Study of complex systems with catastrophes based on Tsallis' nonextensive statistical mechanics

基于Tsallis非广延统计力学的复杂灾难系统研究

基本信息

批准号：
15540360
负责人：
ABE Sumiyoshi
金额：
$ 0.96万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

As an example of complex systems with catastrophes, we have studied the Internet. We have performed the Ping experiment and analyzed the time series data of the round-trip times of the Ping signals. We have discovered that there are striking common features of the Internet time series with seismic time series. In particular, we have identified the Gutenberg-Richetr law and the Omori law for the Internet time series. Next, we proceeded to investigate the seismic time series data taken in California and Japan. We have found that both the spatial distance and the time interval between two successive earthquakes follow Tsallis statistics. We have also studied the Omori regime relevant to aftershocks, and have discovered that there exist a definite aging phenomenon, which obeys a scaling law. This result suggests that the mechanism governing aftershocks can be thought of as a kind of glassy dynamics.After these studies on earthquakes, we have introduced the concept of earthquake network, wh … More ich is a evorvrng-random-network mapping of the seismic time series. We have found that the network is of the small-world type and is scale free. Also, we have investigated the directed-network feature of the seismic time series and seen that the period distribution is also scale free.In addition to these phenomenological studies, we have also developed fundamental theoretical studies on nonextensive statistical mechanics. Firstly, we have shown how the q-expectation value formalism is consistent with the minimum relative entropy principle associated with the maximum Tsallis entropy principle. Secondly, we have discussed thermodynamics ofa nonextensive system with a long-range interaction. We have shown that the thermodynamic scaling relation conjectured by numerical model analysis can affirmatively proved based on the generalized Euler relation. Thirdly, we have considered the phenomenon of anomalous diffusion in view of Einstein's 1905 theory of Brownian motion and have shown how naturally the fractional Fokker-Planck equation can be derived by relaxing the existence of the second moment in Einstein's theory. Less

作为与灾难的复杂系统的一个例子，我们研究了互联网。我们已经进行了PING实验，并分析了PING信号的往返时间的时间序列数据。我们发现，互联网时间序列具有地震时间序列的引人注目的共同特征。特别是，我们已经确定了Gutenberg-Richetr Law和Internet时间序列的Omori法律。接下来，我们开始研究在加利福尼亚和日本获取的地震时间序列数据。我们发现，两个成功地震之间的空间距离和时间间隔都遵循Tsallis统计数据。我们还研究了与余震相关的Omori政权，并发现存在明确的衰老现象，该现象遵守扩展定律。该结果表明，控制余震的机制可以被认为是一种玻璃动力学。在这些关于地震的研究之后，我们介绍了地震网络的概念，WH…更多是地震时间序列的Evorvrng-random网络映射。我们发现该网络是小世界类型的，并且是免费的。此外，我们已经投资了地震时间序列的定向网络特征，并发现该周期分布也是免费的。除了这些现象学研究外，我们还开发了有关非Xtentimentive统计力学的基本理论研究。首先，我们已经展示了Q期望值格式如何与与最大TSALLIS熵原理相关的最小相对熵原理一致。其次，我们讨论了具有远距离相互作用的非Xt脉系统的热力学。我们已经表明，通过数值模型分析猜想的热力学缩放关系可以根据广义的Euler关系得到适当证明。第三，鉴于爱因斯坦（Einstein）的1905年布朗运动理论，我们考虑了异常扩散的现象，并通过放松爱因斯坦理论中第二瞬间的存在来表明如何自然地得出分数fokker-planck方程。较少的