ANALYSIS ON EVOLUTION PATTERN OF PERIODICALLY DISTRIBUTED DEFECTS

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.