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
UR - http://www.scopus.com/inward/record.url?scp=85073160341&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073160341&partnerID=8YFLogxK
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 -