A study on conserved cellular automata and their particle systems by ultradiscrete method

• Project/Area Number: 18560065
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Ryukoku University
• Principal Investigator: MATSUKIDAIRA Junta Ryukoku University, 理工学部, 教授 (60231594)
• Co-Investigator(Kenkyū-buntansha): TAKAHASHI Daisuke 早稲田大学, 理工学術院, 教授 (50188025)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 可積分系 / 離散可積分系 / 超離散 / 離散力学系 / 差分方程式 / 交通流 / セルオートマトン / 最適速度モデル / 可積分 / 超離散化 / アトラクタ

Research Abstract

本研究の主な成果は以下の通りである。(1) 2つの保存量を持つ3階の可積分差分方程式が、2階の可積分差分方程式であるQRT系のペアから構成されることを示した。(2) 2階の可積分差分方程式であるQRT系から、明示的なリャプノフ関数を持つ差分方程式系を構成した。(3) QRT系と周期を持つ変換を組み合わせることによって、高次の保存量を持つ2階の差分方程式を構成する方法を提案した。(4) 交通流モデルとして知られる最適速度モデルの離散化、超離散化に成功した。

Research Products

• [Journal Article] Constructing two-dimensional integrable mappings that possess invariants of high degree (2009)
  • Author(s): Hironori Tanaka, Junta Matsukidaira, Atsushi Nobe and Teruhisa Tsuda
  • Journal Title: to appear in RIMS Kokyuroku Bessatsu
  • Peer Reviewed
• [Journal Article] On a discrete optimal velocity model and its continuous and ultradiscrete relatives (2009)
  • Author(s): Daisuke Takahashi and Junta Matsukidaira
  • Journal Title: JSIAM Lettes Vol.1 Pages: 1-4
  • NAID: 130000104496
  • URL: http://www.jstage.jst.go.jp/article/jsiaml/1/0/1_1/_article
  • Peer Reviewed
• [Journal Article] On a discrete optimal velocity model and its continuous and ultradiscrete relatives (2009)
  • Author(s): Daisuke Takahashi, Junta Matsukidaira
  • Journal Title: JSIAM Letters 1 Pages: 1-4
  • NAID: 130000104496
  • Peer Reviewed
• [Journal Article] 2階可積分差分方程式から生成される高階可積分差分方程式について (2006)
  • Author(s): 長井秀友, 高橋大輔, 松木平淳太
  • Journal Title: 日本応用数理学会論文誌 Vol.16, No.3 Pages: 197-210
  • URL: http://ci.nii.ac.jp/Detail/detail.do?LOCALID=ART0007920586&lang=ja
  • Peer Reviewed
• [Journal Article] Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings (2006)
  • Author(s): H. Inoue, D. Takahashi and J. Matsukidaira
  • Journal Title: Physica D Vol.217 Pages: 22-30
  • Peer Reviewed
• [Journal Article] Third-order integrable difference equations generated by a pair of second-order equations (2006)
  • Author(s): J. Matsukidaira and D. Takahashi
  • Journal Title: J. Phys. A Vol 39 Pages: 1151-1161
  • Peer Reviewed
• [Journal Article] Thind-order integrable difference equations generated by a pair of second-order equations, (2006)
  • Author(s): J.Matsukidaira, D.Takahashi
  • Journal Title: J. Phys. A. Vol.39 Pages: 1151-1161
• [Journal Article] Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings (2006)
  • Author(s): H.Inoue, D.Takahashi, J.Matsukidaira
  • Journal Title: Physica D Vol.217 Pages: 22-30
• [Presentation] QRT型差分方程式の拡張について (2008)
  • Author(s): 田中宏典, 松木平淳太
  • Organizer: 日本応用数理学会年会
  • Place of Presentation: 東京大学柏キャンパス
  • Year and Date: 2008-09-18
• [Presentation] QRT系のある拡張について, 可積分数理の拡がり (2008)
  • Author(s): 松木平淳太
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-08-12
• [Presentation] QRT系のある拡張について (2008)
  • Author(s): 松木平淳太
  • Organizer: 可積分数理の拡がり
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-08-12
• [Presentation] A stochastic traffic cellular automaton model with higher velocity (2008)
  • Author(s): Junta Matsukidaira
  • Organizer: Nonlinear Waves--Theory and Applications
  • Place of Presentation: 清華大学
  • Year and Date: 2008-06-10
• [Presentation] A stochastic traffic cellular automaton model with higher velocity (2008)
  • Author(s): Junta Matsukidaira
  • Organizer: The 7th AIMS Conference on Dynamical Systems and Differential Equations
  • Place of Presentation: University of Texas at Arlington
  • Year and Date: 2008-05-18
• [Presentation] QRT系から生成される高次元保存量を持つ2階差分方程式 (2008)
  • Author(s): 田中宏典, 松木平淳太, 野邊厚, 津田照久
  • Organizer: 日本応用数理学会研究部会連合発表会
  • Place of Presentation: 京都大学
  • Year and Date: 2008-03-08
• [Presentation] Recent Developent of the Study of Discrete and Ultradiscrete Integrable Systems (2006)
  • Author(s): Junta Matsukidaira
  • Organizer: Mini Minisymposium" Integrable Discrete and Ultra-discrete Systems and Their Applications " in the SIAM Conference on Nonlinear Waves and Coherent Structures
  • Place of Presentation: University of Washington
  • Year and Date: 2006-09-09
• [Presentation] Third-order integrable difference equations generated by a pair of second-order equations (2006)
  • Author(s): Junta Matsukidaira and Daisuke Takahashi
  • Organizer: Symmetries and Integrability of Difference Equations (SIDE) VII
  • Place of Presentation: The University of Melbourne
  • Year and Date: 2006-07-10