Related papers: Short-time scaling behavior of growing interfaces
We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical…
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…
We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves \textit{et al}. [Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where the intrinsic…
We study ageing during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple ageing in both correlators and linear responses and its dynamical…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
We explore the critical dynamics of driven interfaces propagating through a two dimensional disordered medium with long range spatial correlations, modeled using fractional Brownian motion. Departing from conventional models with…
The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang (KPZ) equation. It has always been known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical…
Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to…
Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…
We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar-Parisi-Zhang equation for a negative non-linearity \lambda. This is possible…
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…
We perform a numerical study on the two-dimensional nonequilibrium exciton-polariton systems driven by incoherent pumping based on the stochastic generalized Gross-Pitaevskii equation. We calculate the density fluctuation, coherence…
A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…
We introduce a solid on solid lattice model for growth with conditional evaporation. A measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations. The model parameters are chosen…
We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian…
In this paper we discuss the well known Kardar Parisi Zhang (KPZ) equation driven by temporally correlated noise. We use a self consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the…
While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…
We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting…