Showing papers on "Transverse plane published in 1974"

Multipole expansions and plane wave representations of the electromagnetic field

Abstract: A new and conceptually simple derivation is presented of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge‐current distribution. The derivation is obtained with the help of a generalized plane wave representation (known also as the angular spectrum representation) of the field. This representation contains both ordinary plane waves, and plane waves that decay exponentially in amplitude as the wave is propagated. The analysis reveals an intimate relationship between the generalized plane wave representation and the multipole expansion of the field and leads to a number of new results. In particular, new expressions are obtained for the electric and magnetic multipole moments in terms of certain components of the spatial Fourier transform of the transverse part of the current distribution. It is shown further that the electromagnetic field at all points outside a sphere that contains the charge‐current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern.

Elastic waves in a fiber-reinforced composite

Abstract: T he propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.

Temperature fluctuations in the plane turbulent wake

Abstract: Results are presented of temperature measurements made in the slightly heated, plane turbulent wake at stations 400 and 500 diam downstream from a heated cylinder at a Reynolds number of 2800. The results include transverse distributions of the first four moments of the temperature obtained using both conventional and conditional sampling and averaging techniques, the downstream distribution of the root mean square temperature fluctuations on the wake centerline and the probability density function of the temperature. Additionally, there are obtained, as a function of distance from the interface, temperature moments which indicate that there is a definite thermal structure associated with the interface.

Electromagnetic fields in spatially dispersive media

Abstract: The structure of the electromagnetic field in a spatially dispersive model medium occupying a plane parallel slab is obtained, free of several customary ad hoc assumptions made in other theories. The model medium is characterized by a dielectric response function appropriate to the neighborhood of an isolated-exciton transition frequency. The exact mode expansion for the electromagnetic field in the slab is derived and it is found that, unlike in the case of an unbounded medium, a single plane wave cannot be generated in the slab. An elementary solution (a single mode) is found to consist, in general, of six plane waves (four transverse and two longitudinal ones), coupled by two linear relations. These relations are shown to be equivalent to two nonlocal boundary conditions (of the form encountered in connection with the Ewald-Oseen extinction theorem in molecular optics), which the nonlocal contribution to the induced polarization must satisfy on the faces of the slab. This result resolves a long-standing controversy about the nature of the so-called additional boundary conditions that are generally believed to be required for solving problems of interaction of an electromagnetic field with a spatially dispersive medium. The results are applied to the problem of refraction and reflection on a spatially dispersive model medium occupying a half-space and a generalization of the classic formulas of Fresnel are obtained. The behavior of the reflected and transmitted waves as functions of the angle of incidence and of the frequency are illustrated by several figures. Our results are shown to differ from those obtained by Pekar in a well-known paper. The difference is traced to the nature of the additional boundary conditions postulated by Pekar; they are found to be inconsistent with the additional boundary conditions that we derive as an exact consequence of Maxwell's theory. Comparisons with several other theories, especially with those of Sein and Birman and of Maradudin and Mills are also made.

Three-Dimensional Turbulent Wall Jets

Abstract: Experiments on three-dimensional turbulent bluff wall jets originating from circular, elliptic, square, rectangular, and equilateral triangular nozzles have shown that in the region of fully-developed flow, the distribution of the axial velocity in the central as well as transverse planes is similar. The velocity scale varies inversely with the axial distance whereas the length scales vary linearly with the axial distance from the respective virtual origins. The boundary shear stress in the center line has been measured and correlated. The square root of the area of the nozzle serves as a convenient length scale in correlating the data for the nozzles of different shapes.

Angulated views in the sagittal plane for improved accuracy of cinecoronary angiography.

Abstract: It has been a standard practice during selective coronary angiography to obtain multiple angulated views of the coronary vessels in a single transverse plane.These views usually provide an excellent definition of the longitudinally oriented right coronary artery and middle and distal segments of the left coronary artery. However, the proximal branches of the left coronary artery are more transversely oriented and can be parallel to the axis of the x-ray beam in this plane of rotation. This results not infrequently in superimpositions and incomplete tangential views of these segments. Therefore, stenoses in these areas can be overlooked or underestimated.We have found that these difficulties can be overcome, in most instances, by the systematic use of additional views in a sagittal plane, angulated approximately 25° either in a cranial or caudal direction or both.

