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2000 Fiscal Year Final Research Report Summary

Experimental, numerical and mathematical approach to the complexity of the phenomena of interfaces

Research Project

Project/Area Number 11440035
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka Institute of Technology

Principal Investigator

TOMOEDA Kenji  Osaka Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (60033916)

Co-Investigator(Kenkyū-buntansha) IKEDA Tsutomu  Ryukoku University, Faculty of Science and Technology, Professor, 理工学部, 教授 (50151296)
MIYOSHI Tetsuhiko  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (60040101)
MIMURA Masayasu  Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50068128)
KAWAGUCHI Masami  Mie University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30093123)
GIGA Yoshikazu  Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70144110)
Project Period (FY) 1999 – 2000
KeywordsBelousov-Zhabotinsky reaction / reaction-diffusion / Hele-Shaw cell / viscous fingering / support splitting phenomena / fracture mechanics / crystal growth / crystal line algorithm
Research Abstract

In this project we are concerned with the following phenomena.
1) Pattern formation of spiral waves in the photosensitive Belousov-Zhabotinsky reaction and helical waves in self-propagating high-temperature syntheses.
2) Self-organized colony patterns by a bacterial cell population.
3) Hele-Shaw cell experiments of viscous fingering and bubble motion in polymeric solutions.
4) Support splitting phenomena caused by the interaction between diffusion and absorption in porous medium flow.
5) Prediction and analysis for the crack path in fracture mechanics
6) Geometric models in crystal growth problems.
We have obtained the following results.
In 1) and 2) the mechanism of the pattern formation is described by the reaction-diffusion equations and are analyzed by using the method of the singular limit and the theory of bifurcation ([1], [2] , [3] , [4] , [5]).
In 3) The modified Darcy's law is derived by taking account of the index of shear-thinning, and gives a good prediction of the finger velocity ([6], [7]).
In 4) the mathematical models which describe such phenomena are written as the nonlinear diffusion equation with strong absorption. The sufficient conditions under which the support begins to split into two disjoint sets are obtained ([8], [9]).
In 5) some formulas connecting the direction and the curvature of the smooth cracks are derived. The validity of these formulas are shown in simple examples ([10], [11]).
In 6) Models of faceted crystal growth and of grain boundaries are proposed based on the gradient system with nondifferentiable energy. The mathematical basis for justifying and analyzing these models is obtained, and theoretical and numerical approaches show how the solutions of these models evolve ([12], [13], [14]).

  • Research Products

    (74 results)

All Other

All Publications (74 results)

  • [Publications] T.Nakaki and K.Tomoeda: "A finite difference schemes for some nonlinear diffusion equations in absorbing medium : support splitting phenomena"Preprint Series in Mathematics, Kyushu University. 2000-18. 1-42 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakaki and K.Tomoeda: "A finite difference approach to the interface equation for some nonlinear diffusion equation with absorption"To appear in Proc.Japan Acad.Ser.A. 77. 32-37 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"INFORMATION. 3. 331-339 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakaki and K.Tomoeda: "Numerical waiting time of interfaces in one-dimensional porous medium equations"Free Boundary Problems : Theory and Applications, Mathematical Sciences and Applications. 14. 324-333 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.Kawaguchi and M.Mimura: "Collision of travelling waves in a reaction-diffusion system with global coupling effect"SIAM J. Appl.Math.. 59. 920-941 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.N.Dancer,D.Hilhorst,M.Mimura and L.A.Peletier: "Spatial segregation limit of a competition-diffusion system,"European J.Appl.Math.. 10. 97-115 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S.-I.Ei,R.Ikota and M.Mimura: "Segregating partition problem in competition-diffusion systems"Interfaces and Free Boundaries. 1. 57-80 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Rodrigo and M.Mimura: "Exact solutions of a competition-diffusion system"to appear in Hiroshima Math.J..

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Funaki,M.Mimura and T.Tsujikawa: "Travelling front solutions arising in a chemotaxis-growth model"to appear in J.Math.Biol..

