Study of complex systems with catastrophes based on Tsallis' nonextensive statistical mechanics
| Project/Area Number |
15540360
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
ABE Sumiyoshi University of Tsukuba, Graduate School of Pure and Applied Sciences, Associate Professor, 大学院・数理物質科学研究科, 助教授 (70184215)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Tsallis statistics / Complex systems / Catastrophe / Seismicity / Complexnetworks / Maximumentropy principle / Aiging / Scaling / カタストロフを含む複雑系 / スケール不変統計 / Tsallisの非加法的統計力学 / 拡張されたEuler関係式 / 拡張されたGibbs-Duhem関係式 / Shore-Johnsonの定理 / 最小相互エントロピー原理 / インターネット / ミクロカノニカル集団 / 最大エントロピ原理 / ゲージ変換 |
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| Research Abstract |
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
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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
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Report
(3 results)
Research Products
(21 results)
