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Elastic Effects in the Phase Separation of the System with Finite Size

Research Project

Project/Area Number 09650074
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

KOBAYASHI Ryo  Hokkaido Univ., Res. Inst. for Electronic Sci., Asso. Pro., 電子科学研究所, 助教授 (60153657)

Co-Investigator(Kenkyū-buntansha) TANAGATA Tatsuo  Hokkaido Univ., Res. Inst. For Electronic Sci., Inst., 電子科学研究所, 助手 (80242262)
NISHIURA Yasumasa  Hokkaido Univ., Res. Inst. For Electronic Sci., Pro., 電子科学研究所, 教授 (00131277)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1997: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordsgrain boundary / phase field model / recrystallization / singular diffusivity / spiral steps / segregation / granular materials / self-replicating pattern / recrystallization / grain boundarg migration / grain rotation / step dynamics / screw dislocation / spiral step / bunching / phase field model / grain boundary / polycrystal / singular diffusivity / nonlinear semi-group theory / segregation / granular materials / self-replicating / 反応拡散系 / フェーズフィールド / 多結晶 / 相分離 / Cahn-Hilliard / ブロックコポリマー / 散逸系
Research Abstract

(a) Usual phase field models have an essential short coming that they cannot describe the formation of poly-crystals since they are lacking in the information of orientation. We proposed a vectorized phase field model which enables us to simulate a simultaneous crystallization of many particles with various orientations and a formation of grain boundaries.
(b) Recrystallization takes place through the two basic processes, say, (I) grain boundary migration and (ii) grain rotation. Almost all the model of recrystallization handle the process (I) only. We proposed a totally new phase field model which can treat both of the processes (I) and (il) simultaneously.
c In the above recrystallization model the equation for the evolution of angle variable expresses a non-local interaction by introducing a new mathematical concept "singular diffusivity" We justified this new equation and analyzed it mathematically.
(d) It is well known that the mixture of granular materials can segregate in the rotating cylinder. We investigated this phenomena through experiments and modeling and found that it is caused by the property of strong segregation in the suface flow of binary mixture of granular materials.
(e) A mathematical model of step dynamics on the facet of growing crystals are presented. This model is able to describe the motion of steps caused by the arbitrary number of screw dislocations.
(f) Mathematical structure which produces self-replicating patterns were made clear by the approach of experimental mathematics. We demonstrated that the ordered saddle node bifurcation branches and the paths connecting them are essential for the formation of self-replicating patterns.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (38 results)

All Other

All Publications (38 results)

