Reflexion Method Research Articles

Static thin disks with haloes as sources of conformastatic spacetimes

Two new families of exact solutions to the Einstein equations for a conformastatic spacetime with axial symmetry are presented which describe thin disks of dust immersed in a spheroidal halo. The solutions are obtained by expressing the metric function in terms of an auxiliary function which satisfies the Laplace equation, a characteristic property of the conformastatic spacetimes. The first family of solutions is obtained from the displacement, cut and reflexion method, which introduces a discontinuity in the first $z$-derivate of the metric tensor across the plane of the disk. The second family of solutions is obtained by using the oblate spheroidal coordinates because they adapt to the shape of the source and introduce naturally a cutting radius for the disk. The energy densities of the disk and the halo are everywhere positive and well behaved and their energy-momentum tensor agrees with all the energy conditions. Some particular solutions for the energy density of the disk and the halo are presented and the rotational curves are obtained by solving the geodesic equation for a particle that moves in circular orbits in the plane of the disk.

Tracheal section is an independent predictor of asthma in patients with nasal polyposis

Airway anatomy could be a risk factor for asthma in susceptible patients with airway hyperresponsiveness. This anatomy can be described by only two parameters, the tracheal cross-sectional area and the homothety ratio, which describes the reduction of calibre at each subsequent generation. Thus, we hypothesized that the tracheal area would be linked to the risk of asthma presence.Tracheal area (measured by acoustic reflexion method) and airway responsiveness to metacholine (expressed as Dose Response Slope) were evaluated in 71 consecutive adult patients with nasal polyposis and normal baseline lung function.Hyperresponsiveness was evidenced in 30/71 patients (42%), and 20/71 patients (28%) were asthmatics. Forced expiratory flows were related to tracheal areas (mean value: 3.22±1.32cm2). In a logistic multivariate analysis, tracheal area and the degree of responsiveness were independent predictors of asthma.In conclusion, this study suggests that airway anatomy, crudely assessed by tracheal section, is an independent determinant of asthma.

Extending the reflexion method for consolidating software variants into product lines

Software variants emerge from ad-hoc copying in-the-large with adaptations to a specific context. As the number of variants increases, maintaining such software variants becomes more and more diffi...

Automated clustering to support the reflexion method

A significant aspect in applying the Reflexion Method is the mapping of components found in the source code onto the conceptual components defined in the hypothesized architecture. To date, this mapping is established manually, which requires a lot of work for large software systems. In this paper, we present a new approach, in which clustering techniques are applied to support the user in the mapping activity. The result is a semi-automated mapping technique that accommodates the automatic clustering of the source model with the user’s hypothesized knowledge about the system’s architecture. This paper describes three case studies in which the semi-automated mapping technique, called HuGMe, has been applied successfully to extend a partial map of real-world software applications. In addition, the results of another case study from an earlier publication are summarized, which lead to comparable results. We evaluated the extended versions of two automatic software clustering techniques, namely, MQAttract and CountAttract, with oracle mappings. We closely study the influence of the degree of completeness of the existing mapping and other controlling variables of the technique to make reliable suggestions. Both clustering techniques were able to achieve a mapping quality where more than 90% of the automatic mapping decisions turned out to be correct. Moreover, the experiments indicate that the attraction function (CountAttract′) based on local coupling and cohesion is more suitable for semi-automated mapping than the approach MQAttract′ based on a global assessment of coupling and cohesion.

Photochromism of Dithienylethene Derivatives Trapped in Sol-Gel Matrices

Solid-state materials containing photochromic dithienylethene derivatives were prepared by the sol-gel process in the form of thin films of a few μm-thick. The effect of substituents (pyridyl or methoxyphenyl) of the optically active molecules on photochromic properties was investigated. Thicknesses and refractive indices either at 633 nm or 785 nm were determined in the colored and in the discolored state by using the Attenuated Total Reflexion method. Sol-gel films containing methoxphenyl substituted molecules show a large refractive index change, Δn=3.10−3 at 785 nm. This variation is important considering the low doping level (0.7 wt%).

Roughness spectrum for surfaces of silver deposits

The roughness spectrum g( k) (or spectral density function) for surfaces of silver deposits is deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface shadowed carbon replicas. We used a process based on the computation of autocovariance function (ACF) via the fast Fourier transform (FFT) algorithm. Results are compared with those provided by attenuated total reflexion (ATR) method. It is shown that the g( k) function is not perfectly gaussian as it is usually assumed.

