Precision,complexity, and computational schemes of the cubic algorithm

The cubic algorithm (Ref. 1) is a nongradient method for the solution of multi-extremal, nonconvex Lipschitzian optimization problems. The precision and complexity of this algorithm are studied, and improved computational schemes are proposed.     

The effects of streamline curvature and spanwise rotation on near-surface,turbulent boundary layers

A second moment closure model is used to study the mean fields and turbulence structure of spanwise rotating flows and flows with streamline curvature. The effects of flow stabilization and destabilization by rotation and/or curvature and their interpretation in terms of a Rayleigh instability mechanism are discussed in the context of the present model. When applied to the constant flux layer adjacent to a bounding surface, the model provides a similarity theory for flows with spanwise rotation and streamline curvature like that of Monin-Obukhov in the case of density stratified flows. In particular, it is shown that Bradshaw's empirical length scale correction can be derived in terms of the basic constants of the model determined in the absence of rotation and curvature. Also, direct comparisons with experimental data confirm the model predictions. The definitions of strong and mild curvature are discussed and a distinguishing criterion derived.

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Zusammenfassung Gemittelte Strömungsfelder und Turbulenzcharakteristiken werden bestimmt mittels eines numerischen Modelles mit Momenten zweiter Ordnung als Ciosure für lateral rotierende Strömungen und mit gekrümmten Stromlinien. Stabilisierungs- und Destabilisierungseffekte infolge Rotation und/oder Krümmung werden als Raleigh-Instabilitäten im Zusammenhang mit dem Modell diskutiert. Wenn angewandt auf die Konstant-Scherspannungszone in Grenzschichten, liefert das Modell eine Ähnlichkeitstheorie für Strömungen mit lateraler Rotation und Stromlinienkrümmung, vergleichbar dem Falle des Monin-Obukhov Modelles für geschichtete Strömungen. Es wird insbesondere gezeigt, dass Bradshaws empirische Längenkorrektur sich aus den Grundkonstanten des Modelles ergibt für den Grenzfall ohne Rotation und Krümmung. Direkter Vergleich mit experimentellen Daten bestätigt die Rechnungen. Die Definitionen von starker und schwacher Krümmung werden diskutiert und ein Unterscheidungskriterium eingeführt.

     

Linear optical response of current-carrying molecular junction: a nonequilibrium Green's function-time-dependent density functional theory approach

We propose a scheme for calculation of linear optical response of current-carrying molecular junctions for the case when electronic tunneling through the junction is much faster than characteristic time of external laser field. We discuss relationships between nonequilibrium Green's function (NEGF) and time-dependent density functional theory (TDDFT) approaches and derive expressions for optical response and linear polarizability within NEGF-TDDFT scheme. Corresponding results for isolated molecule, derived within TDDFT approach previously, are reproduced when coupling to contacts is neglected.     

Adducts of dicoordinated trivalent phosphorus with carbenes

1,4-Dichloro-3a,6a-diaza-1,4-diphosphapentalene reacts with sodium acetylacetonate to form an adduct of diacylcarbene with trivalent dicoordinated phosphorus. In solution this adduct dimerizes according to the head-to-head type. The phosphorus atoms undergo transformation from the hypervalent state (in the adduct), in which the lone electron pair on the phosphorus atom is not involved in the formation of additional bonds with this phosphorus(III) atom, to the pentavalent pentacoordinated and trivalent tricoordinated state (in the dimer).     

Exchange of halogens in the 3a,6a-diaza-1,4-diphosphapentalene derivatives: Crystal structures of iodides

1,4-Dichloro-3a,6a-diaza-1,4-diphosphapentalene (II) easily exchanges halogen with methyl iodide to form the corresponding 1,4-diiodo derivative (V) in a quantitative yield. The reaction of compound II with diiodine (1 equiv) affords compound III, the crystal structure of which contains 55% II and 45% V. Under the conditions of iodine excess (1 : 3), a ionic compound (IV) is formed, the crystal of which contains alternating layers consisting of planar networks [I₂I₃]? and heterocyclic cations [DDP–Cl]⁺. For the crystallographic information for compounds III–V, see CIF files CCDC no. 1560 410 (V), 1560 411 (III), and 1560 412 (IV).     

