Echelon-mode formation

Abstract

Bifurcation mechanism of the pattern formation in O(2) ×O(2)-invariant domains is studied. Diamond and stripe patterns are produced by direct bifurcations and echelon modes are engendered by secondary bifurcations. Bifurcating patterns are investigated based on experiments of soil, numerical simulations of sand, and image simulations of kaolin and steel. Fundamentals of group representation theory in Chap. 7 and group-theoretic bifurcation theory in Chap. 8 are the foundations of this chapter.