Statistical-mechanics study of earthquake phenomenon based on dynamics of complex networks

我们利用美国南加州和日本的地震资料构造了复杂生长网络，并研究了它们的拓扑和动力学性质。我们已经发现，在这两个地区的连接性的分布衰减的幂律。在无向网络图中，我们已经表明，随机选择的两个地震之间的分离度的值取2和3之间的小值。我们已经发现，聚类系数的值是10倍左右的情况下，完全随机的网络。在有向网络图中，我们研究了两个拓扑不变的统计量：周期分布和路径长度分布。我们已经在相关领域发表了7篇论文。两份文件正在印刷，一份文件正在考虑出版。我们在日本物理学会年会上发表了4次演讲，在国际研讨会上发表了5次演讲。

We have constructed the complex growing networks from the seismic data taken in southern California and Japan, and studied their topological and dynamical properties. We have found that the distributions of connectivity decay as a power law in both regions. In the undirected network picture, we have shown that the values of the degrees of separation between two earthquakes chosen at random take small values between 2 and 3. We have found that the values of the clustering coefficient are about 10 times larger than those in the cases of completely random networks. In the directed network picture, we have studied two topologically-invariant statistical quantities : one is the period distribution and the other is the path length distribution. We have found that both of then are scale free.We have published 7 papers in the related subjects. Two papers are in press and one paper is now under consideration for publication. We have given 4 talks at the annual meetings of the Physical Society of Japan and 5 at the international symposia.