0000000000671344
AUTHOR
Lutz Schimansky-geier
Phase transformation kinetics in d-dimensional grains-containing systems: diffusion-type model
Abstract An analytical approach to the phase transformation in d-dimensional grains-containing complex systems is offered. It is based on considering the mechanism of surface material exchange among neighbouring grains as the so-called state-dependent diffusion process, where the diffusion function is related to the magnitude of the grain boundary. The approach proposed deals with the kinetics of that ensemble under circumstances of a volume increase of the new phase or microstructure. Probabilistic characteristics of the process are derived and analyzed. A comparison with 2D modelling of similar kind is presented for the 3D case, and some possible practical realizations of the situation un…
Moment Equations for a Spatially Extended System of Two Competing Species
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
KINETICS OF CRYSTAL GROWTH LIMITED BY RANDOM VELOCITY FIELDS
A spherical growth process controlled by velocity fluctuations of particles of a saturated solution is investigated. Velocity fluctuations are modeled by a Gaussian random field. The interface evolution is determined by a Langevin-type equation with a multiplicative random field, which in the case of the quasi-homogeneous random Gaussian field is equivalent to Fokker–Planck dynamics. We analyze numerically the Fokker–Planck equation and compare growth kinetics in the case of noisy (i.e. space-independent) fluctuations. It is shown that for a large class of spatially correlated velocity fluctuations, the growth kinetics is universal, i.e. it does not depend on the details of statistics of f…