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Study on Simultaneous Reaction-Diffusion Cellular Automata

Research Project

Project/Area Number 16K21024
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Basic analysis
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

MURATA Mikio  東京農工大学, 工学(系)研究科(研究院), 准教授 (60447365)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords応用数学 / 解析学 / セル・オートマトン / 反応拡散系
Outline of Final Research Achievements

The "simultaneous reaction-diffusion cellular automata" is one of the mathematical models. A mathematical model is a mathematical representation of various problems that occur in the real world, such as equations, and is also needed to efficiently obtain answers using a computer. Cellular automata are mathematical models that are easy to calculate using a computer.
A mathematical model is known that uses a differential equation to represent the problem of reaction and diffusion phenomena called reaction-diffusion system, but it is difficult to calculate the differential equation by computer.
We researched that "simultaneous reaction-diffusion cellular automata" can express the problem that reaction and diffusion phenomenon occur at the same time as reaction-diffusion system.

Academic Significance and Societal Importance of the Research Achievements

数理モデルとは現実の世界で起きる様々な問題を方程式などの数学的な形で表現したものであり、様々な問題を十分に表現できていることと、コンピューターを用いて計算しやすい形であることが必要である。
本研究により、生物学、化学、物理学、工学などの広い分野に見られる反応現象と拡散現象が同時に起こることにより生じる種々の時間的・空間的パターン(模様)の形成に関して、コンピューターを用いて効率よく回答を求めることができると期待される。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (14 results)

All 2020 2019 2018 2017 2016 Other

All Journal Article (6 results) (of which Open Access: 3 results,  Peer Reviewed: 3 results) Presentation (7 results) (of which Int'l Joint Research: 1 results,  Invited: 4 results) Remarks (1 results)

  • [Journal Article] max型拡散セル・オートマトンのチューリング不安定性解析2020

    • Author(s)
      村田実貴生
    • Journal Title

      応用力学研究所研究集会報告

      Volume: 2019AO-S2 Pages: 7-11

    • Related Report
      2019 Annual Research Report
    • Open Access
  • [Journal Article] 方程式の差分化・超離散化2019

    • Author(s)
      村田実貴生
    • Journal Title

      数理科学

      Volume: 57(8) Pages: 61-68

    • Related Report
      2019 Annual Research Report
  • [Journal Article] FitzHugh-Nagumo 方程式の超離散化2018

    • Author(s)
      佐々木幹子、西岡斉治、本郷史也、村田実貴生
    • Journal Title

      応用力学研究所研究集会報告

      Volume: 29AO-S7 Pages: 81-87

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Reaction-Diffusion Equations and Cellular Automata2018

    • Author(s)
      Mikio Murata
    • Journal Title

      Mathematics for Industry (Agriculture as a Metaphor for Creativity in All Human Endeavors)

      Volume: 28 Pages: 21-35

    • DOI

      10.1007/978-981-10-7811-8_4

    • ISBN
      9789811078101, 9789811078118
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] 連立型反応拡散セル・オートマトンの進行波2017

    • Author(s)
      村田 実貴生
    • Journal Title

      九州大学応用力学研究所研究集会報告

      Volume: 28AO-S6 Pages: 7-12

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Reaction-Diffusion Equations and Cellular Automata2016

    • Author(s)
      Mikio Murata
    • Journal Title

      MI Lecture Note

      Volume: 70 Pages: 17-19

    • Related Report
      2016 Research-status Report
  • [Presentation] max型拡散セル・オートマトンのチューリング不安定性解析2019

    • Author(s)
      村田実貴生
    • Organizer
      山形古典解析セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] max型拡散セル・オートマトンのチューリング不安定性解析2019

    • Author(s)
      村田実貴生
    • Organizer
      研究集会「非線形波動研究の多様性」
    • Related Report
      2019 Annual Research Report
  • [Presentation] 反応拡散系のセル・オートマトン化2019

    • Author(s)
      村田実貴生
    • Organizer
      反応拡散系のパターン形成とその応用
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] FitzHugh-Nagumo方程式の超離散化2017

    • Author(s)
      佐々木幹子、本郷史也、西岡斉治、村田実貴生
    • Organizer
      研究集会「非線形波動研究の新潮流 -理論とその応用-」
    • Related Report
      2017 Research-status Report
  • [Presentation] Reaction-Diffusion Equations and Cellular Automata2016

    • Author(s)
      Mikio Murata
    • Organizer
      Forum "Math-for-Industry" 2016
    • Place of Presentation
      クイーンズランド工科大学
    • Year and Date
      2016-11-21
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 連立型反応拡散セル・オートマトンの進行波2016

    • Author(s)
      村田 実貴生
    • Organizer
      研究集会「非線形波動研究の深化と展開」
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2016-11-03
    • Related Report
      2016 Research-status Report
  • [Presentation] 反応拡散方程式とセル・オートマトン2016

    • Author(s)
      村田 実貴生
    • Organizer
      山形古典解析セミナー
    • Place of Presentation
      山形大学理学部数学科
    • Year and Date
      2016-04-22
    • Related Report
      2016 Research-status Report
    • Invited
  • [Remarks] 微分方程式のセルオートマトン類似の構成 | 東京農工大学研究ポータル

    • URL

      http://rd.tuat.ac.jp/activities/factors/search/20150709_4.html

    • Related Report
      2017 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2021-02-19  

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