Monte—Carlo model of the diffusion-limited reaction kinetics in microheterogeneous media. Comparison with the experimental plots of the forward and backward electron phototransfer kinetics on the pore diameter in silica gel

The kinetics of the diffusion-limited decay reaction A + B B was simulated by the Monte—Carlo method on a two-dimensional square lattice with defects presented by randomly distributed sites. The cases were considered where [B] [A] at the random initial distribution (quenching reaction) and [B] = [A] with the initial distribution of the A and B particles on neighboring sites (geminate recombination). The kinetic curves were approximated by the simplest analytical equation [A]/[A]₀ = (1 – )exp[–(kt)^1–h ] + (where k and are constants). The plots of the heterogeneity parameter (h) and time-averaged first-order rate constant vs. concentration of defects (p) or B particles (in the case of quenching) were obtained and compared with similar correlations obtained earlier by the experimental study of the kinetics of forward (quenching reaction) and backward (geminate recombination) electron phototransfer on the surface of different porous silica gels. The experimental plots of h vs. silica gel porosity are in satisfactory agreement with the plots of h vs. p in the model space, if the fraction of volume inaccessible for reactants, calculated from the free silica gel volume, is chosen as the p parameter for silica gel.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1536–1541, August, 2004.     

Orthokinetic Aggregation in Two Dimensions of Monodisperse and Bidisperse Colloidal Systems

Orthokinetic aggregation of colloids trapped at the air–liquid interface was studied by direct imaging in a couette cell. This method allowed us to follow the temporal evolution of both the cluster-mass distribution and the cluster structure at a shear rate where Brownian aggregation is suppressed. The interactions between the monodisperse latex particles floating at the air–liquid interface were controlled either by varying the electrolyte concentration or by creating a bidisperse system through the addition of small particles. The results show that the clusters in all of the systems are characterized by a high fractal dimension, indicating that the clusters are rearranged and densified by the shear. Kinetic analysis suggests that aggregation of monodisperse systems mainly proceeds through homogeneous aggregation, i.e., large clusters sticking to other large clusters. The bidisperse system, finally, with a size ratio around 10, favored a more heterogeneous aggregation among small and large clusters throughout the aggregation process; a slightly lower fractal dimension was observed compared to the strongly aggregated monodisperse system.     

Global stability for a class of mass action systems allowing for latency in tuberculosis

A very general compartmental model of the spread of an infectious disease with mass action incidence is given. The global stability of this system is completely determined using Lyapunov functions. The general system exhibits the traditional threshold behaviour. The dimension of the system is arbitrary, allowing, in particular, for detailed modelling of the distribution of latency times for tuberculosis.     

Orbits in a stochastic Goodwin–Lotka–Volterra model

This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka–Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly non-linear model. We then study a stochastic version, with Brownian noise introduced via a heterogeneous productivity factor. Existence conditions for a solution to the system are provided. We prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurrent domains. Numerical insights are provided.     

STABILITY IN LAGRANGE SENSE FOR A CLASS OF STOCHASTIC STATIC NEURAL NETWORKS WITH MIXED TIME DELAYS

In this paper, the stability in Lagrange sense of a class of stochastic static neural networks with mixed time delays is studied. Based on the Lyapunov stability theory and with the help of stochastic analysis technique, the criteria for the stability in Lagrange sense of stochastic static neural networks with mixed time delays is obtained. One example is given to verify the advantage and applicability of the proposed results.     

Strategic measures in optimal control problems for stochastic sequences

Controlled discrete–time stochastic processes axe studied using the convex–analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.     

A class of transformed Markov processes

This paper considers some properties of a class of transformed Markov processes. The analogy with Whittle's relaxed Markov process is pointed out. Some applications of the transformed Markov processes to queueing networks are described