In this paper we calculate the structure functions of one dimensional Burgers and KPZ equations with and without noise, and we interpret our findings using shocks. Most of our results are based on direct numerical simulation of the KPZ equation. Using the solution of noiseless Burgers equation we show that the exponent cq (< |h(x+r)−h(x)| q >∝ rqcq ) of the structure function of noiseless KPZ i...

An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrat...

Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine the finite size effects in various models The analysis is applied to the discrete linear growth equation and Kardar-Parisi-Zhang (KPZ) equation. A new model ...

We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time singularities in contrast to conventional schemes. The implications of these results to i) previous numerical integration of the KPZ equation, and ii) the non-trivia...

We examine height-height correlations in the transient growth regime of the 2 + 1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus on the spatial covariance of the underlying two-point statistics, higher-dimensional analog of the 1 + 1 KPZ Class Airy1 process. Making comparison to AFM kinetic roughening data in 2d organic thin films, we use our universal 2 + 1 KPZ spatial c...

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the interface equation of motion as functions of phenomenological parameters. The equation features the Kardar-Parisi-Zhang (KPZ) nonlinearity and instabilities...

We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation in 1 + 1 dimensions are investigated by use of the dynamic renormalization group (RG) and direct numerical simulations. It is shown that the noisy KS equation is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in the sense that they have scale invariant solutions with the same scaling exponents...

It has recently been proposed that fluctuating "pulled" fronts propagating into an unstable state should not be in the standard Kardar-Parisi-Zhang (KPZ) universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in d+1 bulk dimensions should be in the universality class of the ((d+1)+1...

We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-ParisiZhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is found to be inconsistent with the nominal one. We propose a novel discretization in 1+1 dimensions which does not suffer from this deficiency and elucidates ...