Gold nanoparticles electrooxidation: comparison of theory and experiment

The article presents the findings of microscopic and electrochemical studies of size-dependent gold particles electrooxidation. Gold particles were immobilized on the surface of carbon-containing screen-printed electrodes. The experiment demonstrated that the transition from macroparticles to nanoparticles caused a shift of the maximum current potential of gold oxidation into the area with more negative potentials. A decrease in particle size resulted in an increase in the electrochemical activity of metal. A positive correlation between experimental and calculated curves confirms a mathematical model (2) and correctness of the calculations. Measured parameters of voltammograms, in particular, maximum current potential, can be used to describe the electrochemical activity and energy properties of nanoparticles.     

Electrochemistry of metal nanoparticles: the effect of substrate

It is shown that nanoparticles localized on a foreign solid electrode may display two opposite shifts of dissolution potential, namely, a shift toward either more positive or more negative values as compared with the equilibrium potential of M ⁿ⁺/M ⁰ or the potential of bulk metal electrooxidation. The observed phenomena are interpreted in view of three energy states of substance, which are realized depending on contribution of the surface Gibbs free energy (ΔG°) to the energy of the system. Literature data concerning different metal-substrate pairs and specially conducted experimental investigations of electrooxidation of gold nanoparticles (radius equal to 10 and 150?nm), which are localized on the surface of glassy carbon, bulk gold, and platinum electrodes are presented and discussed. A shift of maximum current potential of small nanoparticles oxidation toward more positive values is observed in this series. The oxidation potential of large nanoparticles is not affected by the nature of the substrate. In all cases, electrooxidation of gold nanoparticles occurs at the more negative potentials than those of the bulk gold electrooxidation. It is shown that depending on the nature of the substrate and nanoparticle size, the dominating effect is either interaction of nanoparticles with the substrate (ΔG°?<?0) and electrochemical potential shifts toward positive values or impact of surface Gibbs free energy of nanoparticles (ΔG°?>?0) into energy of the system and electrochemical potential shifts toward negative values. The validity of the proposed assumptions is confirmed by good correlation of literature and our experimental data with calculated ones.     

Chemical properties of 3a,6a-diaza-1,4-diphosphapentalene. Addition of polyhalohydrocarbons

3a,6a-Diaza-1,4-diphosphapentalene (DDP, 1), in contrast to common azaphospholes, readily reacts with polyhalohydrocarbons with the formation of 1,1- or 1,4-addition products at the phosphorus atoms. Dibromomethane gives the substitution product of two bromine atoms [CH₂(DDP)₂]Br₂ (2) and diphosphine (DDP-DDP)Br₂ (3) containing a bridging bromine atom. In the course of the reaction of DDP with CF₂Br₂, two products of sequential substitution of the bromine atoms were isolated, which are 1,4-Br₂(DDP) (6) and [CF₂(DDP)₂]Br₂ (7). Tris(pentafluorophenyl)phosphine reacts with DDP at the C—F bond with the formation of 1,1-addition product 8. Compounds 2, 3, 7, and 8 contain hypervalent (tervalent 4-coordinated) phosphorus atoms. X-ray diffraction data indicate that the mutual arrangement of the DDP fragments in compounds 2, 3, and 7 is determined by the non-covalent interaction of one of the bromine atoms simultaneously with two phosphorus atoms of different DDP fragments in such a way that the lines of the N—P bonds converge at this bromine atom.     

Reaction of benzylidenetriphenylphosphorane with 1,4-dichloro-3а,6а-diaza-1,4-diphosphapentalene

The transylidation between 1,4-dichloro-3a,6a-diaza-1,4-diphosphapentalene and benzylidenetriphenylphosphorane (Ph₃P=CHPh) results in either mono- or disubstitution of chlorine atoms by the Ph₃P=C(Ph) group depending on the reactant molar ratio. In the crystal, the monosubstituted product has the planar diazadiphosphapentalene ring and the P—Cl ionic bond. The ³¹P NMR spectra of this compound exhibit a strong solvent-dependent behavior, which indicates that it exists both in the ionic form (in CH₂Cl₂, MeCN) and the molecular form (in THF). In the disubstituted product, the diazadiphosphapentalene skeleton is non-planar and is bent along the N—N bond.     

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