Related papers: Point island dynamics under fixed rate deposition

We develop a theory for nucleation on top of islands in epitaxial growth based on the derivation of lifetimes and rates governing individual microscopic processes. These processes are strongly affected by the additional step edge barrier…

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…

Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial…

We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…

We study one-dimensional models of particle diffusion and attachment/detachment from islands where the detachment rates gamma(m) of particles at the cluster edges increase with cluster mass m. They are expected to mimic the effects of…

Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

We investigate the dynamics of an ensemble of inelastic hard spheres confined between two horizontal plates separated a distance smaller than twice the diameter of the particles, in such a way that the system is quasi-two-dimensional. The…

In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.

We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and…

We study a simplified model for pulsed laser deposition [Phys. Rev. Lett. {\bf 87}, 135701 (2001)] by rate equations. We consider a set of equations, where islands are assumed to be point-like, as well as an improved one that takes the size…

We study the relaxation to equilibrium of two dimensional islands containing up to 20000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion -…

In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

The study of the dynamics of a surface homeomorphism in the neighbourhood of an isolated fixed point leads us to the following results. If the fixed point index is greater than 1, a family of attractive and repulsive petals is constructed,…

We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…

We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We…

We study the morphological evolution of strained islands in growing crystal films by use of a continuum description including wetting, elasticity and deposition flux. Wetting breaks translational invariance, allowing the flux to tune…

Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…