Dynamical properties of large-scale fractal networks

计算机模拟对于深入了解捕集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，揭示了大量详细的定量信息。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。得到了这些大的振动网络的振动态密度。对于二维和三维网络，在特征频率W_c以上的区域，态密度与W_f成正比，d_f接近4/3。我们还发现分形子模具有一个非常独特的性质，即：例如，分形子激发的核心在其边缘急剧福尔斯。这与均匀扩展模式（声子）的情况相反，在均匀扩展模式中，它们的振幅变化在长距离上平滑地相关。

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.