We propose a spatial discretization of the Kardar-Parisi-Zhang ~KPZ! equation in 111 dimensions. The exact steady state probability distribution of the resulting discrete surfaces is explained. The effective diffusion coefficient, nonlinearity, and noise strength can be extracted from three correlators, and are shown to agree exactly with the nominal values used in the discrete equations. Impli...

We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spa...

1. A physical introduction 2 1.1. KPZ/Stochastic Burgers/Scaling exponent 2 1.2. Physical derivation 3 1.3. Scaling 3 1.4. Formal invariance of Brownian motion 4 1.5. Dynamic scaling exponent 6 1.6. Renormalization of the nonlinear term 6 1.7. Cutoff KPZ models 7 1.8. Hopf-Cole solutions 8 1.9. Directed polymers in a random environment 11 1.10. Fluctuation breakthroughs of 1999 12 1.11. The Air...

We generalize the KPZ equation to an O(3) N = 2j + 1 component model. In the limit N → ∞ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent z increases from 3/2 for d = 1 to 2 at the dimension d ≈ 3.6. For d = 1 it can be shown analytically that z = 3/2 for all j. The case j = 2 for d = 2 is investigated by numerical integration ...

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z⋆...

The Kardar-Parisi-Zhang ~KPZ! equation @1# has been very successful in describing a class of dynamic nonlinear phenomena. It is applied to a wide range of topics including vapor deposition, bacterial colony growth, directed polymers, and flux lines in superconductors @2,3#. Computational studies have mostly concentrated on simulations of discrete models such as ballistic deposition models, soli...

In this article we investigate the behaviour of the scaling exponentsof KPZ equation through changing three parameters of the equation. Inother words we would like to know how the growth exponent β and theroughness exponent α will change if the surface tension ν , the averagevelocity λ and the noise strength γchange. Using the discrete form of theequation , first we come to the results α = 0.5 ...

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the KPZ non-linearity. The strong-coupling regime is characterised by a double-peaked height distribution in the stationary state. The nonstationary dynamics is q...