THE SPECTRAL DIMENSION OF AGGREGATES OF TUNABLE FRACTAL DIMENSION

The dynamic properties of fractal aggregates with tunable fractal dime nsion are studied. The fractal dimensions are investigated in the rang e 1.0 less than or equal to D less than or equal to 2.5. The interacti ons are represented by the Born scalar model and two kinds of rule des cribing links between particles are used. The spectral dimension is de termined by computing the integrated density of states (IDOS), using t he very fast spectral moments method. Comparisons with a direct diagon alization prove the efficiency of this method. Furthermore, we give a Brownian diffusion approach, which agrees with the moments method, for D lower than two. It is found that the spectral dimension strongly de pends on the fractal dimension and, for fractal dimension larger than two, it varies with the degree of connectivity taken into account in t he model.