Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic spreads along the cycle graph as a front. We introduce a continuous time Markov chain describing the evolution of the front. The third method we apply is the subsystem approximation using the edges as subsystems. Finally, we compare the steady state value of the number of infected nodes obtained in different ways. © 2012 Versita Warsaw and Springer-Verlag Wien

Isotherm equation of sorption of electrolyte solutions on solids: how to do heterogeneous surface from homogeneous one?

It is a rather common phenomenon in the literature, that the surface accumulation processes are treated by different isotherm equations without taking into account the mechanism of the sorption processes. In this paper, a model calculation is presented for homovalent ion exchange process on energetically homogeneous surface. It reveals all incorrect conclusions which can be drawn in this way

Application of Modified Bentonites for Arsenite (III) Removal from Drinking Water

Four modified bentonites (La(III), Ce(III), Y(III), Fe(III)) were prepared by ion exchange process to remove arsenite (III) ions from water. The modified bentonites were examined with X-ray fluorescence spectroscopy (XRF) and X-ray diffraction (XRD). The rare earth (REE) and Fe(III) ion content in bentonite was higher than the CEC values obtained by ammonium acetate method related to trivalent ions (2.7 x 10-4 mol g-1). The kinetics, equilibrium time, sorption isotherms and desorption experiments were examined. Lanthanum, yttrium and cerium bentonite can bind similar amount of arsenite(III) ions. Iron-bentonite cannot bind significant amounts of arsenite ions. The active sites and the solubilities of the sorption complex were determined. Arsenite (III) ions sorb in the interlayer space as REEAsO3. The solubility of the arsenite complex was two orders of magnitude smaller than that of the phosphate complex. After desorption the eluted amount of arsenite (III) was 55 % related to the sorbed amount of arsenite. The d(001) basal spacing of modified bentonites and that of after sorption and desorption was measured. After the sorption of arsenite ion on lanthanum bentonite, the d(001) basal spacing of montmorillonite was decreased and after desorption an increase in d(001) basal spacing was observed again. Modified bentonites can be used for removing arsenic ions from water