  • [Publications] R.Kobayashi: "Mathematical Models for Solidification and Grain Boundary Formation"ACH-Models in Chemistry. 135. 287-295 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K.Ueda: "Segregation of Granular Materials in a Rotating Tube"Proceedings of the 2^<nd> Tohwa University International Meeting, Statistical Physics. 141-141 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R.Kobayashi: "Vector-valued Phase Field Model for Crystallization and Grain Boundary Formation"Physica D. 119. 415-423 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J.A.Warren: "A Phase Field Model of the Impingement of Solidifying Particles"Physica A. 261. 159-166 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R.Kobayashi: "Equations with Singular Diffusivity"J.Stat.Phys.. 95. 1187-1220 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R.Kobayashi: "A Simple Continuum Model of Grain Boundaries"Physica D. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.-H.Giga: "Very Singular Diffusion Equations"Proceedings of Taniguchi Symposium, Nara 1998, ed.T.Sunada. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Nishiura: "A Skeleton Structure of Self-repricating Dynamics"Physica D. 130. 73-104 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T.Yanagita: "A Three-Dimensional Cellular Automaton Model of Segregation of Granular Materials in a Rotating Cylinder"Phys.Rev.Lett.. 82. 3488-3491 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 西浦廉政: "非線型問題I-パターン形成の数理-"岩波書店. 279 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R Kobayashi J A Warren and W. C. Carter: "Mathematical Models for Solidification and Grain Boundary Formation"ACH-Models in Chemistry. Vol.135. 287-295 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Ueda, R. Kobayashi and T. Yanagita: "Segregation of Granular Materials in a Rotating Tube"Proceedings of the 2nd Tohwa University International Meeting, Statistical Physics, eds. M.Tokuyama and I.Oppenheim. World Scientific. pp.141 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Kobayashi, J.A. Warren and W.C. Carter: "Vector-valued Phase Field Model for Crystallization and Grain Boundary Formation"Physica D. Vol.119. 415-423 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J.A. Warren, W.C. Carter and R. Kobayashi: "A Phase Field Model of the Impingement of Solidifying Particles"Physica A. Vol.261. 159-166 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Kobayashi and Y. Ciga: "Equations with Singular Diffusivity"J. Stat, Phys.. Vol.95. 1187-1220 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Kobayashi, J.A. Warren and W.C. Carter: "A Simple Continuum Model of Crain Boundaries"to be published in Physica D.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.-H. Giga, Y. Gigi and R. Kobayashi: "Very Singular Diffusion Equations"to appear in Proceeding of Taniguchi sympopsium. Nara 1998, ed. T. Sunada.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Nishiura and D. Ueyama: "A skeleton structure of self-replicating dynamics"Physica D. Vol.130. 73-104 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Yanagita: "A Three-Dhnensional Cellular Automaton Model of Segregation of Granular Materials in a Rotating Cylinder"Phys. Rev. Lett.. Vol.82. 3488-3491 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R.Kobayashi: "Equations with Singular Diffusivity"J.Stat.Phys.. 95. 1187-1220 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] J.A.Warren: "A Phase Field Model of the Impingement of Solidifying Particle"Physica A. 261. 159-166 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Kobayashi: "A simple Continuum Model of Grain Boundaries"Physica D. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] M.-H.Giga: "Very Singular Diffusion Equations"Proceedings of Taniguchi Symposium, Nara 1998, ed. T. Sunada. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Nishiura: "A Skeleton Structure of Self-replicating Dynamics"Physica D. 130. 73-104 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Yanagita: "A Three-Dimensional Cellular Automaton Model of Segregation of Granular Materials in a Rotating Cylinder"Rhys.Rev.Lett. 82. 3488-3491 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Kobayashi and Y.Giga: "Equations with Singular Diffusivity" J.Stat.Phys.(to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] J.A.Warren, W.C.Carter and R.Kobayashi: "A Phase Field Model of the Impingement of Solydifying Farticles" Physica A. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Kobayashi, J.A.Warren and W.C.Carter: "Vector-valued Phase Field Model for Crystallization and Grain Boundary Formation" Physica D. 119. 415-423 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Ueda, R.Kobayashi and T.Yanagita: "Segregation of Granular Materials in a Rotating Tube" Statistical Physics-Eeperiments,Theories and Computer Simulation,eds.M.Tokuyama and I.Oppenheim. 141-141 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Nishiura and D.Ueyama: "A Skelton Structure of Self-replicating Dynamics" Physica D. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Yanagita: "A Three-Dimensional Cellular Automation Model of Segreation of Granular Materials in a Rotating Cylinder" Physical Review Letters. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] 西浦 廉政: "非線形問題1-パターン形成の数理" 岩波書店, 279 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Kobayashi, J.A.Warren and W.C.Carter: "Mathematical Models for Solidification and Grain Boundary Formation" Complex Chemical Systems in Polymer Matrices. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Ueda, R.Kobayashi and T.Yanagita: "Segregation of Granular Materials in a Rotating Tube" the proceedings of the 2nd Tohwa University International Meeting on Statistical Physics. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] J.A.Warren, W.C.Carter and R.Kobayashi: "A Phase Field Model of the Impingement of Solidifying Particles" the proceedings of Collective Phenomena in Physics. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] R.Kobayashi, J.A.Warren and W.C.Carter: "Vector-valued Phase Field Model for Crystallization and Grain Boundary Formation" Physica D. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Nishiura and H.Suzuki: "Asymptotic configuration of stationary interfacial patterns for reaction diffusion systems" AMS/IP Studies in Math.3. 333-348 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] I.Ohnishi and Y.Nishiura: "Spectral comparison between the second and the fourth order equations of conservative type with non-local terms" JJAIM. (to appear).

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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