Relaxation and Hysteresis in a Periodically Forced Swift-Hohenberg System

The relaxation and hysteresis of a periodically forced Swift-Hohenberg (SH) equation as a phenomenological model for the magnetic domains of a garnet thin film in an oscillating magnetic field are studied. It is already known that the unforced SH equation settles down to a single type of spatial structure called a stripe pattern, and that the relaxation process yields a scaling law for the structure factor. Two types of temporally oscillating spatial structure consisting of stripe and polka-dot patterns have also been asymptotically observed in the case of a periodically forced SH equation. Relaxation scaling behaviors are studied for these two patterns. It is also shown for the forced case that a hysteresis is observed in the vicinity of the boundary between two different spatial patterns in the phase diagram. Subject Index: 051 Many studies have been compiled on pattern dynamics far from equilibrium such as thermal convection, chemical reactions and biological pattern formation.1)–3) One of the example of such phenomena is the onset of Rayleigh-Benard convection and the formation of roll patterns. It is well known that the thermal convectio