Transverse vibrations of double‐tapered cantilever beams with end support and with end mass

Abstract: The free vibrations of a double‐tapered cantilever beam with (1) end support and (2) end mass have been investigated using the Bernoulli‐Euler equation. The beam was tapered linearly in the horizontal and in the vertical planes simultaneously with the taper ratio in the horizontal plane equal to that in the vertical plane. A table is presented for the first case from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. A chart, plotted from this table, shows the effect of taper ratio on the various harmonics. For the second case, a table and resulting charts show the effect of taper ratio and ratio of end mass to beam mass on the fundamental frequency and higher harmonies. Although previously presented, the case of the beam with free end is also included for purposes of comparison.

Transverse Compressive Moduli and Yield Behavior of Some Orthotropic, High-Modulus Filaments

Abstract: An account is given of the experimental determination of the transverse elastic moduli and yield behavior of some commercially available organic and graphite high-modulus filaments. The experimental technique involves transverse compression of single cylindrical filaments between two parallel flat platens and concurrent measurement of the platen- relative displacements and contact forces on the filaments. A theoretical discussion of the transverse compressional behavior of a linear elastic, homogeneous, orthotropic cylinder is presented. Using the theoretical results and the trans verse load-displacement measurements, a technique is developed for calculating the elastic moduli and maximum shear stresses at yield or fracture.

Combined dual scatter, local oscillator laser doppler velocimeter

Abstract: A laser Doppler velocimeter is described which is capable of effectively measuring two different velocity components of a fluid simultaneously. Such a velocimeter includes a pair of coherent beams of laser light which are focused to an intersection point through which flow particles within the fluid whose velocity is to be measured. Both beams are plane polarized with the plane of polarization of one being rotated normally with respect to the other, with the result that the scattered radiation is separable into two different beams respectively corresponding to the two incident beams. Such scattered radiation is Doppler shifted by the moving particles and is collected for conventionally providing a measurement of the velocity of any particle flowing through the intersection point on a path which is generally transverse thereto. Moreover, the wavelength of the light scattered by the particles from one of the beams is compared to the wavelength of such beam prior to it being Doppler shifted by the moving particles. This comparison provides a measurement of another component of the particle velocity, which measurement can be combined with the first measurement to provide a resultant velocity in a two-dimensional reference frame.

Reflection spectroscopy on monoclinic crystals

Abstract: The properties of the dielectric tensor of a monoclinic crystal are reviewed and the nature of transverse excitations is pointed out. Reflection equations for normal incidence on the (010) plane and (001) plane are presented, by use of which full information on all tensor components may be obtained from reflection measurements and Kramers- Kronig analysis. A reflection equation for oblique incidence on faces ( h 1 , O, h 3 ) with plane of incidence (010) and transverse magnetic polarization allows the comparison of reflectance spectra calculated from the dielectric tensor components with respective experimental spectra. Simple model calculations related to exciton structures in molecular crystals and quasi one-dimensional materials are displayed.

Inelastic neutron scattering in orthorhombic KNbO3

Abstract: Inelastic neutron scattering measurements on single-domain orthorhombic KNbO3 at room temperature show no evidence of overdamped scattering, in contrast with previous neutron results in the cubic phase. As in the case of KTaO3, the observed diffuse x-ray planes are shown to correspond to a highly anisotropic transverse acoustic branch with an unusually flat dispersion in the 'soft' plane. In addition, a well defined optic branch with a polarization related to the orthorhombic-rhombohedral phase transition is seen to become soft as q to 0 in the soft plane. A mode-eigenvector determination confirms the x-ray result that essentially only one atom (niobium) moves in the flat transverse acoustic mode. The connection with other experimental results and with the independent chain model is discussed.

