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Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit

Hans C. Fogedby
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Abstract

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.

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Hans C. Fogedby. 2004-11-10. Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit. https://doi.org/10.1103/physrevlett.94.195702

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