Related papers: KPZ Equation and Surface Growth Model
Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…
We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We…
This work considers an extension of the SIR equations from epidemiology that includes a spatial variable. This model, referred to as the Kermack-McKendrick equations (KM), is a pair of diffusive partial differential equations, and methods…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…
After a brief introduction we review the nonperturbative weak noise approach to the KPZ equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain…
Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…
The focus of this work is the numerical approximation of time-dependent partial differential equations associated to initial-boundary value problems. This master dissertation is mostly concerned with the actual computation of the solution…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
We propose a theoretical model of a non-local dipersive-dissipative equation which contains as a particular case a large class of non-local PDE's arising from stratified flows. Within this fairly general framework, we study the spatial…
In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R_{11} and…
We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…
We study a class of nonlinear Burgers-type stochastic partial differential equations driven by additive space-time white noise in one spatial dimension. Building on the rough path framework initiated by Hairer, which provides a pathwise…
We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the…
We argue differences between the Kardar-Parisi-Zhang with Quenched disorder (KPZQ) and the Ballistic Deposition with Power-law noise (BDP) models, using the multiaffine analysis method. The KPZQ and the BDP models show mono-affinity and…
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…
In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…