Showing papers on "Transverse plane published in 1986"

An analysis of doubly rotated quartz resonators utilizing essentially thickness modes with transverse variation

Abstract: Closed‐form asymptotic expressions for the frequency–wavenumber dispersion relations in doubly rotated quartz plates vibrating in the vicinity of the odd pure thickness frequencies are derived from the equations of linear piezoelectricity and the associated boundary conditions on the major surfaces. The usual assumptions of small piezoelectric coupling and small wavenumbers along the plate are made and it is supposed that the pure thickness frequencies are sufficiently different that one pure thickness wave is dominant at a time. In the treatment the mechanical displacement is decomposed along the eigenvector triad of the pure thickness solution to facilitate the asymptotic analysis. The fact that the wavenumbers along the plate are restricted to be small significantly reduces the complexity of the equations without neglecting any transformed elastic constants. The resulting asymptotic dispersion equation enables the construction of a scalar differential equation describing the transverse behavior of essentially thickness modes of vibration in doubly rotated quartz plates. The scalar equation is applied in the analysis of both trapped energy resonators with rectangular electrodes and contoured crystal resonators using established procedures. In particular, calculations performed for the contoured SC cut and a number of other doubly rotated orientations are shown to be in excellent agreement with experiment. Since the differential equation for each harmonic family depends on the order of the harmonic and in the general doubly rotated case contains mixed derivatives in the plane of the plate, a different transformation is required for each harmonic family to obtain the coordinate system in which the mixed derivatives do not appear and, hence, the equation is separable. An interesting consequence of this transformation is that since the nodal planes of the anharmonics of each harmonic family of the contoured SC‐cut quartz resonator are oriented along the transformed coordinate system for that harmonic family, they are oriented differently for each harmonic family.

Errors in the measurements of T2 using multiple-echo MRI techniques. I. Effects of radiofrequency pulse imperfections.

Abstract: In principle, multiple-echo magnetic resonance imaging (MRI) can be used to estimate the spin-spin relaxation time, T2, which can then be used for quantitative tissue characterization. Although multiple echoes can be used to enhance the signal-to-noise ratio in an image, by echo addition, rf pulse imperfections modify the echo amplitudes resulting in significant errors in the estimate of T2. Imperfect 180 degree pulses do not completely invert the transverse magnetization so that the magnitude of the transverse component is reduced and a longitudinal component is generated. Successive application of such imperfect pulses generates many components that interact in a complex manner. The amplitudes of successive echoes are affected whenever the transverse components refocus, whereas the longitudinal components may be rotated into the transverse plane by subsequent pulses and may often add to the image signal or give rise to an image artifact. These effects have been analyzed theoretically and have been demonstrated for a wide range of rf pulse imperfections using both simple and composite pulses, through computer simulations based on the numerical solution of the Bloch equations. The theoretical and simulation results have been substantiated through experiments performed on a mineral oil phantom using a resistive prototype MR scanner operating at 6.35 MHz. In this paper we report the effects of improper pulse amplitude or duration for nonselective rf pulses on resonance. We separately describe the other types of imperfections caused by off-resonance effects and the use of selective pulses.

Meander flow model. i: development

Abstract: A model for simulating the flow and bed topography in a meandering alluvial channel is developed. The basis is a solution to the equations for conservation of mass and momentum and for lateral stability of the streambed. The bed‐stability equation is a transverse force balance for bed‐sediment particles relating the transverse bed slope to primary flow variables. The main controlling parameters are the channel's width‐depth ratio, radius‐width ratio, resistance characteristics (or gradient), and sediment Froude number. An innovative feature is the use of a simple mass‐flux balance (mass conservation) to link the equation for bed stability to the momentum equations. The mass‐flux balance relates the net lateral transport of flow volume to the streamwise variation of transverse bed slope. Thereby, the equations governing the secondary‐current velocity and the transverse bed slope become those of a damped oscillating system subjected to a driving force, the change in channel curvature. The model is tested wi...

Two-dimensional topographic responses in magnetotellurics modeled using finite elements

Abstract: We simulate the magnetotelluric response to two‐dimensional earth topography using finite elements. Linear interpolation of the secondary field parallel to strike over triangular elements allows accurate modeling of inclined resistivity boundaries, including topographic surfaces. To avoid discontinuities in field derivatives or resistivity, care must be taken that the nodal values of the field parallal to strike used to obtain the auxiliary secondary fields are kept within uniform earth media. The nodal locations may be shifted, but the derivatives still are evaluated at the field points of interest. Correct values may be returned at gentle breaks in slope as well as along straight surfaces. The finite‐element program is verified by comparison with the analytic transverse magnetic response of a hemicylindrical depression and with Rayleigh scattering and transmission surface results for transverse electric and transverse magnetic polarization. Agreement with the other methods generally is excellent, with t...

