Comprehensive study of pattern formation in relaxational systems

Abstract

We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [Phys. Rev. E 69, 011102 (2004)]. We demonstrate that the phase diagrams for these systems are entirely determined by a few geometric properties of the field-dependent relaxational coefficient and the local potential. Numerical simulations support the theoretical predictions.