An analytical discrete-ordinates solution of the S-model kinetic equations for flow in a cylindrical tube

An integro-differential form of the linearized S-model kinetic equations for describing flow in a cylindrical tube is projected in such a way as to yield a pair of coupled transport equations that defines the desired velocity and heat-flow profiles. This system is then solved symbolically to yield a pair of coupled integral equations for the physical quantities required. At this point some transformations are carried out to yield a restatement of the original problem in terms of a “pseudo-problem” defined by plane-geometry variables. An analytical version of the discrete-ordinates method is then used to solve the pseudo-problem, and so, after both MATLAB and FORTRAN versions of the developed algorithm are implemented, results thought to be highly accurate are obtained for the case of diffuse reflection from the walls of a cylindrical tube. In addition to the velocity and heat-flow profiles, for the cases of Poiseuille flow and thermal-creep flow, the velocity slips, the heat-flow profiles evaluated at the wall, the particle-flow rates and the heat-flow rates for these two problems are reported for selected values of the tube radius.     

Generalized boundary conditions for the S-model kinetic equations basic to flow in a plane channel

An analytical version of the discrete-ordinates method is used to solve the classical problems of Poiseuille flow and thermal-creep flow in a plane channel. The kinetic theory for the rarefied-gas flow is based on the S model (a generalization of the BGK model), and in addition to the use of the diffuse-specular reflection model (based on a single accommodation coefficient) for describing particle scattering from the channel walls, the Cercignani-Lampis model defined in terms of normal and tangential accommodation coefficients is implemented. The established solution is tested numerically, and results for the velocity and heat-flow profiles, the particle-flow rate and the heat-flow rate thought to be correct to many significant figures are reported for various values of the channel width.     

The McCormack model for gas mixtures: The temperature-jump problem

An analytical version of the discrete-ordinates method (the ADO method) is used to establish a concise and particularly accurate solution to the temperature-jump problem for a binary gas mixture described by the McCormack kinetic model. The solution yields, in addition to the temperature-jump coefficient for the general (specular–diffuse) case of Maxwell boundary conditions for each of the two species, the density and temperature profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne-Ar and He-Xe) with various molar concentrations. The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium 4 machine to compute all quantities of interest.Received: November 18, 2003; revised April 14, 2004     

Strong evaporation into a half space. II. The three-dimensional BGK model

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the BGK equation for a three-dimensional gas linearized about a drifting Maxwellian distribution. The theory of singular integral equations is used and numerical results are given.

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Zusammenfassung Die Verdampfung einer Flüssigkeit im Vakuum, die den Halbraum füllt, wird untersucht mit Benützung der BGK-Gleichung für ein dreidimensionales Gas, linearisiert in bezug auf eine mitbewegte Maxwell-Verteilung. Es wird die Theorie der singulären Integralgleichungen benützt, und es werden numerische Resultate gegeben.

     

Analytical solutions to two matrix Riemann-Hilbert problems

Two matrix Riemann-Hilbert problems derived from boundary-value problems in the kinetic theory of gases are solved analytically.

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Riassunto Vengono risolti analiticamente due problemi relativi alla matrice di Riemann-Hilbert, che si incontrano in problemi con condizioni al contorno nella teoria cinetica dei gas.

     

Reagent‐Controlled α‐Selective Dehydrative Glycosylation of 2,6‐Dideoxy‐ and 2,3,6‐Trideoxy Sugars

We have found that activating either 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropenone or 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropene‐1‐thione with oxalyl bromide results in the formation of a species that promotes the glycosylation between 2,6‐dideoxy‐sugar hemiacetals and glycosyl acceptors in good yield and high α‐selectivity. Both reactions are mild and tolerate a number of sensitive functional groups including highly acid‐labile 2,3,6‐trideoxy‐sugar linkages.     

Cholesterol shows preference for the interior of polyunsaturated lipid membranes

Recent neutron scattering experiments showed a striking manifestation of the aversion between polyunsaturated fatty acid (PUFA)-containing lipids and cholesterol. Selectively deuterated cholesterol/ 1,2-diarachidonylphosphatidylcholine (DAPC) samples revealed that the hydroxyl of the sterol resides at the center of the bilayer. Here we use a recently parametrized coarse grain simulation model to shed light on these puzzling experimental observations. Using a simulation setup in close correspondence to the experimental conditions, we reproduce the experimental neutron scattering profiles to a large extent. The simulations allow us to analyze the behavior of cholesterol in detail; we show that the interaction of cholesterol with the PUFA chains of DAPC leads to a fast flip-flop rate for the sterol and an increased preference of the sterol for the unusual location embedded between the monolayer leaflets.     

Proton‐Coupled Electron Transfer Reactions Catalysed by 3 d Metal Complexes

Proton‐coupled electron transfer (PCET) reactions are essential for a wide range of natural energy‐conversion reactions and recently, the impact of PCET pathways has been exploited in artificial systems, too. The Minireview highlights PCET reactions catalysed by first‐row transition‐metal complexes, with a focus on the water oxidation, the oxygen reduction, the hydrogen evolution, and the CO₂ reduction reaction. Special attention will be paid to systems in which the impact of such pathways is deduced by comparison to systems with “electron‐only”‐transfer pathways.     

Electrocatalytic Dihydrogen Production with a Robust Mesoionic Pyridylcarbene Cobalt Catalyst

A Co^III complex with a mesoionic pyridylcarbene ligand is presented. This complex is an efficient electrocatalyst for H₂ production at very low overpotential and high turnovers when using a (glassy carbon) GC electrode. The corresponding triazole complexes display no catalytic activity whatsoever under identical conditions. The remarkable robustness of the Co? C(carbene) bond towards acids is likely responsible for the high efficiency of this catalyst. The present results thus open new avenues for carbene‐based ligands for generating functional models for hydrogenases.