ELEMENTARY AND COMPOSITE DEFECTS OF STRIPED PATTERNS

Labyrinthic patterns are observed both in systems where the uniform st ates are metastable, as a result of a front instability, and in system s displaying a cellular instability, when the band of excited Fourier modes is wide enough to support resonant interactions between modes ly ing on different shells. We show that the phase formalism is a suitabl e description for low-density labyrinthic patterns with a relatively l ong range correlation and is capable of describing both its smooth and singular structures. The point defects of roll patterns, the concave and convex disclinations, and the line singularities or phase grain bo undaries across which the wavevector makes an order one transition, ar e found to be singular and weak solutions of the Cross-Newell phase di ffusion equation, which take account of their energetics as well as th eir topologies.