相关论文: Asymptotic step profiles from a nonlinear growth e…
The role played by a kinetic barrier originated by out-of-plane step edge diffusion, introduced in [Leal \textit{et al.}, \href{https://doi.org/10.1088/0953-8984/23/29/292201}{J. Phys. Condens. Matter \textbf{23}, 292201 (2011)}], is…
Epitaxial growth on a surface vicinal to a high-symmetry crystallographic plane occurs through the propagation of atomic steps, a process called step-flow growth. In some instances, the steps tend to form close groups (or bunches), a…
The morphology of a growing crystal surface is studied in the case of an unstable two-dimensional step flow. Competition between bunching and meandering of steps leads to a variety of patterns characterized by their respective instability…
We investigate the growth kinetics on vicinal GaAs(001) surfaces by making detailed comparisons between reflection high--energy electron--diffraction specular intensity measured near in--phase diffraction conditions and the surface step…
We report new results on the non-conserved dynamics of parallel steps on vicinal surfaces in the case of sublimation with electromigration and step-step interactions. The derived equations are valid in the quasistatic approximation and in…
We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We formulate a new (1+1)D step model of potentially unstable vicinal growth that we call "C+ - C-" model and study the step bunching process in it. The basic assumption is that the equilibrium adatom concentrations on both sides of the step…
This is a review of recent theoretical work on complex dynamical behavior of steps on crystal surfaces. The first part of the article is devoted to the electromigration-driven motion of islands and voids, and the second part addresses step…
We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
We investigate the spontaneous meandering of slender rivulets in Hele-Shaw cells and identify the physical mechanism that selects the most unstable wavenumber, a quantity that has remained elusive even since the identification of the…
A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are observed in experiments arise from a…
In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…
Bunching and meandering instability of steps at the 4H-SiC(0001) surface is studied by the kinetic Monte Carlo simulation method. Change in the character of step instability is analyzed for different rates of particle jumps towards step. In…
This study presents a comprehensive and innovative exploration of how the surface potential energy landscape influences meander formation. Using the Vicinal Cellular Automaton model, which distinguishes surface diffusion from adatom…