Related papers: Spacing distribution functions for the one-dimensi…
Nucleation on top of two-dimensional islands with step edge barriers is investigated using scaling arguments. The nucleation rate is expressed in terms of three basic time scales: The time interval between deposition events, the residence…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
The growth and ordering of a Pb layer deposited on Cu(001) at 150 K has been studied using atom beam scattering. At low coverage, ordered Pb islands with a large square unit cell and nearly hexagonal internal structure are formed. This is a…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
In this paper we consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and…
A computational model study for complete frequency redistribution linear incoherent two-level atomic radiation trapping in optically dense media using the multiple scattering representation is presented. This model study discuss at length…
The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of…
The effect of edge and corner diffusions on the morphology and on the density of islands nucleated irreversibly on a flat substrate surface is studied. Without edge and corner diffusion, islands are fractal. As an edge diffusion constant…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
A basic kinetic model that incorporates a coupled dynamics of the carbon atoms and dimers on a copper surface is used to compute growth of a single-layer graphene island. The speed of the island's edge advancement on Cu[111] and Cu[100]…
Invasion percolation is a stochastic growth model that follows a greedy algorithm. After assigning i.i.d. uniform random variables (weights) to all edges of $\mathbb{Z}^d$, the growth starts at the origin. At each step, we adjoin to the…
Surface reconstructions can drastically modify growth kinetics during initial stages of epitaxial growth as well as during the process of surface equilibration after termination of growth. We investigate the effect of activation barriers…
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic…
This paper proposes a lossless point cloud (PC) geometry compression method that uses neural networks to estimate the probability distribution of voxel occupancy. First, to take into account the PC sparsity, our method adaptively partitions…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
We present a simple non-equilibrium model of mass condensation with Lennard-Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to…
This paper introduces a novel approach to investigate the dynamics of state distributions, which accommodate both cross-sectional distributions of repeated panels and intra-period distributions of a time series observed at high frequency.…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
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…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…