Anisotropy of transverse sound in the heavy fermion superconductor UPt3.

Abstract: We report the first measurements of the attenuation of ultrasound in the basal plane of superconducting UPt3. Transverse sound propagating along the b axis shows a marked anisotropy in its temperature dependence when the polarization is rotated in and out of the basal plane. For polarization in the basal plane the attenuation varies linearly with temperature down to 35 mK and the slope scales as the square of the frequency. Our results appear to indicate the presence of an additional attenuation mechanism when compared with recent theories of anisotropic superconductors in the dirty limit.

Thermally Induced Transverse Cracking in Graphite-Epoxy Cross-Ply Laminates:

Abstract: Thermally induced transverse cracking in T300/5208 graphite-epoxy cross-ply laminates was investigated experimentally and theoretically. The six laminate configurations studied were: 0/90(3)s, 0(2)/90(2)s, 0(3)/90s, 90/0(3)s, 90(2)/0(2)s, and 90(3)/0s. The thermal load required to initiate transverse cracking was determined experimentally and compared to a theoretical prediction. Experimental results for the accumulation of transverse cracks under cyclic thermal loading between - 250 and 250 F for up to 500 thermal cycles are presented. The calculated in situ transverse-lamina strength was determined to be at least 1.9 times the unidirectional-lamina transverse tensile strength. All laminate configurations exhibited an increase in crack density with increasing thermal cycles.

TE and TM Modes of Some Triangular Cross-Section Waveguides Using Superposition of Plane Waves (Short Paper)

Abstract: Exact transverse electric and magnetic mode solutions of four triangular cross-section waveguides have been found via a new general method using Snell's law and superposition of plane waves. This paper presents results for 1) equilateral, 2) 30°, 30°, 120°, 3) isosceles right, and 4) 30°, 60° right triangular waveguides. The electric and magnetic field solutions form finite sums of separable rectangular harmonics and are the only waveguides of triangular cross section for which such solutions have been found.

Thin channel split flow continuous equilibrium process and apparatus for particle fractionation

Abstract: A thin channel split flow process for particle fractionation which effects a rapid and efficient separation of the particles comprising introducing a stream of fluid containing the particles to be separated into the inlet end of a thin enclosed channel whose transverse dimension is very small, applying a special field or gradient or combination thereof transversely across the thin dimension of the channel to create a driving force a component of which is perpendicular to the main flow plane, adjusting the flow rate to achieve laminar flow conditions throughout the channel to allow the particles under the influence of the field/gradient to segregate into different stream laminae as they approach different transverse equilibrium positions, splitting the channel stream at the outlet end into substreams containing different separated fractions of the particles in the initial mixture, recovering the substream and thereby recovering the separated fractions.

Adjustable barbell bar with rotating handles

Abstract: A barbell is disclosed having a pair of handles disposed along the length thereof equidistant from the ends of the barbell. The handles are rotatable through an axis transverse to the long axis of the plane of the barbell, so that the handle can be rotated to position comfortable to a user's arms for performing various exercises. The barbell is also optionally adjustable in length so that the handles can be positioned at a predetermined distance from each other.

Normal shoulder: MR imaging.

Abstract: Relatively poor spatial resolution has been obtained in magnetic resonance (MR) imaging of the shoulder because the shoulder can only be placed in the periphery of the magnetic field. The authors have devised an anatomically shaped surface coil that enables MR to demonstrate normal shoulder anatomy in different planes with high spatial resolution. In the axial plane, anatomy analogous to that seen on computed tomographic (CT) scans can be demonstrated. Variations in scapular position (produced by patient positioning) may make reproducibility of sagittal and coronal plane images difficult by changing the relationship of the plane to the shoulder anatomy. Oblique planes, for which the angle is chosen from the axial image, have the advantage of easy reproducibility. Obliquely oriented structures and relationships are best seen in oblique plane images and can be evaluated in detail.

Distributed feedback type semiconductor laser

Abstract: A distributed-feedback type semiconductor laser device having an active layer arranged between a pair of clad layers is provided with a stripe-shaped distributed-feedback mechanism, for example, having the configuration of a diffraction grating, and dummy regions of the same configuration as the distributed feedback mechanism arranged at opposite sides of the latter and being spaced from the distributor-feedback mechanism by relatively narrow plane regions, with the result that the distributed-feedback mechanism can be formed as a narrow stripe with good reproducibility so that it is possible to provide the semiconductor laser device with a long useful life and with the capability of operating in single longitudinal and transverse modes.

