Vibrational dynamics of cluster-cluster aggregations

The vibrational dynamics of diffusion-limited cluster-cluster aggregations (DLCA) and reaction-limited cluster-cluster aggregations (RLCA) are numerically studied. The dependence on particle concentration of the density-density correlation function $g\left(r\right)\mathrm{}$ and the density of states (DOS) D(ω) are investigated. It is shown that the frequency dependence of the DOS depends on a sticking probability of clusters when an aggregate is formed. The spectral dimension $\tilde{d}$ on a three-dimensional system is obtained as $\tilde{d}=1.17\mathrm{}\pm 0.04$ for DLCA, and $\tilde{d}=1.28\mathrm{}\pm 0.03$ for RLCA. In addition, the scaling properties for the dynamical structure factor $S(q,\omega )$ taking into account the fractality of the DLCA are argued.