K. Oguni et al., ANALYSIS ON EVOLUTION PATTERN OF PERIODICALLY DISTRIBUTED DEFECTS, International journal of solids and structures, 34(25), 1997, pp. 3259-3272
A similar pattern is formed in various materials, when periodically di
stributed defects evolve. Mathematically, this pattern formation is un
derstood as the consequence of symmetry breaking, while physically it
is caused by interaction effect which vary depending on materials or d
efects. In examining the nature of the interaction effects, this paper
analyzes the bifurcation induced growth of a periodic array of defect
s. With the aid of group-theoretic bifurcation analysis, it is clearly
shown that when the uniform pattern (the evolution of all defects) is
broken, only the alternate pattern (the evolution of every second def
ect) can take place for smaller defects, as often observed in nature.
Therefore, two defects should be considered to examine a possible bifu
rcation of periodic defects. Furthermore, the conclusion obtained can
be extended to explain the phenomena whereby every second, fourth, and
then eighth defect continue to evolve, and whereby alternate bifurcat
ion is repeated successively until the evolution is localized. (C) 199
7 Elsevier Science Ltd.