NONLOCAL DYNAMICS OF DOMAINS AND DOMAIN-WALLS IN DISSIPATIVE SYSTEMS

The dynamics of domains and domain walls in spatially one-dimensional systems is investigated for the case that the evolution equation contains nonweighted spatial averages of the order parameter or a function of it (strongly nonlocal dynamics). Two ordinary differential equations for reduced order parameters are introduced. The first one governs the dynamics of domain states and domain-wall positions. For large systems, there occurs a separation of time scales that leads to a second reduced equation of motion governing the dynamics of the domain sizes. The time scale of the domain-size dynamics is proportional to the length of the system. Validity conditions of both reduced equations of motion are discussed. The ballast resistor and another current instability system serve as illustrations. © 1990 The American Physical Society.