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Ultradiscrete Analysis on Engineering Systems

Research Project

Project/Area Number 21560069
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionAoyama Gakuin University

Principal Investigator

SATSUMA Junkichi  青山学院大学, 理工学部, 教授 (70093242)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords応用数学 / 数理工学 / セルオートマトン / ヤルオートマトン
Research Abstract

We found several new aspects of the solutions and mathematical structures for ultradiscrete equations, in which both of the independent and dependent variables are discrete. We also studied the relationship between the solutions of the ultradiscrete equationsandthe corresponding nonlinear differential equations and made clear that both are closely related. We also proposed a Kalman filter for the ultradiscrete system, which suggests an applicability of the ultradiscrete equations to engineering systems.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (31 results)

All 2012 2011 2010 2009 Other

All Journal Article (19 results) (of which Peer Reviewed: 19 results) Presentation (10 results) Remarks (2 results)

  • [Journal Article] 超離散系におけるカルマンフィルター2012

    • Author(s)
      礒島伸、白瀬裕己、薩摩順吉
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 23AO-S7巻 Pages: 147-152

    • URL

      http://www.riam.kyushu-u.ac.jp/kyodo/reports.html

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 符号付き超離散Bessel方程式とその特殊解について2012

    • Author(s)
      奈良崎史貴, 礒島伸, 薩摩順吉
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 23AO-S7巻 Pages: 96-101

    • URL

      http://www.riam.kyushu-u.ac.jp/kyodo/reports.html

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 線形化可能な超離散QRT系の厳密解と特異点閉じ込めテストについて2012

    • Author(s)
      三村尚之、薩摩順吉
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 23AO-S7巻 Pages: 77-83

    • URL

      http://www.riam.kyushu-u.ac.jp/kyodo/reports.html

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion?2012

    • Author(s)
      N. Mimura, S. Isojima, M. Murata, J. Satsuma, A. Ramani, B. Gramaticos
    • Journal Title

      J. Math. Phys

      Volume: 53 Issue: 2 Pages: 23510-23510

    • DOI

      10.1063/1.3682229

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discretising the Painlev´e equations ‵a la Hirota-Mickens2012

    • Author(s)
      B. Grammaticos, A. Ramani, J. Satsuma and R. Willox
    • Journal Title

      J. Math. Phys

      Volume: 53 Issue: 2 Pages: 24-24

    • DOI

      10.1063/1.3682240

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linearizable QRT mapping2011

    • Author(s)
      A. Ramani, B. Grammaticis, J. Satsuma, N. Mimura
    • Journal Title

      J. Phys. A

      Volume: 44 Issue: 42 Pages: 425201-425201

    • DOI

      10.1088/1751-8113/44/42/425201

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Class of Special Solutions for the Ultradiscrete Painleve II Equation2011

    • Author(s)
      S. Isojima, J. Satsuma
    • Journal Title

      SIGMA

      Volume: 7 Pages: 74-74

    • DOI

      10.3842/sigma.2011.074

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ultradiscrete PainleveII equation and a special function solution2011

    • Author(s)
      S. Isojima, T. Konno, N. Mimura, M. Murata, J. Satsuma
    • Journal Title

      J. Phys. A

      Volume: 44 Issue: 17 Pages: 175201-175201

    • DOI

      10.1088/1751-8113/44/17/175201

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discretising systematically the Painleve equation2011

    • Author(s)
      M. Murata, J. Satsuma, A. Ramani, B. Grammaticos
    • Journal Title

      Phys. D

      Volume: 240 Issue: 3 Pages: 305-309

    • DOI

      10.1016/j.physd.2010.09.007

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solving the ultradiscrete KdV equation2010

    • Author(s)
      Ralph Willox, Yoichi Nakata, Junkichi Satsuma, Alfred Ramani and Basile Grammaticos
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 43 Issue: 48 Pages: 7-7

    • DOI

      10.1088/1751-8113/43/48/482003

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] How to discretize differential systems in a systematic way2010

    • Author(s)
      M. Murata, J. Satsuma, A. Ramani, B Grammaticos
    • Journal Title

      J. Phys. A

      Volume: 43 Issue: 31 Pages: 315203-315203

    • DOI

      10.1088/1751-8113/43/31/315203

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] How to discretize differential systems in a systematic way2010

    • Author(s)
      M Murata
    • Journal Title

      J.Phys.A : Math.Theor.

