Related papers: Patterns in the Kardar-Parisi-Zhang equation
A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…
We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that…
We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the…
The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…
A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…
The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as…
A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…
We give a brief overview of the seminal paper which introduced the Kardar-Parisi-Zhang equation as a paradigmatic model for random growth in 1986. We describe some of the developments to which it gave rise in mathematics and physics over…
The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the traveling-wave Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions…
The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have…
We investigate the scaling regimes of the Kardar-Parisi-Zhang equation in the presence of spatially correlated noise with power law decay $D(p) \sim p^{-2\rho}$ in Fourier space, using a nonperturbative renormalization group approach. We…
The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that…
We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale…
The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…
Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…
The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the…
We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All…