FRONTS, DOMAIN GROWTH, AND DYNAMICAL SCALING IN A D=1 NONPOTENTIAL SYSTEM

By considering the inclusion of nonpotential terms in a model;system t hat has the basic symmetries of a n=3 clock model, we study the issues of dynamical scaling, front motion, and domain growth in a one-dimens ional nonpotential situation. For such a system without a Lyapunov pot ential, the evolution follows a nonrelaxational dynamics with the cons equence that fronts between otherwise equivalent homogeneous states mo ve at a velocity dictated by the strength delta of the nonpotential te rms and the asymptotic state can no longer be associated with a final equilibrium state. In fact, for large enough delta, the system undergo es a transition towards a situation of spatiotemporal chaos that is in many aspects equivalent to the Kuppers-Lortz instability for Rayleigh -Benard convection in a rotating cell. We have focused on the transien t dynamics below this instability, where the evolution is still nonrel axational and the dynamics is dominated by front motion. We classify t he families of fronts and calculate their shape and velocity. We deduc e that the growth law for the domain size is nearly logarithmic with t ime for short times and becomes linear after a crossover, whose width is determined by the value of delta. This prediction is validated by n umerical simulations that also indicate that a scaling description in terms of the characteristic domain size is still valid:as in the poten tial case.