Transverse coupling in fiber optics part III: Bending losses

Abstract: A general method is proposed to evaluate the radiation loss of bent open waveguides. This method consists in evaluating the coupling between the waveguide mode and the whispering-gallery modes that can be associated with the surrounding medium. The expression obtained for a reactive surface coincides with a previous result by Miller and Talanov.1 We investigate in detail the radiation loss of the fundamental (HE 11 ) mode of a dielectric rod coupled to a slab. This arrangement, described in Part II of this article series,2 provides a useful mode-selection technique. The radiation loss is given by a simple closed-form expression. We find that for a wavelength of 1 µm and a rod radius of 5 µm in physical contact with the slab, the bending loss is less than 1 dB/km if the radius of curvature, in the plane of the slab, exceeds 22 mm.

Hall effects in Gd-Co sputtered films

Abstract: Gd-Co films which have uniaxial magnetic anisotropy perpendicular to the film plane are prepared by the rf-sputtering technique. The transverse Hall effect and the planar Hall effect are studied on these films. Results obtained show that the transverse Hall effect is much larger than the planar one in these films. It is also found that the extraordinary Hall effect plays a dominant role in the transverse Hall effect. At the compensation temperature the polarity of the Hall voltage is reversed. The hysteresis loop of the Hall characteristic corresponds to the M-H loop observed by the Kerr magneto-optic effect.

Effects of Transverse Normal and Shear Strains in Orthotropic Shells

Abstract: Introduction P and shell structures in missile, space, and nuclear applications are often subjected to severe operational conditions. Classical methods of analysis based on the Kirchhoff-Love (K-L) hypothesis (implying neglect of transverse shear deformation and transverse normal stress) may not be applicable in such cases. This is especially true for certain composite and refractory materials which show a high degree of anisotropy in physical and mechanical properties. Typical of such materials is pyrolytic graphite (PG), perhaps the best known of the many pyrolytic refractory materials. Noteworthy among its unusual properties are the following: 1 ) PG is transversely isotropic. 2) The ratio of in-plane Young's modulus to transverse shear modulus (E/G\3) for PG varies between 20-50, as compared to E/G of 2.6 for an isotropic material with v = 0.3. 3) The ratio of transverse to in-plane thermal expansion coefficients (a33/an) varies approximately between 10 and 30. 4) The in-plane Poisson's ratio for PG is negative (v = 0.21) while the transverse ratio (v13 = 0.90-1.0) is quite high. The purpose of the present Note is to illustrate the significance of transverse shear, normal stress effects, and edge conditions on the stress and displacement computations for thin shells subjected to thermal loading and also to point out the hazards of employing classical shell theories for analysis of structures of pyrolytic graphite-type materials.

Analytical expressions for the positions of the longitudinal and transverse resonances in radio-frequency spectroscopy

Abstract: Exact equations determining the positions of the longitudinal and transverse magnetic resonances of a doublet are derived. These equations are simply related. Analytical expressions for the Bloch-Siegert shift and the first three transverse resonances are given which apply over the whole range of RF field strengths with 1% accuracy. The expressions for the three quantum resonances are correct to 3%.

Transverse dispersion in oscillatory channel flow

Abstract: An analysis of published data on dye dispersion in homogeneous esturies shows that the dimensionless transverse dispersion coefficient is large compared with results in steady flow in straight channels. The hypothesis is made that transverse currents of three kinds are responsible for the large coefficients. The results of laboratory tests with oscillatory flow in meandering channels are described. Point injections of dye and subsequent measurements of the dye cloud are made. These results support the hypothesis that the transverse currents cause the large transverse dispersion coefficients. The results suggest that the spiral secondary currents associated with the channel meanders are the principal reason for the large coefficients.

