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The slab-coupled waveguide, consisting of a dielectric rod lying on a slab that in turn covers a substrate, is a multidielectric waveguide that includes such special cases as the single-material fiber, the rib waveguide, and the strip-loaded film guide. These guides have recently become known as potentially useful either for long-distance optical transmission or for integrated optics. Simple, closed-form, approximate solutions have been found to describe the following properties of the guide: number of modes, their field configurations and propagation constants, numerical aperture, requirements for single-mode operation, field penetration in the slab, tolerance to curvature of the guide axis, dispersion, and impulse response.

This paper surveys gas chromatographic methods for making thermodynamic measurements at finite solute concentration. The factors which determine the shape of elution and frontal chromatograms are first described. The retention volume equation is obtained for finite concentration taking into account the sorption effect and curvature of the distribution isotherm. A new and reasonably accurate equation (Equation 20) is then derived for calculation of the isotherm from chromatographic measurements. Comparison is made with an older, much used procedure which is shown to give large errors through neglecting the sorption effect. Experimental results with both accurate and inaccurate procedures are surveyed.

Previously published work on the mechanism of chip curl and on the performance of obstruction and groove type chip formers is examined and new explanations of chip curl and the action of the groove type former are proposed. Experimental evidence is presented which shows that, for a range of materials, when cutting orthogonally with a restricted contact length tool, a chip is formed with no curvature when the length of the zone of sticking friction is equal to the restricted contact length. The results of tests on groove type chip formers indicate that under conditions where the chip does not contact the bottom of the groove, the relationship between chip curl radius, groove geometry and chip thickness can be predicted.

The results of an experimental investigation of the RTD in the low Reynolds number, low Dean number region for helical coils are reported. It is found that, under the conditions of negligible molecular diffusion, for 0·6

An electrostatic hexapole lens is used for the study to correct the image curvature resulting from second order aberration in a mass spectrometer. The mass spectrometer used is a Hitachi RMU-6D double focusing type especially attached a photographic detector. The hexapole lens is located between the electrostatic analyzer and the magnet at the distance 134 mm from the magnet. This lens consists of six stainless steel poles which are 6 mm in diameter, 40 mm long, and the distance from the symmetry axis to the nearest point of the electrodes is 7 mm. When the potentials of ±4.5 V are applied to the poles alternatively, the image curvature can be corrected without any additional effects of in-troduced abrerrations.

This paper is concerned with the limit analysis of curved I-beams made of a rigid perfectly plastic material. After the introduction in Section I, Section II deals with the definition of the problem and the derivation of the yield curve in the space of the bending moment M and axial force N. An experimental verification of the theory is given in Section III, and systematic application to rolled I-beams is described and discussed in Section IV. Section V shows examples of arch problems

Since stress and dislocations are known to affect the performance of GaAs injection lasers, a systematic evaluation of these parameters has been carried out for LPE layers of Ga 1− x Al x As 1− y P y on GaAs substrates. Using an X-ray topographic camera which is also equipped to plot substrate lattice curvature it has been possible to measure room temperature stresses for various values of x with y =0, and for 0 y ≤0.05 with x =0.34. Stress limits at the growth temperature are estimated based on the detection of misfit dislocations. As a result of this study the conditions for room temperature stress-compensated layers can be determined. Also, because of the asymmetric nature of interfacial misfit dislocations, it is possible to simultaneously eliminate those segments of substrate dislocations which have propagated into the LPE layer. The dependence of this phenomenon on layer thickness is specified as well as measurements of asymmetric bending and misfit dislocation arrays.

The use of the b estimator for linear regression on log-normal plots of earthquake recurrence is examined with artificially generated data. The curvature often observed in the data for higher magnitudes may be in part an effect of limiting magnitudes. The estimator gives satisfactory results for data showing curvature and noise (due to too few events), and is preferable to least squares regressions requiring subjective judgements on the quality of data.

