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Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System

Gallego, Rafael; San Miguel, Maximino; Toral, Raul
Physical Review E 58, 3125-3134 (1998)

We present a study of dynamical scaling and front motion in a one dimensional
system that describes Rayleigh-Benard convection in a rotating cell. We use
a model of three competing modes proposed by Busse and Heikes to which spatial
dependent terms have been added. As long as the angular velocity is different
from zero, there is no known Lyapunov potential for the dynamics of the system.
As a consequence the system follows a non-relaxational dynamics and the
asymptotic state can not be associated with a final equilibrium state. When the
rotation angular velocity is greater than some critical value, the system
undergoes the Kuppers-Lortz instability leading to a time dependent chaotic
dynamics and there is no coarsening beyond this instability. We have focused on
the transient dynamics below this instability, where the dynamics is still
non-relaxational. In this regime the dynamics is governed by a non-relaxational
motion of fronts separating dynamically equivalent homogeneous states. We
classify the families of fronts that occur in the dynamics, and calculate
their shape and velocity. We have found that a scaling description of the
coarsening process is still valid as in the potential case. The growth law is
nearly logarithmic with time for short times and becomes linear after a
crossover, whose width is determined by the strength of the non-potential
terms.