Related papers: Modeling rough surfaces with Lorentz equations
Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental…
We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the…
We apply a theoretical approach, originally introduced to describe aeolian ripples formation in sandy deserts, to the study of surface instability in ion sputtered surfaces. The two phenomena are distinct by several orders of magnitudes and…
Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple…
We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…
Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled with stochastic partial differential equations. A widely accepted model is the Cuerno-Barabasi model which is robust in its predictions…
We implement substrate rotation in a 2+1 dimensional solid-on-solid model of ion beam sputtering of solid surfaces. With this extension of the model, we study the effect of concurrent rotation, as the surface is sputtered, on possible…
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
Numerical simulation of pattern formation on plane target surfaces undergoing ion-beam sputtering is carried out. Base of the mathematical model of target ion-sputtering is nonlinear evolutionary equation in which the erosion velocity…
Several, recently proposed methods of surface manufacturing based on ion beam sputtering, which involve dual beam setups, sequential application of ion beams from different directions, or sample rotation, are studied with the method of…
The generalised continuum theory model of the dynamical evolution of surfaces sputtered by ion-bombardment is a noisy Kuramoto-Sivashinsky type partial differential equation. For some generic cases of sputtering parameters, existing similar…
The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the average surface erosion rate is determined by…
Rough surface scattering problems are always very challenging both theoretically and numerically. In this paper, we adopt the Bloch transform and the perturbation theory to investigate a special case, i.e., when the rough surface is a…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
Energetic particle irradiation of solids can cause surface ultra-smoothening, self-organized nanoscale pattern formation, or degradation of the structural integrity of nuclear reactor components. Periodic patterns including high-aspect…
A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
In the continuum theory the time evolution of surfaces eroded by ion bombardment is modelled by stochastic partial differential equations (SPDEs). These determine the scaling regimes and universality classes of the evolving surfaces.…
Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate…
Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…