Topological constraints on quasicrystal transformations

Abstract: The notion of a perfect crystal in d-dimensional physical space may be generalized to the ``deterministic'' quasicrystal generated by a cut by a d-dimensional ``physical'' plane through a periodic array of (D-d)-dimensional hypersurfaces in a D-dimensional space. (The quasicrystal tilings generated by projection from a D-dimensional lattice are a special case.) When these surfaces are smooth, and we impose a noncrystallographic symmetry (e.g., a fivefold axis), then they must intersect, which is unphysical. We explore the topology of the transformations induced on these structures by transverse displacements of the physical plane, which correspond to the phase degree of freedom in incommensurate structures. For the projected structures, the atoms undergo a nontrivial permutation when the physical plane is transported in a small closed loop about a vertex of the D-dimensional lattice. We see no way to build a deterministic model for the quasicrystals of physical interest in which the individual atoms move continuously in response to transverse displacements of the physical plane. Thus the conventional spontaneously broken continuous symmetry arguments for a hydrodynamic ``phason'' mode no longer apply. We suggest that real quasicrystals are nondeterministic and speculate about possible glassy properties of these materials.

Passive optical self-limiter using laser-induced axially asymmetric and symmetric transverse self-phase modulations in nematic liquid crystals.

Abstract: Using low-power cw lasers in conjunction with the symmetric and asymmetric nonlinear transverse self-phase modulation imparted by a nematic liquid-crystal film, we have demonstrated two forms of transverse intensity-switching and power-limiting operations. Applications to high-power nanosecond laser are also feasible.

Simulation of contaminant plumes with large dispersive contrast: Evaluation of alternating direction Galerkin Models

Abstract: The evolution of narrow, sharply defined contaminant plumes, corresponding in shape to those often observed in the field, is examined. It is shown that the transverse dispersion mechanism consistent with such shapes can be as low as of the order of molecular diffusion and that dispersivity contrasts of as much as 4 orders of magnitude are possible. Even at the lowest physically realistic values of transverse dispersion parameters, however, transverse mass spreading is capable of significantly retarding the advance of the plume front. The principal direction and alternating direction Galerkin models together are found to be capable of handling all cases of dispersive contrast including those with dispersivity ratio of infinity. The models are formulated in curvilinear coordinates with certain restrictions on the element deformation. A three-way comparison between principal direction, alternating direction Galerkin, and conventional finite element models is performed with respect to accuracy and efficiency. The effects of longitudinal and transverse numerical dispersion occuring in the various models are examined and related to the discretization. Visual indications of the presence of numerical error are discussed.

TM and TE scattering by a dielectric/ferrite cylinder in the presence of a half-plane

Abstract: An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane

An anisotropic turbulence model for wave propagation near the surface of the Earth

Abstract: A model of turbulent anisotropy of refractive index fluctuations near the surface of the earth is presented and used to calculate the mutual coherence function (MCF) of a propagating plane wave it is found that there are measurable differences in the transverse (horizontal and vertical) MCF's thus making possible active remote sensing of turbulent anisotropy

Screen cloth for the wet end of a paper-making machine

Abstract: 1. A clothing for the sheet-forming section of a papermaking machine, said clothing comprising an upper and a lower layer (1, 2) of transverse threads (3, 4, 5) interwoven with longitudinal threads (6), within each weave repeat each longitudinal thread (6) being interwoven two times with the upper layer (1) of transverse threads (3, 4), the transverse threads (3, 4) of the upper layer (1) and the longitudinal threads (6) forming crimps (7, 8, 9) disposed in a plane, the paper plane (10), and the crimps (7) tangential to the paper plane (10) of first transverse threads (3) of the upper layer (1) being supported in a crimp saddle of the longitudinal threads (6), and the crimps (8) tangential to the paper plane of second transverse threads (4) of the upper layer (1) being supported by two adjacent longitudinal threads (6) one of which ascends from the fabric interior to the paper plane (10), while the other one descends from the paper plane (10) into the fabric interior characterized in that the first transverse threads (3) and the second transverse threads (4) are arranged in alternating sequence.

