional Eden hulls are computed numerically by the continued-fraction recursion method. It is shown that in contrast with the geometrical complexity the density of states for the diagonally self-affine fractals exhibits a simple power-law scaling. Motivated by these suggestive results, we extend the work done by Alexander and Orbach in 1982 and conclude that the concept of fractons is still valid in characterizing the vibrational spectra of all diagonally self-affine fractals. We also relate the fracton dimensionality to other exponents.