The scattering by a headland of the dominant continental shelf wave

The scattering that occurs when a continental shelf wave propagating over an exponential-constant depth profile is incident on a coastal promontory is here investigated by transforming the shelf region differential equation for the mass transport stream function to the wave equation and using high wavenumber asymptotics and the method of successive reflexions. It is found that energy is propagated in the shelf region according to geometrical optics, being reflected at the shoreline, promontory and shelf-ocean boundary. A solution is sought in terms of a distribution of singularities on the boundary of the promontory, and the application of all boundary conditions is facilitated by using plane wave representations. Numerical values obtained experimentally indicate a shelf width of some three times the wavelength which is similar to the maximum projection of the promontory from the shoreline. Thus it is plausible to seek an approximate solution by alternately considering the scattering by the obstacle with the shelf width regarded as infinite and the reflexions at the shelf-ocean boundary in the absence of the promontory. For the semicircular headland, an exact solution is available for the initial scattering but the successive approximation procedure converges less quickly than for the offshore barrier, in which case no exact solutions are available. The reason is that the tendency for energy to become trapped on the shortest offshore line across the shelf is more sharply focused in the latter case. Numerical values are given for the amplitudes of the far field modes excited by the semicircular headland. For the offshore barrier, the density of the singularity distribution corresponds to the velocity discontinuity at the barrier, while at the line of the barrier the alongshore and offshore components of the shelf region velocity field due to scattering are such that, to leading order, corresponding terms differ only by constant phase.

Correction of Integrated X‐Ray Intensities for Preferred Orientation in Hexagonal Close‐Packed Powders Using Edxrd

It is shown that energy‐dispersive x‐ray diffraction (EDXRD) method can be used for correction of integrated intensities for preferred orientation in hexagonal close‐packed powders. The theory is based upon examination of the polar axis density distribution and upon the use of hexagonal harmonics in its representation. The reflexion method by Schulz added with defocusing correction was used. Measurements were carried out on three zinc samples with different degrees of orientation, the largest correction being 54 percent.

Motion of a sphere in the presence of a plane interface. Part 1. An approximate solution by generalization of the method of Lorentz

The motion of a sphere in the presence of a fluid-fluid interface is studied. First, a solution is derived for a point force near a plane interface. Then the solution is extended to include the higher-order terms which are required to describe the motion of a solid sphere. Singularities of higher orders at the centre of the sphere are obtained by using the method of reflexions. For a fluid–fluid interface with an arbitrary viscosity ratio, the drag force and the hydrodynamic torque are calculated for the special cases of motion of a sphere perpendicular and parallel to the interface. In addition, the rotational motion of a sphere is also investigated.

A Laser Instrument for Measuring Tooth Movements

An improved apparatus has been constructed which is based upon the laser reflexion method and is used in a highly accurate direct technique of measuring tooth movement without contact. The possibility of making clinical investigations of tooth movements with the equipment has been investigated by testing its various components. The most critical part of the system is the repositioning of the patient, which has been done with an accuracy of +/- 20 micron. The reflected pattern used during 3 months of experiments was the same. The instrument can be used for measurements down to 50 micron.

The effect of two plane walls on the motion of a small sphere in a viscous fluid

A theoretical study is made of the motion of a small sphere in an incompressible viscous fluid bounded by two plane walls. The analysis is based on the Stokes equations of motion and the method of reflexions is employed to obtain the lowest-order wall effect on the sphere, which is allowed either to rotate or not as it translates in an arbitrary direction. The effect of two plane walls on the force and torque (or angular velocity) experienced by the sphere is not accurately estimated by superposing the contributions from the two individual walls.

Ultrasonic determination of subcutaneous adipose tissue and body fat

We measured with the ultrasonic reflexion method the breadth of the subcutaneous adipose tissue at the following anatomical sites: subscapulare, triceps and on the lateral margin of the m. pectoralis on the chest. The percentual body fat can be calculated from the formula: % body fat = 22 - log / 2 - sum of the breadths on the three sites / -20.5 If we measure also the breadth on the abdominal point the % body fat is 22 - log / 1.5 - sum on the four sites / -20.5. The so calculated numerical results are with the skinfold measurements in best correlation.

The use of laser beams for measuring tooth mobility and tooth movements.

The laser reflexion method, a direct contactless measuring technique with a high accuracy, has been applied for clinical purposes. A prototype has been tested using a laser beam to illuminate a patient's tooth fixed to the equipment by an impression plate. The reflected patterns were thrown onto a screen with a coordinate system and photographically recorded, and the movement of the tooth has been geometrically calculated. The relapse tendency after orthodontic treatment of a patient with periodontal disease and parafunctions was studied by repeated measurements of the left medial upper incisor. By use of the method, it was possible to observe that the velocity of the studied tooth was highest during the 1st day and, besides the horizontal movement, a rotation of the tooth began at the end of the measuring period.

Characterization methods of Gunn oscillators

Three measurement techniques for determining the large-signal characteristics of Gunn-diode oscillator networks are described and compared. These are the reflexion method, the transient method and the steady state oscillation method. It is shown that the technique adopted should depend on the type of device to be tested.

Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow

An expression is derived for the (low Reynolds number) additional pressure drop created by a relatively small sphere moving near the wall of a circular tube through which there is a Poiseuille flow. Two specific applications are examined: (i) the sedimentation of a homogeneous non-neutrally buoyant sphere in a quiescent fluid; and (ii) the motion of a neutrally buoyant sphere. In the latter case a pronounced increase in the additional pressure drop is predicted when the separation between the sphere and the tube wall is reduced to zero.This analysis, which includes the behaviour for a sphere in contact with the tube wall, supplements previous ‘method of reflexions’ treatments valid only when the distance from the sphere centre to the wall is large compared with the sphere radius.

Piecewise linear retractions by reflexion

The reflexion method of Motzkin and Schoenberg is used to generate a class of piecewise linear retractions from X to Y where X is the set of all points within a fixed distance of the convex polyhedral set Y.

A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids

This paper is the first in a series of investigations having the overall objective of developing a new technique for treating the slow viscous motion past finite assemblages of particles of arbitrary shape. The new method, termed the multi-pole representation technique, is based on the theory that any object conforming to a natural co-ordinate system in a particle assemblage can be approximated by a truncated series of multi-lobular disturbances in which the accuracy of the representation is systematically improved by the addition of higher order multipoles. The essential elements of this theory are illustrated by examining the flows past finite line arrays of axisymmetric bodies such as spheres and spheroids which conform to special natural co-ordinate systems. It is demonstrated that this new procedure converges more rapidly and is simpler to use than the method of reflexions and represents the desired boundaries more precisely than the point-force approximation even when the objects are touching one another. Comparison of these solutions with the exact solutions of Stimson & Jeffery (1926) for the two sphere problem demonstrates the rapidity of convergence of this multipole procedure even when the spheres are touching. Drag results are also presented for flows past chains containing up to 101 spheres as well as for chains containing up to 15 prolate or oblate spheroids. The potential value of the technique is suggested by the rapidity with which the drag calculations were made, the 101 sphere problem requiring about 10 seconds on an IBM 360–65 computer to determine both the fluid flow and the drag coefficient.

Phénomène de défocalisation lié à la géométrie de la chambre de texture de Schulz et incidence sur l'intensité mesurée

The Schulz reflexion method used to draw the {hkl} pole figures of a sample having one or several textures does not allow the definition of the outer part of these figures since the diffracted beam defocuses at low values of the tilt angle, ϕ. Relationships are established to correct the recorded diffracted intensity so that the outer part of pole figures can be outlined. The defocusing effects of the various slits are surveyed and correction curves are presented. The intensity diffracted by a theoretical isotropic sample (rather difficult to get in practice) is calculated from diagrams recorded on a textured specimen. A quantitative analysis of the results obtained on various samples and a detailed study of the texture evolution become possible. An example is given for a rolled OFHC copper sample.

On the slow broadside motion of a thin disc along the axis of a fluid-filled circular duct

The study of the slow motion of a solid body through a viscous fluid is of importance in many fields. We may instance viscometry and chemical engineering as two subjects in which a quantitative understanding of such motions is essential. Thus, in recent years systematic attempts have been made to calculate the drag force and couple on slowly sedimenting particles in a bounded viscous fluid. Using the ‘method of reflexions’ Brenner (1) has obtained formulae which give, for a wide class of sedimenting particles, an estimate of the effect of the container walls on the drag force, the error being O(c/l)3, where c is a characteristic particle dimension and l the distance from the centre of the particle to the nearest boundary wall. The reader is referred to the recent book by Happel and Brenner (2) for a complete account of these and other pertinent investigations; also to Williams (3) for an alternative integral equation approach to these results.

Structure of Precipated Cadmium Sulphide as studied by Single-Crystal Electron Diffraction Pattern

CADMIUM sulphide crystallizes in two modifications : a cubic β-form (hawleyite1 ; zinc blende-type) and a hexagonal α-form (greenockite ; wurtzite-type). According to Milligan2, the former tends to be precipitated from cadmium nitrate (or sulphate) solutions and the latter from cadmium chloride (or bromide, iodide) solutions. Now, in the course of electron diffraction investigations of the action of a number of aqueous heavy metal salts upon a number of sulphide mineral surfaces3, cadmium sulphide in single-crystal orientation has been obtained on a cleavage face of galena (sodium chloride-type cubic ; cleavage, {001}) exposed to an acidic cadmium salt solution. The function of galena in this surface reaction is supposed to lie, first, in supplying sulphur ions to the solution by dissolving, leading to the precipitation of cadmium sulphide, and, secondly, in assigning an epitaxy to the precipitate without modifying its nature. Electron diffraction reflexion methods were used to discriminate between the two modifications of the precipitate. The results are summarized below.