Transverse Dispersion in Oscillatory Channel Flow

Abstract: An analysis of published data on dye dispersion in homogeneous estuaries shows that the dimensionless transverse dispersion coefficient is large compared with results in steady flow in straight channels. The hypothesis is made that transverse currents of three kinds are responsible for the large coefficients. The results of laboratory tests with oscillatory flow in meandering channels are described. Point injections of dye and subsequent measurements of the dye cloud are made. These results support the hypothesis that the transverse currents cause the large transverse dispersion coefficients. The results suggest that the spiral secondary currents associated with the channel meanders are the principal reason for the large coefficients.

Cyclic behaviour of exterior reinforced concrete beam-column joints

Abstract: This paper is concerned with the experimental behaviour of beam-column joints of reinforced concrete frames with low axial load when subjected to high intensity cyclic loading such as occurs during major earthquakes. An experimental program was conducted to investigate the behaviour of the external joints of two storey buildings. The parameter varied was the effect on the joint of the addition of transverse beam stubs. The amount of transverse hooping, as specified by the present design code was unchanged for units with and without transverse beams. Both units were subjected to the same program of static cyclic loading and the experimental moment-curvature characteristics are compared. The unit with transverse intersecting beams formed a plastic hinge in the main beam while the unit without intersecting beams failed within the joint region.

Cooling device for tubular sheeting

Abstract: The cooling device consists of a plurality of cooling elements which are arranged in such a manner that they surround the tubular sheeting without interspace. Cooling elements with plane inner surface alternate with cooling elements with curved inner surface, the plane surfaces and the projections of the curved surfaces each have the shape of a regular trapezoid. The cooling elements can be adjusted to the diameter of the tubular sheeting in transverse as well as in oblique direction with respect to the axis of the hollow space formed by the cooling elements.

Turbulent spectral broadening of backscattered acoustic pulses

Abstract: The analysis studies the broadening of the frequency spectrum of an acoustic plane‐wave pulse backscattered into a finite‐angle receiver by the action of a transverse mean wind which moves turbulent velocity and temperature fluctuations through the beam. The results include the frequency spectrum I(k) of the acoustic pressure as a function of wavenumber and the spectral equivalent width b, as a function of mean transverse wind speed and receiver aperture. For broad beams, both temperature and velocity fluctuations contribute to the apparent 180°‐backscatter intensity, and the contributing eddy scales vary from λ/2 to λ/√2. Again for broad beams and for typical experimental parameters for atmospheric echosondes, the broadening effects of mean transverse wind in the scattering volume outweigh the broadening effects of turbulence trransported by a mean transverse wind during propagation to the scattering volume. However, as the receiver beam angle decreases, the spectral broadening drops to zero, regardless of mean wind. Figures are included to show the effects of wind broadening for the case of intermediate receiver beam angles.The analysis studies the broadening of the frequency spectrum of an acoustic plane‐wave pulse backscattered into a finite‐angle receiver by the action of a transverse mean wind which moves turbulent velocity and temperature fluctuations through the beam. The results include the frequency spectrum I(k) of the acoustic pressure as a function of wavenumber and the spectral equivalent width b, as a function of mean transverse wind speed and receiver aperture. For broad beams, both temperature and velocity fluctuations contribute to the apparent 180°‐backscatter intensity, and the contributing eddy scales vary from λ/2 to λ/√2. Again for broad beams and for typical experimental parameters for atmospheric echosondes, the broadening effects of mean transverse wind in the scattering volume outweigh the broadening effects of turbulence trransported by a mean transverse wind during propagation to the scattering volume. However, as the receiver beam angle decreases, the spectral broadening drops to zero, regardless ...

Tool for edging around sprinkler heads

Abstract: A lawn edger, normally having a flat blade driven in a vertical plane for edging the perimeter of a lawn and in a horizontal plane for trimming, is provided with a U-shaped blade having a transverse section which rotates in a plane parallel to the plane of rotation of the flat blade, and end sections perpendicular to the transverse section. When the transverse section is rotating in a horizontal plane over a sprinkler head, the leading edges of the end sections cut vertically into the grass and root structure. A segment of each end section trailing and leading edge thereof is bent inwardly towards the axis of rotation. The end segments break up the cut grass and root structure, and propel the debris up and out of the circular area being cut around a sprinkler head.