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mimura,M.Nagayama and T.Ohta: "Non-Annihilation of travelling pulses in reaction-diffusion systems"to appear in J.Methods and Appl.of Analysis.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Rodrigo and M.Mimura: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"to appear in Japan J.Indsutrial and Appl.Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.Hilhorst,M.Ida,M.Mimura and H.Ninomiya: "A competition-diffusion system approximation to the classical two-phase Stefan problem"to appear in Japan J.Indsutrial and Appl.Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada and H.Suito: "Hybridized Fuzzy and GAs Distributed Optimization Method"EUROGEN99,Jyvaskyla,Finland,May 1999.. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada and H.Suito: "Influence of Spilled Oil to bring about on Coastal Ecosystem"Differential Equations and their Applications, An International Symposium dedicated to J.L.Lions on the occasion of his 70th birthday, University of Houston, October 1999.. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada and H.Siuto: "Optimal Shape of Pine for Sound Absorption in Water"Domain Decomposition Methods in Science and Engineering, Proceedings of 11th International Conference on Domain Decomposition Methods, Domain Decomposition Press, Bergen.. 270-281 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada,E.Baba and H.Suito: "Effect of spilled oil on Coastal Ecosystems"ECCOMAS2000 CD-ROM Proceedings. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] C.Bernardi,V.Girault,F.Hecht,H.Kawarada and O.Pironneau: "A Finite Element Problem issued from Fictitious Domain Techniques"To appear in Computational Mechanics. (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Suito and H.Kawarada: "Shape Optimization for an Acoustic Problem"Domain Decomposition Methods in Science and Engineering, Proceedings of 12th International Conference on Domain Decomposition Methods. 419-426 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuhiko Miyoshi: "Direction and curvature of the cracks in two-dimensional elastic bodies"Japan Journal of Industrial and Applied Mathematics. 12-2. 295-307 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuhiko Miyoshi: "Computational crack path prediction and the singularities in elastic-plastic stress fields"Mathematical Modeling and Numerical Simulation in Continuum Mechanics (Eds.Babuska,Ciarlet and Miyoshi) Springerより発行予定.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuhiko Miyoshi: "Direction and curvature of two-dimensional cracks"京都大学 数理解析研究所講究録. 1145. 135-144 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Itakura and M.Tabata: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Suzuki,M.Tabata,and S.Honda: "Numerical solution of an unsteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata and D.Tagami: "A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tension"SIAM Journal on Numerical Analysis. 38. 40-57 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata and D.Tagami: "Error estimates for finite element approximations of drag and lift in nonstationary Navier-Stokes flows"Japan Journal of Industrial and Applied Mathematics. 17. 371-389 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata and A.Suzuki: "A stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell"Computational Methods in Applied Machanics and Engineering. 190. 387-402 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"To appear in Japan Journal of Industrial and Applied Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems"Journal of Dynamics and Differential Equations. 12. 117-167 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Ikeda,H.Ikeda and M.Mimura: "Hopf bifurcation of traveling pulses in some bistable reaction-diffusion systems"Methods and Applications of Analysis. 7. 165-194 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mimura,M.Nagayama,H.Ikeda and T.Ikeda: "Dynamics of travelling breathers arising in reaction-diffusion systems-ODE modelling approach-"Hiroshima Mathematical Journal. 30. 221-256 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.-H.Giga and Y.Giga: "Stability for evolving graphs by nonlocal weighted curvature"Comm. in Partial Differential Equations. 24. 109-184 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] P.Aviles and Y.Giga: "On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg-Landau type energy for gradient fields"Proc.Royal Soc. Edinburgh. 129A. 1-17 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Giga and K.Ito: "Loss of convexity of simple closed curves moved by surface diffusion, Topics in Nonlinear Analysis"The Herbert Amann Aniversary volume, (eds.J.Escher and G.Simonett), Progress in Nonlinear Differential Equations, Birkhauser. 305-320 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Giga,M.Ohnuma and M.-H.Sato: "On strong maximum principle and large time behaviour of generalized mean cuvature flow with the Neumann boundary condition"J.Differential Equations. 154. 107-131 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Kobayashi and Y.Giga: "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
  • [Publications] Y.Giga and M.-H.Sato: "On semicontinuous solutions for general Hamilton-Jacobi equations"Proc. Japan Acad.,Ser.A. 75-9. 159-162 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.-H.Giga and Y.Giga: "Crystalline and level set flow-Convergence of a crystalline algorithm for a general anisotropic curvature flow in the plane"Proc.Free Boundary Problems'99, Theory and Applications (ed.N.Kenmochi), Chiba, Japan(1999), Gakuto International Series, Math.Sci.Appl.. 13. 64-79 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Amemiya,T.Ohmori,T.Yamamoto and T.Yamaguchi: "Stochastic resonance under two-parameter modulation in a chemical model system"J.Phys.Chem.A. 103. 3451-3454 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Amemiya,T.Ohmori,M.Nakaiwa,T.Yamamoto and T.Yamaguchi: "Modeling of nonlinear chemical reaction systems and two-parameter stochastic resonance"J.Biol.Phys.. 25. 73-85 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] P.Kettunen,T.Amemiya,T.Ohmori and T.Yamaguchi: "Spontaneous spiral formation in two-dimensional oscillatory media"Phys.Rev.E. 60. 