Dynamics of fronts present the simplest spatio-temporal
model systems. The dynamics describes a non-equilibrium process
where old states (represented by a height variable h(x) are replaced with
new fronts. There is no consideration of detailed balance, and as a result the
system reaches steady state dynamical state where particular modes of
excitation across the system. In the applet we show the two, philosophically quite different
approaches to front dynamics: One based on annealed noise, and another based on
quenched noise and extremal dynamics.
In the annealed case (KPZ), the noise of the update changes from time to time,
even at the same point (x,h(x)). As a result the front always move a little on
In the quenched case, then when there is no movemenet at a given point (x,h(x))
at some time, then there is typically no movement either at the subsequent timestep.
The fronts gets pinned. This is in particular captured by the exremal dynamics
of the Sneppen interface model.
M. kardar, G. Parisi and Y.-C. Zhang, Physical Review Letter 56 889 (1986).
K. Sneppen, Physical Review Letter 70 3833 (1992).
M. Paczuski, S. Maslov and P. Bak, Physical Review E53 414 (1996).