Related papers: A Simple Model for Anisotropic Step Growth
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
The surface orientation can have profound effects on the atomic-scale processes of crystal growth, and is essential to such technologies as GaN-based light-emitting diodes and high-power electronics. We investigate the dependence of…
We examine the step dynamics in a 1+1 dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step…
Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…
The step motions considered are those in which crystallization is controlled by a single diffusion process, either the substance diffusion for growth from solution or the flow of latent heat from the step for growth from melt. Quasi-static…
Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic-hydrophobic substrates. We consider different transverse-striped micropatterns, characterized…
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…
We present an original approach for predicting the static recrystallization texture development during annealing of deformed crystalline materials. The microstructure is considered as a population of subgrains and grains whose sizes and…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…
We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…
We develop and analyze a model for a flat microbial droplet growing on the surface of a three-dimensional viscous fluid. The model describes growth-induced stresses at the fluid surface, density variations in the bulk due to nutrient…
In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for…
A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…
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…
Effect of an anisotropic detachment on a heteroepitaxial island shape is studied by means of a kinetic Monte Carlo simulation of a square lattice gas model. Only with molecular deposition followed by surface diffusion, islands grow in a…
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…
The conformation and scaling properties of self-avoiding fluid vesicles with zero extrinsic bending rigidity subject to an internal pressure increment $\Delta p>0$ are studied using Monte Carlo methods and scaling arguments. With increasing…
We present a Monte Carlo study of external surface anchoring in nematic cells with partially disordered solid substrates, as well as of intrinsic anchoring at free nematic interfaces. The simulations are based on the simple hexagonal…
Stochastic growth of binary alloys on a weakly interacting substrate is studied by kinetic Monte Carlo simulation. The underlying lattice model relates to fcc alloys, and the kinetics are based on deposition, atomic migration with…
We analyze the dynamics of crystal surfaces in the presence of electromigration. From a phase field model with a migration force which depends on the local geometry, we derive a step model with additional contributions in the kinetic…