Comprehensive study of pattern formation in relaxational systems.
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.
Wood
Kevin
K
Department of Chemistry and Biochemistry 0340, and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
Buceta
Javier
J
Lindenberg
Katja
K