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Theoretical study of inhomogeneous-nonlinear deformation mechanics in earth continuum

Research Project

Project/Area Number 25400451
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Solid earth and planetary physics
Research InstitutionKobe University

Principal Investigator

Yamasaki Kazuhito  神戸大学, 理学(系)研究科(研究院), 講師 (20335417)

Co-Investigator(Kenkyū-buntansha) YAJIMA Takahiro  宇都宮大学, 大学院工学研究科, 准教授 (00548141)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords断層 / 欠陥場 / 変位場 / 変形場 / 分数階微分 / 非線形 / 非局所 / 非平衡 / 岩石変形 / フラクタル / 連続体力学 / 破砕帯 / 非整数微分 / 非整数次元 / ラプラス方程式 / グリーン関数 / 固体地球科学 / 変形 / 破壊 / 流動 / 理論
Outline of Final Research Achievements

Based on fractional calculus, we considered the fault zone as a typical example of the deformed medium including internal structures characterized by the fractional dimension. The fractional notation of the Green’s function for the generalized Laplace field gives a relationship between the fractional dimension and the fractional order of the equation. We applied the relationship to the displacement field around the strike-slip fault characterized by the generalized Laplace equation. From the observed data for the strike-slip fault, we calculated the fractional dimension of the fractional deformation field. This result implies that the non-locality of the deformation field increases toward the fault. Moreover, we suggest the heuristic method of deriving the displacement field of the fractional Navier equation in the semi-fractional case.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (8 results)

All 2016 2015 2013

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (4 results)

  • [Journal Article] Jacobi stability for dynamical systems of two-dimensional second-order differential equations and application to overhead crane system2016

    • Author(s)
      T. Yajima and K. Yamasaki
    • Journal Title

      International Journal of Geometric Methods in Modern Physics

      Volume: 13 Issue: 04 Pages: 1650045-1650061

    • DOI

      10.1142/s0219887816500456

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Fractional Calculus Approach to the Deformation Field near the Fault Zone2015

    • Author(s)
      K. Yamasaki and T. Yajima
    • Journal Title

      Austin Journal of Earth Science

      Volume: 2 Pages: 1018-1022

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Lotka-Volterra system and KCC theory : Differential geometric structure of competitions and predations2013

    • Author(s)
      Kazuhito Yamasaki and Takahiro Yajima
    • Journal Title

      Nonlin. Anal. RWA

      Volume: 14 Issue: 4 Pages: 1845-1853

    • DOI

      10.1016/j.nonrwa.2012.11.015

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Geometry of stress function surfaces for asymmetric continuum2013

    • Author(s)
      T. Yajima, K. Yamasaki and H. Nagahama
    • Journal Title

      Acta Geophysica

      Volume: 61 Issue: 6 Pages: 1703-1721

    • DOI

      10.2478/s11600-013-0142-0

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 断層破砕帯における岩石変形の分数階微分に基づく考察2015

    • Author(s)
      山崎和仁
    • Organizer
      日本地質学会
    • Place of Presentation
      信州大学(長野県・松本市)
    • Year and Date
      2015-09-11
    • Related Report
      2015 Annual Research Report
  • [Presentation] 古生物学における生物間相互作用の微分幾何学的考察2013

    • Author(s)
      山崎 和仁, 谷島 尚宏
    • Organizer
      日本古生物学会
    • Place of Presentation
      熊本大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 断層・欠陥場における変形場と磁場の相互作用:非Riemann幾何学とFeynman証明2013

    • Author(s)
      山崎 和仁 ; 中村 望
    • Organizer
      日本地質学会
    • Place of Presentation
      東北大学
    • Related Report
      2013 Research-status Report
  • [Presentation] KCC理論に基づくロトカボルテラ系の非平衡安定性解析2013

    • Author(s)
      山崎 和仁 ; 谷島 尚宏
    • Organizer
      日本数理生物学会
    • Place of Presentation
      静岡大学浜松キャンパス
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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