Related papers: Distributional fixed-point equations for island nu…
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates…
We use visibility graphs as a tool to analyse the results of kinetic Monte Carlo (kMC) simulations of submonolayer deposition in a one-dimensional point island model. We introduce an efficient algorithm for the computation of the visibility…
The morphological stability of two-dimensional islands nucleated on a substrate during vacuum or vapour-phase atom deposition is investigated. Using simple scaling arguments, it is shown that, contrary to expectation, dendritic islands may…
We explore the stability of isotropic, spherical, self-gravitating systems with a double-power law density profile. Systems with rapid transitions between the inner and outer slopes are shown to have an inflection in their isotropic…
When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with…
We consider the influence of realistic island diffusion rates to homoepitaxial growth on metallic surfaces using a recently developed rate equation model which describes growth in the submonolayer regime with hyperthermal deposition. To…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
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 report simulations of submonolayer epitaxial growth using a continuum phase field model. The island density and the island size distribution both show scaling behavior. When the capillary length is small, the island size distribution is…
Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in moder power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view,…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…
Diffusion reconstruction plays a critical role in various applications such as image editing, restoration, and style transfer. In theory, the reconstruction should be simple - it just inverts and regenerates images by numerically solving…
In this paper we propose a solution for the time evolution of the island density with irreversible aggregation and a time dependent input of particle in the space dimensions $d=1,2$. For this purpose we use the rate equation resulting from…