Bifurcation behaviors of cylindrical soils

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages29
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


  • Axisymmetry
  • Bifurcation
  • Cylindrical specimen
  • Group-theoretic bifurcation theory
  • Mode switching
  • Recursive bifurcation
  • Sand
  • Soil
  • Upside-down symmetry

ASJC Scopus subject areas

  • Applied Mathematics


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