Related papers: Irreversible nucleation in multilayer growth
During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the…
We have constructed a complete hydrodynamic theory of nucleation and growth in a one--dimensional version of an elastic shear martensitic transformation with open boundary conditions where we have accounted for interfacial energies with…
We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a…
We consider a model to describe stable configurations in epitaxial growth of crystals in the two dimensional case, and in the regime of linearized elasticity. The novelty is that the model also takes into consideration the adatom density on…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
This chapter starts with a summary of the atomistic processes that occur during epitaxy. We then introduce density functional theory (DFT) and describe its implementation into state-of-the-art computations of complex processes in condensed…
We describe a theoretical study of the role of adsorbate interactions in island nucleation and growth, using Ag/Pt(111) heteroepitaxy as an example. From density-functional theory, we obtain the substrate-mediated Ag adatom pair interaction…
The effects of a surfactant on two-dimensional pattern formation in epitaxial growth are explored theoretically using a simple model, in which an adatom becomes immobile only after overcoming a large energy barrier as it exchanges positions…
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
It is demonstrated by analyzing real examples that phase transitions in layered crystals occur like all other solid-state phase transitions by nucleation and crystal growth, but have a specific morphology. There the nucleation is epitaxial,…
The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
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 numerically the equilibrium shapes, shape transitions and dislocation nucleation of small strained epitaxial islands with a two-dimensional atomistic model, using simple interatomic pair potentials. We first map out the phase…
In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. In such cases, nucleation of the solid phase from the melt may…
We present a model in which pit nucleation in thin films is considered to arise from a near-equilibrium nucleation process. In this model the adatom concentration plays a central role in controlling the morphological development of the…
The growth of a diffusion limited aggregation (DLA) cluster with mass $M$ and radius of gyration $R$ is described by a set of growth probabilities $\{ p_i\}$, where $p_i$ is the probability that the perimeter site $i$ will be the next to…
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients.…
The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolution of the infiltration. We study this problem in two- and…
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…