Mathematical Modeling and Analysis
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, persistent patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions.