An important class of problems of spontaneous pattern formation concerns those that have to do with growing interfaces - well known examples are dendritic growth and viscous fingering, but questions similar to those that arise for these problems, also come up for problems in which there is not a microscopically sharp interface, but a smooth though thin reaction or transition zone.
Examples are chemical waves, combustion, fronts in nerves, etc.
A few years ago, we realized that in low temperature plasmas, a similar type of problem occurs, streamer formation. The formation of a streamer occurs when a nonlinear ionization wave propagates into a previously unionized region, creating a nonequilibrium plasma behind it. Our analysis has identified the propagation of streamer fronts as an example of front propagation into unstable states in virtually all models analyzed. For such problems, it is well known that the velocity cannot be obtained just by analyzing uniformly translating fronts using standard methods. Instead, the velocity and properties of fronts propagating into unstable states is governed by a mechanism of dynamical front selection which has become largely understood in the last decade.