Group-theoretic bifurcation mechanism of pattern formation in three-dimensional uniform materials

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 12, Issue 12, 2002, Pages 2767-2797

  Tanaka, Reiko ^a   Saiki, Isao ^b   Ikeda, Kiyohiro ^c  

^a KEIO UNIVERSITY   (Japan)

^b UTSUNOMIYA UNIVERSITY   (Japan)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

Group theoretic bifurcation theory; Pattern formation; Pattern simulation; Three dimensional uniform material

Indexed keywords

CALCITE; DEFORMATION; FRACTALS; ROCKS;

PATTERN FORMATION;

BIFURCATION (MATHEMATICS);

EID: 0037003975     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127402006163     Document Type: Article

References (18)

1. Bai, Y. & Dodd, B. [1992] Adiabatic Shear Localization - Occurrence, Theories and Applications (Pergamon).
2. Chossat, P. & Iooss, G. [1994] The Couette-Taylor Problem (Springer).
3. Crawford, J. D. & Knobloch, E. [1991] "Symmetry and symmetry-breaking bifurcations in fluid dynamics," Ann. Rev. Fluid Mech. 23, 341-387.
4. Curtis, C. W. & Reiner, I. [1962] Representation Theory of Finite Groups and Associative Algebras (John Wiley).
5. Davis, G. H. [1984] Structural Geology of Rocks & Regions (John Wiley).
6. Golubitsky, M., Stewart, I. & Schaeffer, D. G. [1988] Singularities and Groups in Bifurcation Theory, Vol. 2 (Springer).
7. Ikeda, K., Murota, K. & Nakano, M. [1994] "Echelon modes in uniform materials," Int. J. Solids and Structures 31, 2709-2733.
8. Ikeda, K., Murakami, S., Saiki, I., Sano, I. & Oguma, N. [2001] "Image simulation of uniform materials subjected to recursive bifurcation," Int. J. Eng. Sci. 39(17), 1963-1999.
9. Ikeda, K. & Murota, K. [2002] Imperfect Bifurcation in Structures and Materials - Engineering Use of Group-Theoretic Bifurcation Theory (Springer).
10. Iooss, G. [1986] "Secondary bifurcations of Taylor vortices into wavy inflow or outflow boundaries," J. Fluid Mech. 173, 273-288.
11. Kettle, S. F. A. [1995] Symmetry and Structure, 2nd edition (John Wiley).
12. Kim, S. K. [1999] Group Theoretical Methods and Applications to Molecules and Crystals (Cambridge University Press).
13. Koschmieder, E. L. [1996] "On convection of a uniformly heated plane," Beiträge zur Physik der Atmosphäre 39, 1-11.
14. Murota, K., Ikeda, K. & Terada, K. [1999] "Bifurcation mechanism underlying echelon-mode formation," Comput. Meth. Appl. Mech. Engrg. 170, 423-448.
15. Sattinger, D. H. [1979] Group Theoretic Methods in Bifurcation Theory (Springer).
16. Schaeffer, D. G. [1980] "Qualitative analysis of a model for boundary effects in the Taylor problem," Math. Proc. Camb. Phil. Soc. 87, 307-337.
17. Taylor, G. I. [1923] "The stability of a viscous fluid contained between two rotating cylinders," Phil. Trans. R. Soc. London A223, 289-343.
18. Turcotte, D. L. [1997] Fractal and Chaos in Geology and Geophysics, 2nd edition (Cambridge University Press).