This paper is concerned with the formation of spiral patterns in a broad range of physical, chemical, and biomolecular systems. An overview of a series of experiments is presented followed by an analysis of spiral reductions for several types of Landau-Ginzburg equations which are applicable to these examples. The main result here is that spiral patterns occur as exact solutions of the highly nonlinear order-parameter equations of motion under three types of conditions: first, at criticality; second, at tricriticality; and third, in the presence of special types of defects which we have modeled with a nonautonomous term. A particularly timely application to ferromagnetic thin films is discussed and provides a physical interpretation of the spiral domain structures found experimentally to arise there.

• Received 16 April 1991

DOI:https://doi.org/10.1103/PhysRevB.44.9201