Temperature dependence of the low-frequency reflectance spectrum of a sodium nitrate single crystal: Effect of the phase transition on the lattice modes parameters

Conclusion Reflectivity of a single crystal sodium nitrate have been measured as a fonction of temperature and crystallographic orientations over a frequency region which spans all infrared active lattice modes. The data have been fitted with a series of five independent oscillators and an overdamped oscillator of A_2u symmetry at temperatures between 250 and 276°C. None of them behaves as a soft mode. Our measurements show also the influence of the phase transition on the lattice modes parameters.     

Kinetic theory of hydrodynamic flows. I. The generalized normal solution method and its application to the drag on a sphere

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemented by boundary conditions imposed on the distribution function at the surface of the object. The remainder of the paper is devoted to a study of the solution of the extended Boltzmann equation in the case that the mean free path of a gas molecule is small compared to some characteristic dimension of the macroscopic object. We show that the Chapman-Enskog normal solution of the ordinary Boltzmann equation is not in general a solution of the extended equation near the surface of the object and must be supplemented by a boundary layer term. We then introduce a projection operator method which allows us to decompose the solution of the extended equation into a normal solution part and a boundary layer part when the gas flow is sufficiently slow. As a specific example of the method we consider the flow around a sphere, and derive the Stokes-Boussinesq form for the frequency-dependent force on the sphere for arbitrary slip coefficient. This derivation is the first one that starts from the Boltzmann equation for a general dilute gas and incorporates the effect of the boundary layer on the drag force.Work supported by the National Science Foundation.     

Cyclooligomerization with Transition Metal Catalysts

This report is concerned not only with the syntheses of new ring systems and the preparation of derivatives of known rings but also with new types of catalysts based upon, e. g., nickel, iron, molybdenum, manganese, and palladium. The broad applicability of the methylene insertion reaction as a method for identifying mono- and di-methyl-substituted eight-, ten-, and twelve-membered rings is also demonstrated. A further section is concerned with the possible mechanism of C? C bond formation in transition metal complexes; several earlier suggestions have been revised in the light of new experimental data. In addition, experimental results are discussed which indicate that the reactivity and selectivity of the complexes formed by the nickel-ligand catalyst and olefins or alkynes depend upon the structure of the ligands.     

A unified approach to direct and inverse boundary layer solutions

A unified approach is presented for solving the two-dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth-order spline discretization approximates normal derivatives with two- and three-point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two-point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non-similar flows and compared with published results.     

Quantitative evaluation of thin-layer chromatograms. 5. Calculation of reflectance and transmission using Markov chains

Changes of reflected and transmitted light in cases where a band lies in different sublayers of a thin-layer chromatogram are calculated by the use of Markov chains. The problem of a “random walk with absorbing barriers” is described and compared with the problem of transmission and reflectance of light in a layer of sorbent.     

Numerical calculation of transitional boundary layers

A computational procedure for compressible axisymmetric boundary layers, on bodies of revolution, in transition from laminar to turbulent flow, is introduced. The procedure is an extension of a former method, due to Patankar and Spalding. The flow field is computed by solution of four simultaneous equations for the momentum, the thermal energy, the turbulence energy amplitude and the turbulent scale. The results show good agreement with existing theoretical and experimental data.     

Phonon dispersion in quasiperiodic semiconductor superlattices

The phonon spectra of unstrained and strained quasiperiodic semiconductor superlattices (QSSL) have been calculated using one-dimensional linear chain model. We consider two types of quasiperiodic systems, namely cantor triadic bar (CTB) and Fibonacci sequences (FS), constituting of AlAs, GaAs and GaSb of which the latter two have a lattice mismatch of about 7%. The calculations have been made using transfer matrix method and also with and without the inclusion of strain. We present the results on phonon spectra of two component CTB and two as well as three component FS semiconductor superlattices (SSL), thickness and order dependence on LO mode of GaAs, effect of strain on LO frequency of GaAs. The calculated results show that the strain generated due to lattice mismatch reduces significantly the magnitudes of the confined optical phonon frequency of GaAs.     

A PRELIMINARY STUDY ON THE IMPACT OF MESOSCALE IRRIGATION OVER ARID LAND ON MESOSCALE CLIMATE

The present study investigated the modification of mesoscale inhomogeneous distribu-tion of soil wetness, resulting from mesoscale irrigation over arid or semiarid lands in mid-latitude in the later summer or early autumn, on mesoscale climate under conditions withand without synoptic flow influence, using an interactive model between soil and atmo-sphere. The simulations indicated that after a mesoscale irrgation, a wet soil breeze circu-lation was thermally forced, which was, in many features, similar to that of the sea breezecirculation. The influence of synoptic flows on the structure of thermally--induced wet soilbreeze circulation was also discussed.     

双电层相互作用时胶体表面电位的分布及电荷密度的计算

本文以实验为基础,运用计算机数值解解出双电层相互作用时平面胶体表面电位ψ随距离X的分布,依据作者导出的双电层相互作用时胶体表面阴离子负吸附方程,计算出胶体表面外Hclmhotz面(OHP)处的表面电荷密度σ_δ;讨论了双电层相互作用程度(ψ_d/ψ_δ)对胶体表面电位分布及其表面电荷密度的影响。     

Numerical method for unsteady compressible boundary layers driven by compression or expansion wave

A numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non-linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non-linearity and the coupling with the thermal boundary layer equation. Because the non-linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions.