Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice-based model is that a proliferative population will always eventually fill the lattice. Here, we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also...

We develop electrochemical mean-field kinetic equations to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the ...

We develop and study a model of the Kondo lattice system under the mean field approximation using a HartreeFock procedure as the spin polarization of the system is varied. The goal of this investigation is to provide a realistic model and a starting point for further investigations using more sophisticated techniques, as well as to provide information on mean field solutions calculated on large...