Vibrations in regular and disordered fractals : from channeling waves to fractons

2014 Computer simulation of the vibrational properties of a Sierpinski carpet are reported. From the computed density of states, we find the spectral dimension d = 1.6 and the presence of singularities attributed to edges of the Brillouin zones of the underlying Bravais lattice. Then, we present mode patterns showing a new form of « channeling wave » at weak disorder becoming Anderson-localized at strong disorder. This is reflected in a non-monotonic variation of the participation ratio as a function of disorder. Analysing the mode patterns, we find no evidence supporting the conjecture of superlocalization. This study shows that the concept of a universal fracton is not appropriate to describe the two types of vibrational excitations we observe. J. Phys. France 50 (1989) 3331-3345 15 NOVEMBRE 1989, Classification Physics Abstracts 63.50 71.55J