1512-1515 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Mahara,T.Yamaguchi and Y.Amagishi: "A numerical study of the decomposition of chemical waves in a closed system"Chem.Phys.Lett.. 317. 23-27 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Mahara,T.Saito,Y.Amagishi,H.Nagashima and T.Yamaguchi: "Ring-shaped model of the pacemaker in oscillatory reaction-diffusion system"J.Phys.Soc.Jpn.. 69. 3552-3554 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Amemiya,T.Yamamoto,T.Ohmori and T.Yamaguchi: "Electrochemical control of bifurcation points for stochastic resonance in a model of the photosensitive Belousov-Zhabotinsky reaction"Macromol.Symp.. 160. 1-6 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] V.A.Davydov,V.S.Zykov and T.Yamaguchi: "Drift of spiral waves on nonuniformly curved surfaces"Macromol.Symp.. 160. 99-106 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Yamaguchi,T.Amemiya,T.Ohmori,Y.Morikawa,T.Kusumi and H.Nagasawa: "Preparation of anisotropic mesoporous glass and measurement of anisotropy in diffusion by traveling chemical waves"Macromol.Symp.. 160. 131-136 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Amemiya,T.Ohmori and T.Yamaguchi: "An Oregonator-class model for photoinduced behavior in the Ru(II)(bpy)_3-catalyzed Belousov-Zhabotinsky reaction"J.Phys.Chem.A. 104. 336-344 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kawaguchi,K.Shimomoto,A.Shibata and T.Kato: "Effect of Anisotropy on Viscous Fingering Patterns of Polymer Solutions in Linear Hele-Shaw Cells"Chaos. 9. 323-328 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川口正美,牧野恭子,加藤忠哉: "高分子溶液のヴィスコスフィンガリング"化学工学論文集. 25. 516-519 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川口正美: "高分子系のヴィスコスフィンガリング"高分子論文集. 56. 597-608 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kawaguchi: "Viscous Fingering in Polymer Solutions"Macromolecular Symposia. 160. 85-90 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kawaguchi: "Viscous Fingering in Polymeric Systems"to appear in Nonlinear Analysis.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakaki: "Numerical analysis to the motion of some point and finite vortices"Math.Sci.Appl.. 12. 85-94 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakaki: "Numerical computation to the advection in the field of some point vortices"数理解析研究所講究録. 1145. 145-152 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakaki: "The analysis to some point vortex problems using computers"to appear in Journal of Nonlinear Analysis, Series A Theory and Methods.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nakane: "Numerical Computations for Ginzburg-Landau equation with a variable coefficient by using the discrete Morse semiflow"京都大学数理解析研究所講究録. 1145. 153-160 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nagasawa,K.Nakane and S.Omata: "Numerical computations for a hyperbolic Ginzburg-Landau system"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Nakane : "Numerical simulation to the behavior of the thin film peeling from the plato"INFORMATION. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Imai,K.Kikuchi,K.Nakane,S.Omata and T.Tachikawa: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional hyperbolic free boundary problem"JJIAM. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川口正美: "高分子の界面・コロイド科学"コロナ社. 199 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 儀我美一,儀我美保: "非線形偏微分方程式-解の漸近挙動を自己相似解"共立出版. 300 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mimura, H.Sakaguchi and M.Matsuyama: "Reaction-diffusion modelling of bacterial colony patterns"Physica A. 282. 283-303 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems"Journal of Dynamics and Differential Equations. Vol.12, No.1. 117-167 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Ikeda, H.Ikeda and M.Mimura: "Hopf bifurcation of traveling pulses in some bistable reaction-diffusion systems"Methods and Applications of Analysis. Vol.7, No.1. 165-194 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] P.Kettunen, T.Amemiya, T.Ohmori and T.Yamaguchi: "Spontaneous spiral formation in two-dimensional oscillatory media"Phys.Rev.E. 60. 1512-1515 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Amemiya, T.Yamamoto, T.Ohmori and T.Yamaguchi: "Electrochemical control of bifurcation points for stochastic resonance in a model of the photosensitive Belousov-Zhabotinsky reaction, Macromol."Symp.. 160. 1-6 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masami Kawaguchi, Kohkichi Shimomoto, Atsushi Shibata, and Tadaya Kato: "Effect of Anisotropy on Viscous Fingering Patterns of Polymer Solutions in Linear Hele-Shaw Cells"Chaos. 9. 323-328 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masami Kawaguchi: "Viscous fingering in polymeric systems"in Nonlinear Analysis.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"INFORMATION. Vol.3. 331-339 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Nakaki and K.Tomoeda: "A finite difference approach to the interface equation for some nonlinear diffusion equation with absorption"Proc.Japan Acad.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuhiko Miyoshi: "Direction and curvature of the cracks in two-dimensional elastic bodies"Japan Journal of Industrial and Applied Mathematics. Vol.12-2. 295-307 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuhiko Miyoshi: "Computational crack path prediction and the singularities in elastic-plastic stress fields"Mathematical Modeling and Numerical Simulation in Continuum Mechanics, (Eds.Babuska, Ciarlet and Miyoshi). (To appear in Springer- Verlag)..

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Giga, M.Ohnuma and M.-H.Sato: "On the strong maximum principle and the large time behavior of generalized mean curvature flow with the Neumann boundary condition"J.Differential Equations. 154. 107-131 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Giga and R.Kobayashi: "Equations with singular diffusivity"J.Stat.Phys.. 95. 1187-1220 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.-H.Giga and Y.Giga: "Crystalline and level set flow - Convergence of a crystalline algorithm for a general anisotropic curvature flow in the plane"Proc.Free Boundary Problems '99, Theory and Applications (ed.N.Kenmochi), Chiba, Japan (1999), Gakuto International Series, Math.Sci.Appl.13. 64-79 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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