Thermally insulated window sash construction for a casement window

Abstract: A window sash member includes first and second generally parallel sidewalls. First and second spaced, generally parallel transverse walls, extending between and oriented generally perpendicular to the first and second sidewalls, connect the first and second sidewalls to define a first hollow chamber. A third transverse wall, located without the first hollow chamber adjacent to and generally parallel to the first transverse wall, extends from the first transverse wall and terminates short of the second sidewall. A first interior wall, oriented generally parallel to the first sidewall, extends from the third transverse wall to the first transverse wall to define a second hollow chamber. A fourth transverse wall, located without the first hollow chamber adjacent to and generally parallel to the second transverse wall, extends from the first sidewall and terminates short of the second sidewall. A second interior wall, oriented generally parallel to the second sidewall, extends from the fourth transverse wall to the second transverse wall to define a third hollow chamber. A window sash employs at least one of such sash members.

Optically non-linear materials and thin films incorporating such materials

Abstract: A multi-layer Langmuir-Blodgett film having non-linear optical properties is described. Alternate layers of the film are composed of first and second elongate chromophore molecules extending transverse to the plane of the film in a Y-configuration. The molecules are synthesised so that when deposited in a Y-configuration they are non-centrosymmetric and therefore exhibit significant optical nonlinearity.

An anisotropic turbulence model for wave propagation near the surface of the earth

Abstract: A model of turbulent anisotropy of refractive index fluctuations near the surface of the earth is presented and used to calculate the mutual coherence function (MCF) of a propagating plane wave. it is found that there are measurable differences in the transverse (horizontal and vertical) MCF's thus making possible active remote sensing of turbulent anisotropy.

A statistical analysis on the reliability of the proximal articular set angle.

Abstract: The authors investigated the statistical relationship and significance between the transverse and sagittal plane proximal articular set angles both radiographically and intraoperatively. The analysis revealed a highly significant difference between the means of the respective measurements. Although the radiographic and intraoperative findings were found to be related for the transverse plane proximal articular set angle, the transverse plane PASA was approximately 7 degrees greater when measured intraoperatively. The concept of a sagittal plane PASA was also introduced. The significance of accurate measurements in the surgical correction of hallux valgus was also examined.

Accurate reconstruction of the refractive-index profile of fibers and preform rods from transverse interferometric data

Abstract: A closed-form strict correlation between the interference fringe shift and the ray deflection function is derived which enables an accurate determination of the refractive-index distribution in fibers, preform rods, and GRIN-rod lenses to be performed by transverse interferometric methods. The refraction of the probing rays as well as the defocusing effect are entirely compensated and the immersion-object index mismatch is also taken into account. The comprehensive analysis presented proves that nondestructive transverse interferometry can be utilized as a reliable tool in the examination of both GRIN and step-index fibers and rods with low as well as with high numerical apertures.

Average transverse momentum and energy density in high-energy nucleus-nucleus collisions

Abstract: Emulsion chambers were used to measure the transverse momenta of photons or pi(0) mesons produced in high-energy cosmic-ray nucleus-nucleus collisions. A group of events having large average transverse momenta has been found which apparently exceeds the expected limiting values. Analysis of the events at early interaction times, of the order of 1 fm/c, indicates that the observed transverse momentum increases with both rapidity density and energy density.

CARS signals: phase matching, transverse modes, and optical damage effects.

Abstract: The transverse modes of the lasers used in coherent anti-Stokes Raman spectroscopy (CARS) affect the signal strength, spatial resolution, and noise. A general formulation for CARS signal calculations with arbitrary TEM modes and 3-D phase matching is presented. Numerical calculations for useful beam geometries are reported and compared with calculations based on simple models. The variation of intensity and phase across a laser beam is shown to have significant effect on the CARS signal strength. The effects of the transverse modes on window damage are discussed. Estimates of CARS signal strengths are presented for nitrogen thermometry near windows.

Thick rectangular plates on an elastic foundation

Abstract: The refined theory for moderately thick plates presented in references is used for the bending of plates on elastic foundations. This theory incorporates the transverse normal strain effect in addition to the transverse shear and normal stress effects. Investigation of various types of fixity of edges involving three boundary conditions is presented. The solution of the governing equations using the Navier and Levy type semi-inverse methods is demonstrated. Results are tabulated for the deflection at the center of a uniformly loaded, simply-supported rectangular plate. Applications of the theory also include an infinite plate with a line load of intensity P. Comparisons are made with the classical plate theory and the corresponding Reissner plate theory. The results show the increasing influence of the transverse normal strain on the plate behavior as the parameters characterizing the influence of the plate thickness, h/a, and the modulus k are increased.