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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
Project Status Completed (Fiscal Year 2004)
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)
KeywordsTsallis 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
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

Report

(3 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • Research Products

    (21 results)

All 2005 2004 Other

All Journal Article (15 results) Publications (6 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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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: 16139-16139

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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
    • Related Report
      2004 Final Research Report Summary
  • [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: 16139-16139

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [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: 16139-16139

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Scale-free statistics of time interval between successive earthquakes2005

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

      Physica A (掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Scale-invariant statistics of period in directed earthquake network2005

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

      European Physical Journal B (掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Scaling relations in equilibrium nonextensive thermostatistics2005

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

      Physics Letters A (掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stabilities of generalized entropies2004

    • Author(s)
      S.Abe, G.Kaniadakis, A.M.Scarfone
    • Journal Title

      Journal of Physics A : mathematical and General 37

      Pages: 10513-10519

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Aging in coherent noise models and natural time2004

    • Author(s)
      U.Tirnakli, S.Abe
    • Journal Title

      Physical Review E 70

      Pages: 56120-56120

    • Related Report
      2004 Annual Research Report
  • [Publications] S.Abe, N.Suzuki: "Gutenberg-Richter law for Internetquakes"Physica A. 319. 552-556 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Abe, N.Suzuki: "Itineration of the Internet over nonequilibrium stationary states in Tsallis statistics"Physical Review E. 67. 016106 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Abe, N.Suzuki: "Law for the distance between successive earthquakes"Journal of Geophysical Research. 108. 2113 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Abe, T.Kobayashi: "Hidden gauge structure and derivation of microcanonical ensemble theory of bosons from quantum principles"Physical Review E. 67. 036119 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Abe, N.Suzuki: "Omori's law in the Internet traffic"Europhysics Letters. 61. 852-855 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Abe: "Generalized entropy optimized by a given arbitrary distribution"Journal of Physics A. 36. 8733-8738 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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