Asymmetric focusing of a laser beam in TEM 01 doughnut mode in a nonlinear dielectric

Abstract: We have studied the self-focusing/defocusing of a laser beam in a nonlinear dielectric when the laser is operating in the TEM01 doughnut mode. The cylindrical asymmetry of the irradiance distribution increases inside the medium; the power gets concentrated around the points of maximum irradiance. The maximum irradiance in different directions (in a plane transverse to the direction of propagation) occurs at different values of r, the distance from the z axis. The polar representation of maximum irradiance in the transverse plane turns out to be a figure of eight.

Rotating-anode x-ray tube

Abstract: A rotating anode for an X-ray tube is constructed with a broad rim on to which the radiation - exciting electron beam is focused from a direction perpendicular to the axis of rotation. In order to distribute the thermal loading over the surface of the rim a transverse scanning motion is applied to the electron beam. Viewing the source conventionally from a direction nearly parallel to the axis of rotation the scanning spot is required to appear stationary and this is achieved by forming the surface of the anode rim in a uniform pattern of transverse channels. The scanning waveform must conform generally to the cross-section of the channels and the frequency and phase of the scanning motion must bear a defined relationship to the rate of rotation of the channel pattern.

Electrically pumped, solid-state distributed feedback laser with particular grating spacing

Abstract: A distributed feedback, (DFB) electrically pumped diode laser in which the spacing of the periodic structure within the diode is selected to optimize the interaction between the periodic structure and the electromagnetic waves in the diode laser. The degree to which the waves interact with the periodic structure is described mathematically by a coupling constant K, with larger values of K corresponding to lower gains required to produce laser operation. It is shown that in DFB diode lasers higher order transverse modes have a higher coupling constant K with the periodic structure than does the lowest order transverse mode and thus the higher order transverse modes will lase more easily than the lowest order transverse mode.

Pulse spreading in multimode, planar, optical fibers

Abstract: A dielectric slab can keep optical beams confined transversely in its plane if it is tapered, with the slab thickness having a maximum along some straight line. When the square of the local wave number of the slab (k2) is a quadratic function of the transverse coordinate (y), the rays in the plane of the slab are sinusoids whose optical length is almost independent of the amplitude. For thin slabs (2d « λ) as well as for thick slabs (2d » λ), pulse spreading is large because the ratio of the local phase to group velocity is strongly dependent on the distance (y) from axis. We show that pulse spreading is almost negligible, however, if the thickness of the slab is properly chosen. For example, if the slab thickness on axis is 2.5 micrometers and the refractive index of the slab is 1 percent higher than that of the surrounding medium, pulse spreading is only 0.05 nanosecond per kilometer at a wavelength of 1 micrometer. Pulses in clad fibers having the same width (0.2 millimeter) and carrying the same number of modes (15) spread 50 times faster. Splicing and matching to injection lasers may be easier with planar fibers than with conventional fibers. Low-dispersion planar fibers are therefore attractive when used in conjunction with sources that are multimoded in one dimension. Closed-form expressions are given for square-law and linear-law profiles.

Length adjustable plank

Abstract: A length adjustable plank comprising at least two parts longitudinally adjustable relative to each other, each including two parallel longitudinal beams constituting profile rods, and forming a longitudinal guide, and transverse beams forming a standing surface covering the longitudinal beams and connecting the latter to each other. The longitudinal beams of one part are guided between the longitudinal beams of the other part, and the length of the transverse beams on top of the outer lying longitudinal beams equals the width of the plank, whereas those on top of the inner lying longitudinal beams are somewhat smaller in length than the open spacing of the outer lying longitudinal beams. A fastening device secures the inner lying longitudinal beams in the use condition such that the respective transverse beams of both parts over the inner and outer lying longitudinal beams, respectively, mesh with each other in the manner that the upper surfaces of the transverse beams lie substantially in the same plane.