The structure of spiral domain patterns

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Abstract
We analyse cellular patterns which appear spontaneously in a number of non-equilibrium systems governed by the dynamics of a complex field, and we show that their structure can be understood in very simple terms. In the case of the complex Ginzburg-Landau equation disordered cells of effectively frozen spirals appear, separated by thin walls on a scale much larger than the basic wavelength of the spirals. We show that the walls are segments of hyperbolae and that the transverse structure depends on their angle relative to the phase contours and that it can be oscillatory. Finally, we emphasize the importance of the phase constants, which make these structures different from Voronoi cells.