A Parabolic Spline on a Nonuniform Grid

We obtain estimates for errors of interpolation on a nonuniform grid for a parabolic nonperiodic spline of defect 1.     

Mixing mechanisms of vortex ring formed by gravity slumping motion

 This paper is concerned with an experimental investigation of the mixing inside the vortex ring formed by the gravity slumping motion of a dense cloud in a less dense atmosphere. The dynamics of the spreading and instantaneous structures of the turbulent flow were examined by visualization, single and multi-point measurements of velocity and concentration for two heavy gases, carbondioxide (CO₂) and dichlorodifluoromethane (CCl₂F₂), in a configuration in that heavy gas, initially trapped in a reservoir, was released with the rise of a shutter into calm air of a sector-shaped dispersion channel. Visualization of the cloud as a whole showed a spreading motion in which an advancing frontal structure was followed by a stratified flow with a layer of dense fluid of higher velocities near the wall and, on top of it, a layer of dilute fluid whose concentration is controlled by the mixing mechanisms within the head. During the course of spreading, there was always a phase in which the head attained to a constant speed of advance, which occurred as 0.13 m/s for CO₂ and 0.48 m/s for CCl₂F₂. It was interesting to observe for CO₂ that the phase of constant speed took place in between two acceleration phases; the former was due to the initial slumping of the cloud at the exit of the reservoir, and the latter was attributed to the collapse of the head on the transition to the passive dispersion phase. Instantaneous two-dimensional velocity field, measured with particle image velocimeter (PIV), showed that the cloud overran the ambient air which caused the approaching dense fluid deflected away from the wall with significant vertical velocities and downstream-moving separation, and the air trapped under the head resulted in the density inversion which introduced further intricacy to the turbulent structure of the head. Instabilities at the upper free shear layer due to density and velocity discontinuity rolled into periodic array of vortices which engulfed a considerable amount of air as they were convected backwards over the head, but the incorporation of heavy and light fluids was completed with the appearance of microscales after the collapse on the stratified layer. Analyses of the cloud head at different downstream locations also revealed that its size remained unchanged when the speed of advance was constant, allowing the rate of change of the cloud volume being modeled with the rate of spreading. Contours of concentration obtained from digitized PIV pictures confirmed the kinematic features of the mixing revealed by the velocity field and that the concentration values within the large structures were higher than those at the upper part of the stratified layer. Motivated by the experimental observations, a semi-empirical analysis was presented to describe the results and based on local values of the Richardson and Reynolds numbers. Received: 4 October 1995 / Accepted: 4 July 1996     

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Stationary soliton on a charged surface of liquid helium and hydrogen films

A change in the shape of a charged surface of liquid hydrogen and helium — the formation of a solitary wave (a positively charged hump for hydrogen and a negatively charged dimple for helium)-is observed in an electric field exceeding a critical value under conditions of total compensation of the applied field by the surface charge. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 547–552 (10 April 1997)     

Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

New synthesis of 2',3'-didehydro-2',3'-dideoxynucleosides.

The 3'-iodonucleoside 4 and the 3'-O-methylsulfonylthymidine 9 have been synthesized by condensation of silylated uracils 2 with methyl 5-O-tert-butyldiphensilyl-2,3-dideoxy-3-iodo-D-threo-pentofuran oside (3) and methyl 5-O-tert-butyldiphenylsilyl-2-deoxy-3-methylsulfonyl-D-erythro- pentofuranoside (8), respectively. The nucleoside 4 and 9 produced the corresponding 2',3'-didehydro-2',3'-dideoxynucleosides 5 in an elimination reaction on treatment with sodium methoxide. The compounds 5b showed no antiviral activity against HIV-1.     

Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

Analysis of atmospheric particular matter and water using atomic emission spectrometry with inductively-coupled plasma and two-jet plasmatron

Summary A method for the atomic emission spectrometric analysis of air and water with inductively coupled and two-jet direct current plasmas has been developed. The method has been applied to the determination of impurity contents with good accuracy and sensitivity.     

High-performance liquid chromatographic method for quantitating plasma levels of amiloride and its analogues.

An assay for amiloride was devised for efficient use with the wide variety of analogues available. Amiloride was extracted from 1-ml plasma samples by elution from a C8 preparative column with 6% acetonitrile-45% methanol-5.4% acetic acid, adjusted to pH 4.0 with trimethylamine. Samples were lyophilized, resuspended in 50% methanol, filtered through 0.22-microns Spin-X cartridges, applied to a reversed-phase C18 column, and eluted in a 0-50% acetonitrile gradient in 0.4% acetic acid, pH 4.5 (1.2 ml/min). Detection by ultraviolet absorbance at 360 nm was linear from 1 to 1000 ng. Versatility of the method was demonstrated with the analogues benzamil, 6-hydro-, 6-iodo-, 5-hexamethylene-, and 5-chlorobenzyl-2',4'-dimethylbenzyl-amiloride.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.