Aspects of Nonequilibrium: Growth and Pattern Formation
in the Kardar Parisi Zhang equation for
a growing interface
A nonperturbative weak noise scheme is applied to the
Kardar-Parisi-Zhang equation for a growing interface in all
dimensions. It is shown that the growth morphology can be
interpreted in terms of a dynamically evolving texture of
localized growth modes with superimposed diffusive modes.
Applying Derrick's theorem it is conjectured that the upper critical
dimension is four.