The structure of spiral domain patterns

¹ The Niels Bohr Institute - Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
² University of California - Berkeley, CA 94720, USA
³ University of Maryland (Institute for Plasma Research, Departments of Physics and of Electrical Engineering and Institute for Systems Research.) - College Park, MD 20742, USA

Received: 11 September 1995
Accepted: 22 January 1996

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.