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2004 Fiscal Year Final Research Report Summary

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

Research Project

Project/Area Number 15540360
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionUniversity of Tsukuba

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)

Project Period (FY) 2003 – 2004
KeywordsTsallis statistics / Complex systems / Catastrophe / Seismicity / Complexnetworks / Maximumentropy principle / Aiging / Scaling
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 … 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

  • Research Products

    (9 results)

All 2005

All Journal Article (9 results)

  • [Journal Article] Origin of the Usefulness of the Natural-Time Representation of Complex Time Series2005

    • Author(s)
      S.Abe, N.V.Sarlis, E.S.Skordas, H.Tanaka, P.A.Varotsos
    • Journal Title

      Physical Review Letters (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion2005

    • Author(s)
      S.Abe, S.Thurner
    • Journal Title

      Physica A (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Scale-invariant statistics of period in directed earthquake network2005

    • Author(s)
      S.Abe, N.Suzuki
    • Journal Title

      European Physica Journal B 44

      Pages: 115-117

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Scaling relations in equilibrium nonextensive thermostatistics2005

    • Author(s)
      S.Abe, A.K.Rajagopal
    • Journal Title

      Physics Letters A 337

      Pages: 292-295

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Scale-free statistics of time interval between successive earthquakes2005

    • Author(s)
      S.Abe, N.Suzuki
    • Journal Title

      Physica A 350

      Pages: 588-596

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Necessity of q-expectation value in nonextenesive statistical mechanics2005

    • Author(s)
      S.Abe, G.B.Bagci
    • Journal Title

      Physical Review E 71

      Pages: 016139

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Origin of the Usefulness of the Natural-Time Representation of Complex Time Series2005

    • Author(s)
      S.Abe, N.V.Sarlis, E.S.Skordas, H.Tanaka, P.A.Varotsos
    • Journal Title

      Physical Review Letters (in press)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion2005

    • Author(s)
      S.Abe, S.Thurner
    • Journal Title

      Physica A (in press)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Necessity of q-expectation value in nonextensive statistical mechanics2005

    • Author(s)
      S.Abe, G.B.Bagci
    • Journal Title

      Physical Review E 71

      Pages: 016139

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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