      Volume: 43巻 Pages: 315203-315217

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the ultradiscrete KdV equation2010

    • Author(s)
      Ralph Willox
    • Journal Title

      J.Phys.A : Math.Theor.

      Volume: 43巻 Pages: 482003-482009

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularity confinement Test for ultradiscrete equations with parity variables2009

    • Author(s)
      N. Mimura, S. Isojima, M. Murata, J. Satsuma
    • Journal Title

      J. Phys. A

      Volume: 42 Issue: 31 Pages: 315206-315206

    • DOI

      10.1088/1751-8113/42/31/315206

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions of the ultradiscrete Sine-Gordon equation2009

    • Author(s)
      S. Isojima, J. Satsuma
    • Journal Title

      JSIAM Letters

      Volume: 1 Pages: 25-27

    • URL

      https://www.jstage.jst.go.jp/article/jsiaml/1/0/1_0_25/_pdf

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions in ultradiscrete system2009

    • Author(s)
      S. Isojima, T. Konno, J. Satsuma
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B13 Pages: 85-93

    • URL

      http://www.kurims.kyoto-u.ac.jp/kenkyubu/bessatsu/open/B13/pdf/B13-07.pdf

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions of the ultradiscrete Sine-Gordon equation2009

    • Author(s)
      S.Isojima
    • Journal Title

      JSIAM Letters 1巻

      Pages: 25-27

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On oscillatory solutions in ultradiscrete system2009

    • Author(s)
      S.Isojima
    • Journal Title

      RIMS Kokyuroku Bessatsu B13巻

      Pages: 85-93

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularity confinement test for ultradiscrete equations with parity variables2009

    • Author(s)
      N.Mimura
    • Journal Title

      J.Phys.A 42巻

      Pages: 315206-315212

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] qAi関数の超離散極限と分割数2012

    • Author(s)
      礒島伸、薩摩順吉、時弘哲治
    • Organizer
      日本応用数理学会2012年研究部会連合発表会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-03-09
    • Related Report
      2011 Final Research Report
  • [Presentation] qAi関数の超離散極限と分割数2012

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会
    • Place of Presentation
      九州大学伊都キャンパス
    • Year and Date
      2012-03-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] 符号付き超離散型方程式の特殊解の系列2011

    • Author(s)
      礒島伸、薩摩順吉
    • Organizer
      日本数学会2011年度秋季総合分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Final Research Report
  • [Presentation] 符号付き超離散Painleve II型方程式の特殊解の系列2011

    • Author(s)
      礒島伸
    • Organizer
      日本数学会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超離散パンルヴェII型方程式の様々な特殊解系列2011

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本応用数理学会2011年度年会
    • Place of Presentation
      同志社大学今出川キャンパス
    • Year and Date
      2011-09-14
    • Related Report
      2011 Final Research Report
  • [Presentation] 超離散パンルヴェII型方程式の様々な特殊解系列2011

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会
    • Place of Presentation
      同志社大学今出川キャンパス
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超離散パンルヴェII型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸, 薩摩順吉
    • Organizer
      日本応用数理学会2010年度年会
    • Place of Presentation
      明治大学
    • Year and Date
      2010-09-07
    • Related Report
      2011 Final Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之, 薩摩順吉
    • Organizer
      日本応用数理学会2010年度年会
    • Place of Presentation
      明治大学
    • Year and Date
      2010-09-07
    • Related Report
      2011 Final Research Report
  • [Presentation] 超離散パンルヴェII型方程式とその特殊解の系列について2010

    • Author(s)
      礒島伸
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超離散特異点閉じ込めテストと方程式の可積分性について2010

    • Author(s)
      三村尚之
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://raweb.jm.aoyama.ac.jp/aguhp/KgApp?kojinId=gaab

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://raweb.jm.aoyama.ac.jp/aguhp/KgApp?kojinId=gaab

    • Related Report
      2011 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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