The spectral dimension of aggregates of tunable fractal dimension

The dynamic properties of fractal aggregates with tunable fractal dimension are studied. The fractal dimensions are investigated in the range 1.0 less than or equal to D less than or equal to 2.5. The interactions are represented by the Born scalar model and two kinds of rule describing links between particles are used. The spectral dimension is determined by computing the integrated density of states (IDOS), using the very fast spectral moments method. Comparisons with a direct diagonalization 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 depends on the fractal dimension and, for fractal dimension larger than two, it varies with the degree of connectivity taken into account in the model.