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2001 Fiscal Year Final Research Report Summary

Studies on the Discrete Calculus and Its Application to Engineerings

Research Project

Project/Area Number 10650065
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

HIROTA Ryogo  Waseda School of Science & Engineering, Professor, 理工学部, 教授 (00066599)

Co-Investigator(Kenkyū-buntansha) IWAO Masataka  Waseda School of Science & Engineering, Research Assistant, 理工学部, 助手 (70318806)
TUJIMOTO Satoshi  Osaka Univ., Grad. School. Fundamental Engineering, Research Assistant, 大学院・基礎工学研究科, 助手 (60287977)
TAKAHASHI Daisuke  Waseda School of Science & Engineering, Professor, 理工学部, 教授 (50188025)
Project Period (FY) 1998 – 2001
Keywordsdifference equation / ultradiscrete equation / integrable systems / difference calculus / cellular automaton / Traffic flow / pattern formation / singular values
Research Abstract

Our first object is the studies on the difference calculus which have been successfully developed as described in the books(see below) :
Our second object is the integrable discretization of the differential equations which is also very successful as described in the articles (1,2,5,7,9,10,11,12,14,17).
Avariety of applications of the difference (or ultradiscrete) calculus to the engineerings has been investigated in the fields such as cellular automaton, traffic flow and pattern formation in the articles (3,4,6,13,19,20), and a numerical scheme to computes singular values (16).

  • Research Products

    (44 results)

All Other

All Publications (44 results)

