Ionization potentials and geometrical structure of pure and oxygenated barium clusters

In this article, we present results obtained on structures of small bare and oxygenated barium clusters produced by the laser vaporization technique. Contrary to the very weak Ba—Ba binding (0.202 eV), the Ba—O binding is rather strong (5.8 eV). As a consequence, extremely small amounts of oxygen in the cluster source are sufficient to induce the nucleation of oxygenated barium clusters. Surprisingly, at least for substoechiometric systems, Ba_nO_m clusters exhibit the same icosahedral structure as bare clusters do. Mass spectra seem to indicate that replacing a barium atom with a strongly polar BaO molecule does not affect the geometrical structure of the cluster. This aspect is more easily understandable if we assume that the oxygen atom takes place inside the structure of the Ba_n cluster without significant distortions. Ab-initio calculations have been undertaken in order to give a satisfactory account of this hypothesis.     

Selective crystallization of calcium salts by poly(acrylate)-grafted chitosan

The biopolymer chitosan was chemically modified by grafting polyacrylamide or polyacrylic acid in a homogeneous aqueous phase using potassium persulfate (KPS) as redox initiator system in the presence of N,N-methylene-bis-acrylamide as a crosslinking agent. The influence of the grafted chitosan on calcium salts crystallization in vitro was studied using the sitting-drop method. By using polyacrylamide grafted chitosan as substrate, rosette-like CaSO4 crystals were observed. This was originated by the presence of sulfate coming from the initiator KPS. By comparing crystallization on pure chitosan and on grafted chitosan, a dramatic influence of the grafted polymer on the crystalline habit of both salts was observed. Substrates prepared by combining sulfate with chitosan or sulfate with polyacrylamide did not produce similar CaSO4 morphologies. Moreover, small spheres or donut-shaped CaCO3 crystals on polyacrylic acid grafted chitosan were generated. The particular morphology of CaCO3 crystals depends also on other synthetic parameters such as the molecular weight of the chitosan sample and the KPS concentration.     

Charge transfer in FeO: a combined molecular-dynamics and ab initio study

Molecular-dynamics simulations and ab initio electronic structure calculations were carried out to determine the rate of charge transfer in stoichiometric wustite (FeO). The charge transfer of interest occurs by II/III valence interchange between nearest-neighbor Fe atoms, with the Fe(III) constituting a "hole" electronic defect. There are two possible nearest-neighbor charge transfers in the FeO lattice, which occur between edge-sharing or corner-sharing FeO(6) octahedra. Molecular-dynamics simulations predict charge-transfer rates of 3.7 x 10(11) and 1.9 x 10(9) s(-1) for the edge and corner transfers, respectively, in good agreement with those calculated using an ab initio cluster approach (1.6 x 10(11) and 8.0 x 10(8) s(-1), respectively). The calculated rates are also similar to those along the basal and c-axis directions in hematite (alpha-Fe(2)O(3)) determined previously. Therefore, as is the case for hematite, wustite is predicted to show anisotropic electrical conductivity. Our findings indicate that a rigid-ion model does not give acceptable results, thus showing the need to account for the change in polarizability of the system upon charge transfer. Our model achieves this by using a simple mechanical shell model. By calculating the electronic coupling matrix elements for many transition state configurations obtained from the molecular-dynamics simulations, we found evidence that the position of the bridging oxygen atoms can greatly affect the amount of electronic coupling between the donor and acceptor states. Finally, we address the effect of oxygen vacancies on the charge transfer. It was found that an oxygen vacancy not only creates a driving force for holes to transport away from the vacancy (or equivalently for electrons to diffuse toward the vacancy) but also lowers the free-energy barriers for charge transfer. In addition, the reorganization energy significantly differed from the nondefective case in a small radius around the defect.     

Dirichlet Series and Curious infinite Products

By number-theoretical methods we give a result generalizingthose of J. O. Shallit, one particular case of which reads asfollows: ...=2^–;, where a(n) is equal to 1 if the sum of the digits of n in basetwo is even, and – 1 if this sum is odd. Moreover we provea conjecture of Shallit concerning a way of approximating 2^–     

Theoretical study of the adsorption of silver atoms on the (111) face of silicon

The adsorption of one or many silver atoms on a (111) silicon face (reduced to 61 dangling atomic orbitals) is investigated by means of a self-consistent Hartree–Fock method parametrized from atomic and thermodynamical data. The valley sites (above three Si atoms) are favored over the top sites (above one Si atom). The extrapolation of the results obtained for several structures corresponding to the adsorption of n = 1, 2, 3, 4, 6, and 7 Ag atoms allows us to conclude that the most stable structures correspond: for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{1}{3} $\end{document} to linear Ag chains (3 × 1 phase), for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{2}{3} $\end{document} to an honeycomb lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), and for θ = 1 to a centred hexagonal lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), the Ag atoms located at the centers of the hexagons being beneath the plan of the hexagons. The adsorption energies corresponding to the various θ are practically equal (ca. 3 eV/Ag). The net charges of Ag atoms are equal to 0.35.     

Free energy of adsorption of water and calcium on the [10 1 4] calcite surface

Molecular dynamics simulations of the calcite-water interface have shown that the free energy of adsorption of water is relatively small compared to the previously calculated enthalpy of adsorption implying a large entropy change and that the free energy profile of a calcium adsorbing on the surface correlates with the solvent density; these calculations allow us to begin to address the rates of adsorption and desorption which are essential for studying growth and dissolution.     

Provably stable and time‐accurate extensions of Runge–Kutta schemes for CFD computations on moving grids

Extending fixed‐grid time integration schemes for unsteady CFD applications to moving grids, while formally preserving their numerical stability and time accuracy properties, is a nontrivial task. A general computational framework for constructing stability‐preserving ALE extensions of Eulerian multistep time integration schemes can be found in the literature. A complementary framework for designing accuracy‐preserving ALE extensions of such schemes is also available. However, the application of neither of these two computational frameworks to a multistage method such as a Runge–Kutta (RK) scheme is straightforward. Yet, the RK methods are an important family of explicit and implicit schemes for the approximation of solutions of ordinary differential equations in general and a popular one in CFD applications. This paper presents a methodology for filling this gap. It also applies it to the design of ALE extensions of fixed‐grid explicit and implicit second‐order time‐accurate RK (RK2) methods. To this end, it presents the discrete geometric conservation law associated with ALE RK2 schemes and a method for enforcing it. It also proves, in the context of the nonlinear scalar conservation law, that satisfying this discrete geometric conservation law is a necessary and sufficient condition for a proposed ALE extension of an RK2 scheme to preserve on moving grids the nonlinear stability properties of its fixed‐grid counterpart. All theoretical findings reported in this paper are illustrated with the ALE solution of inviscid and viscous unsteady, nonlinear flow problems associated with vibrations of the AGARD Wing 445.6. Copyright © 2011 John Wiley & Sons, Ltd.