Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

Abstract

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a=<|h(x_1)-h(x_2){|}^a>$ behave as $|x_1-x_2{|}^{{\xi }_a}$ with ${\xi }_a=a$ for length scales $|x_1-x_2|<<\sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.

arXiv comment13 pages, 9 figures

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• Invited review: KPZ. Recent developments via a variational formulation
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• The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime
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• Stochastic ${\varphi }^4-$Theory in the Strong Coupling Limit