Dynamical properties of large-scale fractal networks

计算机模拟对于深入了解渗滤网的动力学是必不可少的。我们已经成功地处理了超过10^5个粒子的非常大的渗流团簇，揭示了丰富的详细定量信息。随着阵列处理超级计算机的出现，以及不需要对角化的数值方法的使用，这些都成为可能。得到了这些大型渗流网络的振动态密度。对于二维和三维网络，证实了态的振动密度与w^df成正比，在特征频率w_c以上的区域d_f接近4/3.我们还发现，分数子模有一个非常独特的特征，即分数子激发的核心在其边缘急剧脱落.这与均匀扩展模(声子)的情况相反，在这种情况下，它们幅度的变化在很长的距离内是平稳相关的。

Computer simulations are essential to develop the insight into dynamics of percolating nets. We have succeeded in treating very large percolation clusters of more than 10^5 particles, revealing a wealth of detailed quantitative information. These have become possible with the advent of array-processing supercomputers, and with the use of a numerical method that does not require diagonalization. The vibrational densities of states for these large percolating networks obtained. It was confirmed for both 2d- and 3d-networks, that the vibrational denisity of states is proportional to w^df with d_f close to 4/3 in the regime above the characteristic frequency w_c. We also found that fracton modes possess a quite unique character, i. e., the core of fracton excitations falls off sharply at their edges. This is in contrast with the case of homogeneously extended modes (phonons), in which the change in their amplitudes is correlated smoothly over a long distance.