Intense relativistic electron beams were propagated around a 180° toroidal sector to study beam dynamics in toroidal fields. The major beam drift under conditions for neutralization of self‐fields was along ‐ R × B and scaled as γZ/Bt, where Z is the propagated distance, Bt the toroidal field, and γ the relativistic factor. This is indicative of curvature and ∇B drifts. Use of conducting walls caused an additional F × B drift around the chamber due to image current forces. Analysis of the distortion of a propagating rectangular beam shows that beam electrons follow field lines. Preliminary experiments on counterstreaming beams show inefficient reflection of beams from opposing diodes. Application of these results to beam injection and confinement in toroidal magnetic fields is discussed.

Low frequency radar scattering data is used for the identification of aircraft. It is shown that such radar data lies on two-dimensional surfaces in n -space. A bilinear approximation for these surfaces is described. Surface intersections using this approximation can be found simply and directly without solving a system of n simultaneous nonlinear equations. This intersection information can be used to show separability and effect feature reduction. The approximation is utilized to construct a modified nearest neighbor algorithm, which is evaluated by computer simulation experiments. These experiments showed a phenomenon of “bias”, where one aircraft data surface is more susceptible to misclassification in the presence of noise than the surface corresponding to another aircraft. This “bias” observed is shown to be related to the surface characteristics of the data surfaces involved, specifically proximity and relative curvature of corresponding points on the two surfaces.

The effects of wave front curvature, wind, and temperature on the determination of the direction of propagation of thunder at an array of microphones is examined, and it is shown that the direction of propagation can be measured at the array with an error of less than ±1° under the following conditions: the wind velocity at the array should be measured with an accuracy of ±1 m/s, the temperature at the array with an accuracy of ±2°C, and the range to the source with an accuracy of ±20%. The positions of the source points on the lightning channel, which represent the total lightning event at that location, are mapped by acoustic ray tracing techniques; this procedure requires information on the temperature and wind velocity as a function of altitude; without this information and in adverse conditions, errors of 10% for high-altitude sources and 25% for sources near the horizon will occur. By using supportive data on wind and temperature profiles all error estimates can be reduced to 5%, which is more than sufficient to do comparative studies of lightning channel structures inside clouds with the macrophysical properties of the clouds.

This paper presents a numerical procedure to calculate the loss of prestress, the strain at centroid, and the curvature in concrete beams prestressed in a number of stages. The loss calculated is caused by instantaneous deformations, relaxation of steel, shrinkage, and creep of concrete. Account is made of the elastic and creep recoveries of concrete and the effect of variation of stress level on the relaxation of steel. Included is an application to find the losses and deflections of a prestressed concrete bridge built by the cantilever method (consecutive segments cast and prestressed in multistages).

Two previously developed ray methods for conformal arrays on surfaces with variable curvature are further systematized and applied to arrays of equispaced identical slits on perfectly conducting parabolic cylindrical surfaces. The two methods differ in their definition of the canonical problems that are fundamental to the scattering process. In the first method, multiple scattering on the smooth cylinder surface accounts for interaction between isolated elements, while in the second, surface rays are defined on a local periodically loaded surface. The first method is valid under quite general conditions and yields reliable numerical results for mutual-coupling coefficients and radiation patterns. The second provides a simple explanation of a variety of coupling and radiation phenomena when the array possesses aspects of periodicity, and it is preferable for numerical calculation of mutual coupling in large arrays. These features are illustrated in detail on a particular example. The results obtained confirm the utility of the ray analysis in furnishing solutions for coupling coefficients and element patterns in conformal arrays, and they also demonstrate the fundamental insight gained by the local periodic-structure approach.

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality.

The formic acid molecule is used as a model for a computational comparison of the Willi‐Wolfsberg curvature parameter (K) method (Type K calculations) and the Johnston‐Bonner‐Wilson method (Type II calculations), both including bond order (N) and barrier curvature (ν1‡ ≠ 0) effects, for calculation of 13C kinetic isotope effects involving reaction coordinate eigenvectors consisting nominally of two nonzero elements. Results obtained by the two methods cover similar ranges of value of calculated k12C/k13C. Reaction coordinate eigenvectors (uncontaminated for Type II results) may involve as much as 20% extraneous displacement in Type K results when ν1‡ ≅ 800 i cm−1; however, the effect on (ν1‡/ν′1‡), the temperature independent factor (TIF) in k12C/k13C, is so small as to be of limited practical significance. The remainder (TDF) of the isotopic rate constant ratio for various combinations of K and N (Type K) or of ν1‡ and N (Type II) can be arranged well into magnitude sequence by invocation of details of t...

