English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We extend the previously developed weak noise scheme, applied to the noisyBurgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growinginterface in arbitrary dimensions. By means of the Cole-Hopf transformation weshow that the growth morphology can be interpreted in terms of dynamicallyevolving textures of localized growth modes with superimposed diffusive modes.In the Cole-Hopf representation the growth modes are static solutions to thediffusion equation and the nonlinear Schroedinger equation, subsequentlyboosted to finite velocity by a Galilei transformation. We discuss the dynamicsof the pattern formation and, briefly, the superimposed linear modes.Implementing the stochastic interpretation we discuss kinetic transitions andin particular the properties in the pair mode or dipole sector. We find theHurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipolesector. Finally, applying Derrick's theorem based on constrained minimizationwe show that the upper critical dimension is d=4 in the sense that growth modescease to exist above this dimension.Comment: 27 pages, 19 eps figs, revte

Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension