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Labyrinthic patterns are observed both in systems where the uniform states are metastable, as a result of a front instability, and in systems displaying a cellular instability, when the band of excited Fourier modes is wide enough to support resonant interactions between modes lying on different shells. We show that the phase formalism is a suitable description for low-density labyrinthic patterns with a relatively long 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 boundaries across which the wavevector makes an order one transition, are found to be singular and weak solutions of the Cross-Newell phase diffusion equation, which take account of their energetics as well as their topologies

Elementary and Composite Defects of Striped Patterns