Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak-noise limit.
A weak-noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the solutions can be interpreted in terms of a growth morphology of a dynamically evolving texture of localized growth modes with superimposed diffusive modes. By applying Derrick's theorem, it is conjectured that the upper critical dimension is four.
Fogedby
Hans C
HC
Department of Physics and Astronomy, University of Aarhus, Denmark. fogedby@phys.au.dk