Related papers: A pseudo-spectral approach to inverse problems in …
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 study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…
We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth…
We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. (2 PostScript figures available…
We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any…
This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of…
A resolution-independent data-driven stochastic parametrization method for subgrid-scale processes in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby…
Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative…
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
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…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…
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…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
We introduce a new kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-…
We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is…
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…
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…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…