The influence of the “hot”-dimer adsorption mechanism on the kinetics of a monomer-dimer surface reaction

Hot dimers are molecules which after adsorption dissociate and each of the remaining hot monomers fly apart up to a maximum distance R from the original adsorption site. The influence of the hot-dimer adsorption mechanism on relevant aspects of the bimolecular catalyzed reaction of the type A – (1/2)B ₂(hot) AB is studied by means of the Monte-Carlo simulation technique. The temporal evolution of both the reactant's coverages as well as the rate of AB-production is evaluated and discussed. Due to the enhanced probability of hot species for encounters with other adsorbed particles, the rate of AB-production becomes faster when increasing R. This behavior may be relevant in the dynamic of some catalyzed reactions such as for example the oxidation of carbon monoxide on transition metal surfaces, i.e. ACO, B ₂O₂, and ABCO₂. Also the sticking coefficient of hot dimers and the average distance traveled by the hot monomers are evaluated and discussed.     

An interpolation problem in the Denjoy–Carleman classes

Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on $[a,b]\subset \mathbb{R}$ and given an increasing divergent sequence $d_n$ of positive integers such that the derivative of order $d_n$ of f has a growth of the type $M_{d_n}$, when can we deduce that f is a function in the Denjoy–Carleman class $C^M([a,b])$? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence $d_n$ is needed.