Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

Cell Pattern in Adult Human Corneal Endothelium

A review of the current data on the cell density of normal adult human endothelial cells was carried out in order to establish some common parameters appearing in the different considered populations. From the analysis of cell growth patterns, it is inferred that the cell aging rate is similar for each of the different considered populations. Also, the morphology, the cell distribution and the tendency to hexagonallity are studied. The results are consistent with the hypothesis that this phenomenon is analogous with cell behavior in other structures such as dry foams and grains in polycrystalline materials. Therefore, its driving force may be controlled by the surface tension and the mobility of the boundaries.