Complementary Variational Principles for Knudsen Flow Rates

A collisionless gas flows through the interior of a tube ofcircular cross-section, having both an entrance and an exitand which reflects molecules diffusely. Suitable complementaryvariational principles are used to obtain upper and lower boundsfor the transmission probability of the tube. The numericalresults, believed to be the most accurate to date, are comparedwith those of other authors.     

易化输运过程的简单化学模型及其在Wyman-Murray扩散中的应用(英文)

A simple chemical kinetic model is developed which describes the behavior of small ligands that can bind reversibly with large carrier molecules with slower intrinsic rates of transport. Under certain conditions, which we describe, the presence of the slower carriers in fact enhances the transport of the ligand. This is the chemical version of Wyman-Murray′ s facilitated diffusion. The simple model illuminates the driven nature of the enhancement of the transport by the carrier molecules: we show that the facilitated transport depends crucially on a"grand canonical" setting in which the free ligand concentrations are kept constant in the presence of the facilitating protein, in contrast to a canonical setting with constant total ligand concentrations. Results from the simple model are compared to previous experimental and theoretical results for Wyman-Murray facilitated diffusion of oxygen and carbon monoxide in muscle. A relation is established between the association-dissociation rates and the down-stream ligand concentration, or back pressure for oxygen, required for the facilitation effect to occur.     

Solution of Linear Generalized Eigenvalue Problems Containing Singular Matrices

A general method is presented for the solution of the lineargeneralized eigenvalue problem Ax = Bx, where matrices A andB may both be singular but ||A — B|| 0. The procedurecan easily be implemented on a digital computer using a Gaussianelimination algorithm with pivoting together with a QR eigensolutionpackage. Results are given for two problems with sensitive eigenvalues.     

A hydrogen bonded complex C2H2…HBr isolated and characterized in the gas phase using pulsed-jet,Fourier transform microwave spectroscopy

A complex formed from ethyne and hydrogen bromide has been isolated and characterized by using a fast-mixing nozzle in conjunction with a pulsed-jet, Fourier transform microwave spectrometer. Any possible chemical reaction between the two components when mixed in the usual way was thereby precluded. The rotational constants A, B and C, the quartic centrifugal distortion constants δ_J, δ_Jk and δ_J and the Br nuclear hyperfine coupling constants X_aa and X_bb—X_cc (nuclear quadrupole) and M_bb (spin-rotation) were determined for each of the five isotopomers C₂H₂…H⁷⁹Br, C₂H₂…H⁸¹ Br, C₂H₂…D⁷⁹Br, C₂H₂…D⁸¹Br and C₂D₂…H⁷⁹Br. Interpretations of the spectroscopic constants show that the complex is planar and T shaped in the equilibrium conformation, with HCCH internuclear axis forming the cross of the T and the HBr internuclear axis lying along the C₂ axis of C₂H₂. The H of HBr is closer to the centre (?) of the π bond of ethyne, and therefore HBr is involved in a hydrogen bond to the π system, in which the distance of H from ? is r (?…H) = 2.469(1) A. The intermolecular stretching force constant is estimated as kσ = 5.38(2) Nm^?1 for the species involving a hydrogen bond (C₂H₂…H⁷⁹Br, C₂H₂…H⁸¹Br and C₂D₂…H⁷⁹Br) while this quantity increases to kσ = 5.68(2)Nm^?1 for those complexes bound through a deuterium bond (C₂H₂…D⁷⁹Br and C₂H₂…D⁷⁹Br). The opportunity is taken to consider similarities in the properties of complexes within the two series B…HBr and B…HC1 for a range of Lewis bases B, including B = C₂H₂. Some family relationships are identified in the two series.     

Noise Problem in Semiconductors

This paper deals with the problem of calculating the variancesand covariances of the fluctuating numbers of conduction electronsin semiconductors, since the noise power associated with thecurrents passing through the material can be obtained in termsof these quantities. The usual finite difference equation isobtained for the probability distribution of these electronnumbers, and it is shown how present methods of calculationare too cumbersome to apply to realistic semiconductor models.In a new calculation it is shown that it may be possible toobtain a better signal-to-noise ratio in the material by introducinga critical number of impurities. To study this principle ingeneral a more rapid and straightforward method must be foundof obtaining the required quantities. To achieve this aim anew method is tried—the difference equation is transformedinto a partial differential equation for the probability generatingfunction and is solved exactly for a case in which there isone type of impurity present. The equation has not yet beensolved when the material contains more than one type of impurity.