The remarkable properties of fronts propagating into an unstable state.
Wim van Saarloos (Instituut Lorenz , Leiden)

Jeudi 9 novembre 2000

With an allusion to George Orwell’s "Animal Farm", in this talk I hope to demonstrate the idea that "All fronts are equal, but some fronts are more equal than others". Non-equilibrium patterns form through the motion of interfaces or fronts separating essentially homogeneous domains. In most cases, we deal with fronts that separate two linearly stable states. Their properties are well understood, and to a large degree such fronts all respond to changes in the driving force in the same way ("all fronts are equal"). Fluctuating fronts of this type are typically in one and the same universality class (that of the KPZ equation).

However, certain patterns involve the motion of fronts which propagate into a linearly unstable state. The dynamics of such fronts is quite remarkable, in particular when their dynamics is essentially driven by the growth and spreading of perturbations about the unstable state. Unlike those which separate two stable states, their velocity approaches an asymptotic value with a universal power law, which is independent of the non-linearities in the dynamical equation. Moreover, we will present arguments and evidence that fluctuating fronts of this type are not in the standard KPZ universality class.