TY - CHAP

T1 - Bifurcation behaviors of cylindrical soils

AU - Ikeda, Kiyohiro

AU - Murota, Kazuo

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Cylindrical soils undergo complicated bifurcation behaviors due to the loss of symmetry. As a first step to model its symmetry, the dihedral group symmetry of their cross section is exploited in Chaps. 9 and 11. To exploit symmetry breaking in the axial direction, this chapter deals with a larger group D∞h (≅ O (2 ) × ℤ2), which denotes the combination of upside-down symmetry and axisymmetry of a cylindrical domain. Recursive bifurcation and mode switching are highlighted as important behaviors. The perfect system is recovered with reference to imperfect behaviors of cylindrical soils using the procedure advanced in Chap. 6. Group-theoretic bifurcation theory presented in Chap. 8 and its application to the dihedral group in Chap. 9 are foundations of this chapter. An extension to a larger symmetry group O(2) ×O(2) is to be given in Chap. 16 to detect patterns with high spatial frequencies.

AB - Cylindrical soils undergo complicated bifurcation behaviors due to the loss of symmetry. As a first step to model its symmetry, the dihedral group symmetry of their cross section is exploited in Chaps. 9 and 11. To exploit symmetry breaking in the axial direction, this chapter deals with a larger group D∞h (≅ O (2 ) × ℤ2), which denotes the combination of upside-down symmetry and axisymmetry of a cylindrical domain. Recursive bifurcation and mode switching are highlighted as important behaviors. The perfect system is recovered with reference to imperfect behaviors of cylindrical soils using the procedure advanced in Chap. 6. Group-theoretic bifurcation theory presented in Chap. 8 and its application to the dihedral group in Chap. 9 are foundations of this chapter. An extension to a larger symmetry group O(2) ×O(2) is to be given in Chap. 16 to detect patterns with high spatial frequencies.

KW - Axisymmetry

KW - Bifurcation

KW - Cylindrical specimen

KW - Group-theoretic bifurcation theory

KW - Mode switching

KW - Recursive bifurcation

KW - Sand

KW - Soil

KW - Upside-down symmetry

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U2 - 10.1007/978-3-030-21473-9_14

DO - 10.1007/978-3-030-21473-9_14

M3 - Chapter

AN - SCOPUS:85073160341

T3 - Applied Mathematical Sciences (Switzerland)

SP - 405

EP - 433

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -