Construction of particle cellular automata models using the ultradiscretization method

• Project/Area Number: 22560068
• 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 龍谷大学, 理工学部, 教授 (60231594)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: セルオートマトン / 超離散 / Max-Plus / 粒子系 / 束

Research Abstract

We have succeeded in obtaining the general solutions for four-neighborhood particle cellular automata using expression of rules in terms of Max-Plus algebra. We have also succeeded in analyzing asymptotic behavior of the general solutions. Furthermore, we have obtained Max-Min-Plus expressions for five-neighborhood particle cellular automata from fundamental diagrams. The equation transformed by ultradiscrete Cole-Hopf transformation and Lagrange representation of the equation are also obtained. We have succeeded in obtaining the general solutions of ECA using Max-Min lattice.

Research Products

• [Journal Article] 束とECA (2012)
  • Author(s): 池上貴俊,高橋大輔,松木平淳太
  • Journal Title: 九州大学応用力学研究所研究集会報告 Pages: 13-18
  • Peer Reviewed
• [Journal Article] Hiroaki Hara and Bao-Feng Feng, Max-plus analysis on some binary particle systems (2011)
  • Author(s): Daisuke Takahashi, Junta Matsukidaira
  • Journal Title: J. Phys. A. Volume: Vol 44 Pages: 135102-135102
  • Peer Reviewed
• [Journal Article] Max-plus analysis on some binary particle systems (2011)
  • Author(s): Daisuke Takahashi, Junta Matsukidaira, Hiroaki Hara, Bao-Feng Feng
  • Journal Title: Journal of Physics A Volume: 44 Pages: 135102-135102
  • Peer Reviewed
• [Presentation] Max-min-plus expressions for one-dimensional partcle cellular automata obtained from fundamental diagram (2013)
  • Author(s): Junta Matsukidaira
  • Organizer: China-Japan Joint Workshop on Integrable Systems 2013
  • Place of Presentation: 京都大学
• [Presentation] 基本図による5近傍粒子セルオートマトンの解析 (2012)
  • Author(s): 奥村敬済、松木平淳太
  • 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
• [Presentation] 基本図による5近傍粒子セルオートマトンの解析 (2012)
  • Author(s): 奥村敬済、松木平淳太
  • Organizer: 日本応用数理学会
  • Place of Presentation: 九州大学伊都キャンパス(福岡県)
  • Year and Date: 2012-03-09
• [Presentation] セルオートマトンの漸近挙動の解析-数式処理によるMax-Min計算 (2011)
  • Author(s): 松木平淳太
  • Organizer: 研究集会/数式処理-その研究と目指すもの-
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-12-09
• [Presentation] Constructing two-dimensional integrable mappings that possess invariants of high degree (2010)
  • Author(s): Junta Matsukidaira
  • Organizer: Symmetry Plus Integrability 2010
  • Place of Presentation: South Padre Travelodge, SouthPadre Island, TEXAS
  • Year and Date: 2010-06-14
• [Presentation] Constructing two-dimensional integrable mappings that possess invariants of high degree (2010)
  • Author(s): Junta Matsukidaira
  • Organizer: Symmetry Plus Integrability 2010
  • Place of Presentation: South Padre Travelodge, South Padre Island, TEXAS
  • Year and Date: 2010-06-14
• [Presentation] Constructing two-dimensional integrable mappings that possess invariants of high degree (2010)
  • Author(s): Junta Matsukidaira
  • Organizer: 8th AIMS Conference on Dynamical Systems
  • Place of Presentation: Dresden University of Technology, Dresden, Germany
  • Year and Date: 2010-05-27
• [Remarks]
  • URL: http://www.a.math.ryukoku.ac.jp/~junta/paper.html