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Visualization-system of spatio-temporal patterns in natural sciences

Research Project

Project/Area Number 63840001
Research Category

Grant-in-Aid for Developmental Scientific Research

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

MIMURA Masayasu  Hiroshima University, Faculty of Science, Professor, 理学部, 教授 (50068128)

Co-Investigator(Kenkyū-buntansha) KOBAYASHI Ryo  Ryukoku Univ. Fac. of Sci. & Tech., Lecturer, 理工学部, 講師 (60153657)
ITOH Masayuki  Tokushima Univ. Fac. of Integral Sci., Associate Prof., 総合科学部, 助教授 (70136034)
HAYASHI Takaya  National Inst. of Fusion Sci., Associate Professor, 助教授 (60156445)
NISHIDA Takaaki  Kyoto Univ. Fac. of Sci., Professor, 理学部, 教授 (70026110)
FUJIKOSHI Yasunori  Hiroshima Univ. Fac. of Sci., Professor, 理学部, 教授 (40033849)
俣野 博  東京大学, 理学部, 助教授 (40126165)
Project Period (FY) 1988 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥9,600,000 (Direct Cost: ¥9,600,000)
Fiscal Year 1989: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1988: ¥8,000,000 (Direct Cost: ¥8,000,000)
KeywordsNumerical simulations of reaction-diffusion equations / Visualization of numerical simulations / Numerical study of Interfacial patterns / 数値シミュレーションの動画化処理 / 界面パターンの数値計算
Research Abstract

In 1988, we developed visualization system of numerical simulations which connected with mini-super computer under local network systems in the department of Mathematics at Hiroshima University. By using this system, our first study is to visualize spatio-temporal patterns dynamics in combustions, by numerically solving two mathematical models of reaction-diffusion type. The first example is to demonstrate the propagation of combustion waves in one dimension. We can observe that there occurs a bifurcation phenomenon in the wave velocity. That is, when we change the difference of the temperatures at the both side X = <plus-minus>*, the wave which propagates with constant velocity becomes unstable through Hopf-bifurcation and there appears a new wave which propagates with periodic velocity. This phenomenon can be also observed in real experiments. Another example is the pattern formation of cellular flame in a 2 dimensional annular domain. We find that radially symmetric flame patterns become unstable and then there appear cellular flame patterns through static bifurcatio
In 1989, we are interested in visualizing the phenomena of phase separation and coarsening process in binary alloy from a theoretical view point. We numerically solved several reaction-diffusion equation models which has been proposed so far to understand these phenomena. The results show so complex and beautiful patterns which has not been expected until now.

Report

(3 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 三村昌泰: "Phase separation in an activator-inhibitor medium" Forma. 4. 65-73 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 辻川亨: "Stability properties of traveling pulse solutions of the higher dimensional FutzHugh-Nagumo equations" Japan Journal of Applid Mathematics. 6. 341-366 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] J.C.Elibeck: "Stationary states associated with phase separation in a pure material" Physics Letter A. 139. 42-46 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 松村昭孝: "Periodic solutions of viscous gas equation" Matheamtics Studies. 160. 49-82 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 藤越康祝: "Error bounds for asymptotic expansions of the maximums of the multivariable t-and F-variables with common dynominator" Hiroshima Mathematical Journal. 19. 319-327 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 西浦廉政: "Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion systems" SIAM Journal of Mathematical Analysis. (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 太田隆夫: "Formation dynamics and statistics of patterns" World Scientific Press, (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Masayasu Mimura: "Phase separation in an activator-inhibitor" Forma, 4, 65-73, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Tohru Tsujikawa: "Stability properties of traveling pulse solutions of the higher dimensional FitzHugh-Nagumo equations" Japan J. Appl. Math., 6, 341-366, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] J. C. Elibeck: "Stationary states associated with phase separation in a pure material" Physics Letter A, 139, 42-46, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Akitaka Matsumura: "Periodic solutions of viscous gas equation" Mathematics Studies, 160, 49-82, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Yasunori Fujikoshi: "Error bounds for asymptotic expansions of the maximums of the multivariable t- and F-variables with common dynominator" Hiroshima Mathematical Journal, 19, 319-327, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Yasumori Nishiura: "Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion systems" SIAM J. Math. Anal., to appear, 1990.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Takao Ohta: "Formation dynamics and statistics of patterns" World Scientific Press, to appear, 1990.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 三村昌泰: "Phase separation in an activatorーinhibitor medium" Forma. 4. 65-73 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 辻川享: "Stability properties of traveling pulse solutions of the higher dimensional FitzHughーNagumo equations" Japan Journal of Applied Methematics. 6. 341-366 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] J.C.Elibeck: "Stationary states associated with phase separation in a pure material" Physics Letter A. 139. 42-46 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 松村昭孝: "Periodic solutions of viscous gas equation" Mathematics Studies. 160. 49-82 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 藤越康祝: "Error bounds for asymptotic expansions of the maximums of the multivariable tーand Fーvariables with common dynominator" Hrroshima Mathematical Journal. 19. 319-327 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 西浦廉政: "Singular limit analysis of stability of traveling wave solutions in bistable reactionーdiffusion systems" SIAM Journal of Mathematical Analysis. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 太田隆夫: "Formation dynamics and statistics of patterns" World Scientific Press, (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 三村昌泰: Japan J.Aple.Math.5. 33-51 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 池田栄雄: Japan J.Appl.Math.6. 1-66 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 太田隆夫: Physica D. 34. 115-144 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 藤越康祝: J.Multivariate Anal.27. 194-205 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 西田孝明: Lecture Notes in Num.Apple.Anal.(1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 西浦廉政: SIAM J.Math Anal.(1989)

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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