  • [Publications] S.Tsujimoto, R.Hirota: "Ultradiscrete KdV Equation"Journal of the Physical Society of Japan. 67. 1809-1810 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Hirota: "Discretization of the Potential Modified KdV Equation"Journal of the Physical Society of Japan. 67. 2234-2236 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nishinari, D.Takahashi: "Analytical Properties of Ultradiscrete Burgers Equation and Rule-184 Cellular Automaton"J.Phys.A. 31. 5439-5450 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nishinari, D.Takahashi: "A new deterministic CA model for traffic flow with multiple states"J.Phys.A. 32. 93-104 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Ramani, D.Takahashi, B.Grammaticos, Y.Ohta: "The ultimate discretization of the Painleve equations"Physica D. 114. 185-196 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Nagai, D.Takahashi, T.Tokihiro: "Soliton cellular automaton, Toda molecule equation and sorting algorithm"Physics Letters A. A255. 265-271 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Hirota: "Discretization of coupled modified KdV equation"Chaos, Solitons and Fractals. A11. 77-84 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Iwao, R.Hirota: "Soliton Solutions of a Derivative Coupled Modified KdV Equations"Journal of the Physical Society of Japan. 69. 59-72 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryogo Hirota, Masataka Iwao: "Time-Discretization of Soliton Equations"CRM Proceedings and Lecture Notes. 25. 217-229 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryogo Hirota, Kinji Kimura: "Discretization of the Euler Top"Journal of the Physical Society of Japan. A69. 627-630 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kinji Kimura, Ryogo Hirota: "Discretization of the Lagrange Top"Journal of the Physical Society of Japan. A69. 3193-3199 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Tokihiro, D.Takahashi, J.Matsukidaira: "Box and ball system as a realization of ultradiscrete nonautonomous KP equation"J.Phys.. A33. 607-619 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nishinari, D.Takahashi: "Multi-value cellular automaton models and metastable states in a congested phase"J.Phys.A. 33. 7709-7720 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryogo Hirota, Kinji Kimura, Hideyuki Yahagi: "How to find the conserved quantities of nonlinear discrete equations"Journal of Physics A : Math.Gen.. 34. 10377-10386 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ryogo Hirota, Masataka Iwao, Satoshi Tsujimoto: "Soliton Equations Exhibiting Pfaffian Solutions"Glasgow Mathematical Journal. 43A. 33-41 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Satoshi Tsujimoto, Ypshimasa Nakamura, Masashi Iwasaki: "The discrete Lotka-Volterra system computes singular values"Inverse Problems. 17. 53-59 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] C.R.Gilson, J.J.C.Nimmo, S.Tsujimoto: "Pfaffianisation of the Discrte KP equation"J.Phys.A ; Math.Gen.. 34. 10569-10575 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nishinari, J.Matsukidaira, D.Takahashi: "Two dimensional Burgers cellular automaton"J.Phys.Soc.Jpn.. 70. 2267-2272 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.Takahashi, A.Shida, M.Usami: "On pattern formation mechanism of 2+1D max-plus models"J.Phys.A. 34. 10715-10726 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Fukui, K.Nishinari, D.Takahashi, Y.Ishibashi: "Metastable Flows in a Two-Lane Traffic Model Equivalent to Extended Burger's Cellular Automaton"Physica A. 303. 226-238 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 広田 良吾: "差分方程式講義"サイエンス社. 167 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 辻本 諭: "可積分系の応用数理(第一章 可積分系の離散化について)"裳華房. 1-52 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Satoshi Tsujimoto and Ryogo Hirota: "Ultradiscrete KdV Equation"J. of Phys. Soc. Jpn.. Vol. 66. 1809-1810 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota: "Discretization of the Potential Modified KdV Equation"J. of Phys. Soc. Jpn.. Vol. 66. 2234-2236 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Nishinari and D. Takahashi: "Analytical Properties of Ultradiscrete Burgers Equations and Rule-187 Cellular Automation"J. Phys. A.. Vol. 31. 5439-5450 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Nishinari and D. Takahashi: "A new deterministic Camodel for traffic flow with multiple states"J. Phys. A. Vol. 32. 93-104 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Ramani, D. Takahashi, B. Grammaticos and Y. Ohta: "The ultimate discretization of the Painleve equations"Physica D. Vol. 114. 185-196 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Nagai, D. Takahashi and T. Tokihiro: "Soliton cellular automaton, Toda molecule equation and sorting algorithm"Physics Letters A. Vol. A 255. 265-271 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota: "Discretization of coupled modified KdV equations"Chaos, Solitons and Fractals. Vol. 11. 77-84 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masataka Iwao and Ryogo Hirota: "Soliton Solutions of a Coupled Derivative Modified KdV Equations"J. of Phys. Soc. Jpn. Vol. 69. 59-72 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota and Masataka Iwao: "Time-Discretization of Solitons Equations"CRM Proceedings and Lecture Notes. Vol. 25. 217-229 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota and Kinji Kimura: "Discretization of the Euler Top"J. of Phys. Soc. Jpn.. Vol. 69. 627-630 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota and Kinji Kimura: "Discretization of the Lagrange Top"J. of Phys. Soc. Jpn.. Vol. 69. 3193-3199 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Tokihiro, D. Takahashi and J. Matsukidaira: "Box and ball system as a realization of ultradiscrete nonautonomous KP equation"J. Phys. A. 33. 607-619 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Nishinari and D. Takahashi: "Multi-value cellular automaton models and metastable states in a congested phase"J. Phys. A. 33. 7709-7720 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota, Kinji Kimura and Hideyuki Yahagi: "How to find the conserved quantities of nonlinear discrete equations"J. Physics A : Math. And Gen.. Vol. 34. 10377-10386 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota, Masataka Iwao and Satoshi Tujimoto: "Soliton Equations Exhibiting Pfaffian Solutions"Glasgow Math. J. Vol. 43A. 33-41 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Satoshi Tujimoto, Yoshimasa Nakamura and Masashi Iwasaki: "The discrete Lotka-volterra system computes singular values"Inverse Problems. Vol. 17. 53-59 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] C. R. Gilson, J. J. C. Nimmo and S. Tujimoto: "Pfaffianization of the Discrete KP equation"J. Phys. A. Math. Gen.. Vol. 34. 10569-10575 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Nishinari, J. Matsukidaira and D. Takahashi: "Two dimensional Burgers cellular automaton"J. Phys. Soc. Jpn.. 70. 2267-2272 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D. Takahashi, A. Shida and M. Usami: "On pattern formation mechanism of 2+1D max-plus models"J. Phys. A. 34. 10715-10726 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Fukui, K. Nishinari, D. Takahashi and Y. Ishibashi: "Metastable Flows in a Two-Lane Traffic Model Equivalent to Extended Burger's Cellular Automaton"Physica A. 303. 226-238 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ryogo Hirota: "Lectures on Difference Calculus (in Japanese)"Saiennsu Pub. Company. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Satoshi Tsujimoto: "Applied Mathematical Science of the Integrable Systems (Chapter 1 : On the discretization of the Integrable System) (in Japanese)"Ed. Yoshimasa Nakamura, Syouka-bou Pub. Company. (2000)

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

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Published: 2003-09-17  

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