Reversible Diffusion Processes Research Articles

Dirichlet processes associated to diffusions

Let be a reversible diffusion process with values in . We give sufficient conditions on the initial law of W and on a function ƒ for the stochastic process to be a Dirichlet process

Properties of the crossover from nonclassical to classical chemical kinetics in a reversibleA+B↔Creaction diffusion process

We study the properties of the reaction front formed in a reversible reaction diffusion process A+B<-->C, with initially separated reactants. The case of the mobile C component is considered. In accordance with Chopard et al. [Phys. Rev. E 47, R40 (1993)] the dynamics of the front is described as a crossover between the "irreversible" regime at short times and the "reversible" regime at long times. A refined definition for the rate of C production is suggested, taking into account both the forward and the backward reaction rates. By this definition within the framework of the mean-field equations it is shown that the reversible regime is characterized by scaling of the local rate of C production as R(local) approximately t(-1) and by scaling of the global rate of C production as R(global) approximately t(-1/2). It is also established that in the considered special case of equal diffusion coefficients and equal initial concentrations, the macroscopic properties of the reaction front, such as the global rate of the C production R(global) and the concentration profiles of the components outside the front reaction, are unchanged through this crossover.

Malliavin Calculus and Euclidean Quantum Mechanics II. Variational Principle for Infinite Dimensional Processes

A class of time reversible non-stationary diffusion processes with values on the classical Wiener space is constructed. These processes should be relevant to ("2-dimensional") Euclidean quantum field theory since they generalize those constructed before for non-relativistic quantum mechanics, along the lines of a strategy suggested by Schrödinger. Those processes are shown to be characterized by a stochastic variational principle and provide a probabilistic representation of the solutions of some infinite-dimensional heat equation. The Feynman-Kac formula on the Wiener space needed for this construction is also proved.

Ergodicity of reversible reaction diffusion processes with general reaction rates

In this paper, a class of reaction diffusion processes with general reaction rates is studied. A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given, and then the ergodicity of these processes is proved.

Hollow fiber contained liquid membrane separation of citric acid

AbstractCitric acid was successfully separated from an aqueous solution using the hollow fiber contained liquid membrane (HFCLM) technique. In this technique, the organic liquid membrane is contained in the shell side between two sets of hollow fibers; feed solution flows through one set of fibers and the strip solution flows through the other set. Tri‐n‐octylamine diluted in various organic solvents was used as a complexing agent for facilitated transport of citric acid from an aqueous solution. Pure water and aqueous sodium hydroxide were used as stripping agents. Membrane life and stability problems encountered in supported liquid membranes are eliminated. A mathematical model of facilitated solute transport through HFCLM that accounts for the interfacial reversible reaction kinetics and diffusion process inherent in carrier‐facilitated transport is presented. Experimental data agreed well with the theoretical predictions for permeators achieving almost complete solute recovery.

Ergodicity of reversible reaction diffusion processes

Reaction-diffusion processes were introduced by Nicolis and Prigogine, and Haken. Existence theorems have been established for most models, but not much is known about ergodic properties. In this paper we study a class of models which have a reversible measure. We show that the stationary distribution is unique and is the limit starting from any initial distribution.

A. N. Kolmogorov - the founder of the theory of reversible Markov processes

CONTENTS § 1. Introduction § 2. Reversible processes § 3. Reversible locally discrete Markov processes with interaction § 4. Reversible diffusion processes with interaction § 5. The invariance principle for reversible processes § 6. The concept of reversibility in the theory of queues References

Absorption of Silicone Oil by a Dimethylsiloxane Elastomer

Abstract Polydimethylsiloxane elastomer immersed in DC 200 silicone oil at temperatures of 180–200°C absorbs oil by two concurrent processes, a rapid and reversible diffusion process and a slower, irreversible process resulting from the chemical degradation of the sample. Absorption by diffusion reaches equilibrium in 200 h, and the absorption capacity depends on the amount of curing agent used in the preparation of the elastomer composite. The oil absorbed during this period can be removed by extraction. The absorption capacity is less for the elastomer composites containing silica and decreases linearly with the volume fraction of elastomer in the sample, indicating that only the elastomer absorbs oil. The rate of absorption depends on t1/2 and has a weak temperature dependence. The diffusion coefficients are in the range 10−12 m2/s, and do not seem to be affected by the presence of filler. While the diffusion of oil does not appear to produce chemical changes in the elastomer, the elastomer is gradually destroyed by the slower chemical process, which promotes the absorption of additional amounts of oil.