We prove the existence of self-similar solutions to the Fradkov model for twodimensional grain growth, which consists of an infinite number of nonlocally coupled transport equations for the number densities of grains with given area and number of neighbours (topological class). For the proof we introduce a finite maximal topological class and study an appropriate upwind-discretization of the ti...

Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the step edge orientation angle, θ. Basic ingredients of the model are: (i) the diffusion of point defects (“adatoms”) on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive l...

human capital has always been of high importance in economic growth literature. in this regard, several studies have tried to explain the role of this variable via the use of different models. the present study, in line with the previous ones, going to estimate the share of human capital in iranian economy production from 1974 to 2011 within the framework of ozawa (1965) and lucas’s (1988) endo...

Microbial activity governs elemental cycling and the transformation of many anthropogenic substances in aqueous environments. Through the development of a dynamic cell model of the well-characterized, versatile, and abundant Geobacter sulfurreducens, we showed that a kinetic representation of key components of cell metabolism matched microbial growth dynamics observed in chemostat experiments u...

Prediction of shelf life based on growth of specific spoilage organisms (SSO) in model substrates was studied. The effect of CO2 on the growth kinetics for Photobacterium phosphoreum and Shewanella putrefaciens was quantified and modelled. Results showed that microbial spoilage of packed cod stored with various concentrations of CO2 was accurately predicted from the effect of CO2 on P. phosphor...

We study the growth process of ferroelectric materials by kinetic Monte Carlo simulations. An ionic model with long-range Coulomb interactions is used to model the relaxor single crystals. The growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions. An algorithm is developed in order to simulate growth under such a model, for whi...

this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed

A mathematical model for the interaction kinetic in phage-bacterium culture is proposed. An appropriate analytical relationship between phage and bacterial concentrations has been derived. Characteristic kinetic constants have been obtained by comparing the experimental growth curves with computer-simulation analysis. The model allows also to evaluate the phage-yield as a function of the initia...

The early stages of thin film formation by thermal atom deposition are modeled by a system of kinetic rate equations which describe atomic clustering phenomena. Specifically, a set of discrete kinetic rate equations, used to model small atomic clusters, is coupled to a set of kinetic moment equations which model large atomic clusters with a continuum description. Cluster growth and dissociation...

The first kinetic study of transient growth for a collisionless homogeneous Maxwellian plasma in a uniform magnetic field is presented. A system which is linearly stable may display transient growth if the linear operator describing its evolution is non-normal so that its eigenvectors are nonorthogonal. In order to include plasma kinetic effects, a Landau fluid model is employed. The linear ope...