Dynamical Inequality in Growth Models

Abstract

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.

6 pages, 4 figures

References in corpus (6)

• Numerical study of the Kardar-Parisi-Zhang equation
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Roughness of tensile crack fronts in heterogenous materials
• Roughness of moving elastic lines - crack and wetting fronts
• Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
• Patterns in the Kardar-Parisi-Zhang equation

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• Thermally driven elastic membranes are quasi-linear across all scales
• Nonlinear field theories during homogeneous spatial dilation
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process