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    Near critical catalyst reactant branching processes with controlled immigration

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    Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. Such models are motivated by problems in chemical kinetics where one wants to keep the level of a catalyst above a certain threshold in order to maintain a desired level of reaction activity. A diffusion limit theorem for the scaled processes is presented, in which the catalyst limit is described through a reflected diffusion, while the reactant limit is a diffusion with coefficients that are functions of both the reactant and the catalyst. Stochastic averaging principles under fast catalyst dynamics are established. In the case where the catalyst evolves "much faster" than the reactant, a scaling limit, in which the reactant is described through a one dimensional SDE with coefficients depending on the invariant distribution of the reflected diffusion, is obtained. Proofs rely on constrained martingale problem characterizations, Lyapunov function constructions, moment estimates that are uniform in time and the scaling parameter and occupation measure techniques.Comment: Published in at http://dx.doi.org/10.1214/12-AAP894 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Surface diffusion in catalysts probed by APGSTE NMR

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    In this work we report the application of a recently developed experimental protocol using Pulsed Field Gradient (PFG) Nuclear Magnetic Resonance (NMR) techniques to simultaneously assess bulk pore and surface diffusion coefficients in liquid saturated porous catalysts. This method has been developed to study solvent effects on the diffusion of methyl ethyl ketone (MEK) in mesoporous 1 wt% Pd/Al2O3 catalyst trilobes. The selection of solvents used in this work is known to have a complex effect on reaction rates and hence catalyst performance in heterogeneous liquid phase catalysis. Here, we report the bulk pore and surface diffusion characteristics of MEK, water and isopropyl alcohol (IPA) in 1 wt% Pd/Al2O3 catalyst trilobes. The results show that the physicochemical interactions of molecules in the porous catalyst matrix are very different for the different molecules. We also find that the mobility of water appears to be affected strongest by the catalyst surface
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