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.
Refs:
Hans C.
Fogedby
"Localized
growth modes, dynamic textures,
and upper
critical dimension for the
Kardar-Parisi-Zhang
equation in the weak noise limit"
Phys. Rev.
Lett. 94, 195702 (2005)
"Kardar-Parisi-Zhang
equation in the
weak noise
limit: Pattern formation and upper critical dimension"
Phys. Rev. E
73, 031104 (2006)