It has been experimentally observed that one-inch thick soil-cement slab (fine-grained soil), upon drying from the top face, first deforms with a concave surface at the top and gradually assumes an opposite curvature with convex surface at the top. The latter shape contradicts the classical analysis ofPickett. A theory whereby the doming can be predicted is proposed in this paper.

The generalized field equations for an arbitrary curved and twisted beam in space are presented and discussed. A numerical algorithm is generated from these equations yielding a computer code which is capable of determining the static, dynamic and free vibration characteristics of a non-uniform, non-homogeneous, anisotropic beam which has arbitrary curvature and arbitrary twist. The static portion of this analysis is shown to be directly applicable to the study of force systems delivered by simple and complex orthodontic appliances. Several orthodontic configurations are studied using the subject model. Clinical considerations are discovered as a result of this study.

It is shown that the momentum transfer theorem implies a rough correlation of the diffusion cross section with the slope of the intermolecular potential energy. This is a particular case of the collision Ehrenfest theorem which can be applied in like manner to all of the collision cross sections arising in kinetic theory, thus allowing a qualitative discussion of their dependence on the potential. As an example, relative to the diffusion cross section the viscosity has an increased sensitivity to the curvature of the potential.

The pressure temperature stability of the phase Mn-cordierite hitherto not recorded as a mineral has been determined at temperatures ranging from 400° C up to the melting mainly using standard hydrothermal techniques at the oxygen fugacities provided by the buffering power of the bomb walls. Manganocordierite is a pronounced low-pressure phase with a maximum pressure stability of about 1 kb near 400° C and decreasing pressure limits at higher temperatures. Throughout the temperature range investigated the stable high-pressure breakdown assemblage of Mn-cordierite is spessartine, an Al-silicate, and a SiO2-polymorph. Due to the variable water contents of Mn-cordierite and spessartine there is a pronounced curvature in the negative dP/dT-slope of the requisite upper pressure breakdown curve of Mn-cordierite. Only theoretical deductions were possible concerning the stable hydrous low-temperature breakdown assemblage of Mn-cordierite below about 400° C.

The sliding microtubule model of ciliary motility predicts that cumulative local displacement (Deltal) of doublet microtubules relative to one another occurs only in bent regions of the axoneme. We have now tested this prediction by using the radial spokes which join the A subfiber of each doublet to the central sheath as markers of microtubule alignment to measure sliding displacements directly. Gill cilia from the mussel Elliptio complanatus have radial spokes lying in groups of three which repeat at 860 A along the A subfiber. The spokes are aligned with the two rows of projections along each of the central microtubules that form the central sheath. The projections repeat at 143 A and form a vernier with the radial spokes in the precise ratio of 6 projection repeats to 1 spoke group repeat. In straight regions of the axoneme, either proximal or distal to a bend, the relative position of spoke groups between any two doublets remains constant for the length of that region. However, in bent regions, the position of spoke groups changes systematically so that Deltal (doublet 1 vs. 5) can be seen to accumulate at a maximum of 122 A per successive 860-A spoke repeat. Local contraction of microtubules is absent. In straight regions of the axoneme, the radial spokes lie in either of two basic configurations: (a) the parallel configuration where spokes 1-3 of each group are normal (90 degrees ) to subfiber A, and (b) the tilted spoke 3 configuration where spoke 3 forms an angle (theta) of 9-20 degrees . Since considerable sliding of doublets relative to the central sheath ( approximately 650 A) has usually occurred in these regions, the spokes must be considered, functionally, as detached from the sheath projections. In bent regions of the axoneme, two additional spoke configurations occur where all three spokes of each group are tilted to a maximum of +/- 33 degrees from normal. Since the spoke angles do not lie on radii through the center of bend curvature, and Deltal accumulates in the bend, the spokes must be considered as attached to the sheath when bending occurs. The observed radial spoke configurations strongly imply that there is a precise cycle of spoke detachment-reattachment to the central sheath which we conclude forms the main part of the mechanism converting active interdoublet sliding into local bending.