Cylinder Of Elliptic Cross Section Research Articles

Magnetostatic energy of paramagnetic particles in magnetic separators

A series expansion is obtained for the magnetostatic interaction energy of an infinitely long cylinder of arbitrary cross section, uniformly magnetized in a direction perpendicular to its long axis, and a spherical paramagnetic particle, in powers of the radius of the paramagnetic particle. For a cylinder of elliptic cross section magnetized in an arbitrary direction, the first three terms in this series are evaluated explicitly.

Circular oscillations of a cylinder in a viscous fluid

The steady streaming velocity induced by the circular motion of a cylinder of elliptic cross-section in a viscous fluid is considered. The amplitude of this circular motion is supposed small compared with a typical diameter of the cylinder, which maintains a fixed orientation throughout the motion. Outside the Stokes shear-wave layer Reynolds stresses contribute to the induced steady streaming. The outer flow is calculated in the case of large streaming Reynolds numbers for two particular cylinders.

Scattering matrix for elastic waves. II. Application to elliptic cylinders

Using the scattering-matrix approach to elastic wave scattering, numerical results are presented for the scattering of P, SV, and SH waves from a cylinder of elliptic cross section for ratios of minor to major axis ranging from 0.25 to 1.0 and for nondimensional wave numbers in the range 0.1–3.2. Calculations were made for a tungsten cylinder embedded in aluminum and also for a cylindrical cavity in aluminum. The incident waves are taken to be plane waves incident obliquely with respect to the major axis of the ellipse.

Free Convection Boundary Layers on Cylinders of Elliptic Cross Section

Numerical results are presented for free convection boundary layers over horizontal cylinders of elliptic cross section when the major axis is both horizontal and vertical and when the cylinder is isothermal and has constant heat flux. The particular case of a circular cylinder is considered and these results are compared with the various series expansions suggested for solving the equations.

Magnetostatic energy of paramagnetic particles in magnetic separators

A series expansion is obtained for the magnetostatic interaction energy of an infinitely long cylinder of arbitrary cross section, uniformly magnetized in a direction perpendicular to its long axis, and a spherical paramagnetic particle, in powers of the radius of the paramagnetic particle. For a cylinder of elliptic cross section magnetized in an arbitrary direction, the first three terms in this series are evaluated explicitly.

The scattering of electromagnetic radiation from dielectric scatterers

The problem of electromagnetic wave scattering from arbitrarily shaped scatterers recently solved by using an integral equation formulation is extended to treat the case of scattering by infinite cylinders. The method is based on describing the internal field of the scatterer in terms of an independent set of plane wave functions. Numerical stability conditions are satisfied. Numerical results are presented for cylinders of elliptic cross section for two independent incident waves. Results are also given for scattering by three-dimensional spheroidal scatterers of refractive index n0=1.33. The solution presented is applicable for scatterers with size parameter (k0a) from the Rayleigh region (k0a >1) provided for each given scatterer certain matrix elements can be calculated.

Experimental verification of the electromagnetic analogue of a theorem due to Dean

Experimental results are presented which confirm that a metallic cylinder of elliptic cross-section may have zero reflection coefficient to l.s.e. electromagnetic surface waves when the ellipticity is appropriately chosen.

Transverse critical fields of small superconducting elliptical cylinders

Using the Ginzburg-Landau theory the transverse critical field of small (a«ξ0,b»ξ0) cylinders of elliptical cross section has been calculated for an arbitrary angle between the field and the axes of the ellipse. The criterion for second-order phase transitions has been found. While the equations readily reduce to the case of the circular cylinder, they do not reduce to the case of the flat film. The reasons for this are discussed.

Meissner shielding currents and magnetic flux penetration in thin-film superconductors

We have observed the magnetic flux penetration at 4.2 K into superconducting lead films of about 4 µm thickness using a high-resolution magnetooptical technique. The specimens had the shape of small squares or long strips. In increasing magnetic field it was found that magnetic flux starts to penetrate into the bulk of the specimens in the form of flux tubes containing about 60 flux quanta. For the samples with the strip geometry the magnetic fieldH*, at which flux penetration into the bulk sets in, was investigated in the presence of an external electrical currentI along the strip superimposed on the Meissner shielding currents. The fieldH* was found to decrease linearly with increasing transport currentI. The magnetic field near a long superconducting cylinder in the presence of both a transverse applied magnetic field and an applied electrical current parallel to the cylinder axis has been calculated. The calculation is valid for a cylinder of elliptical cross section, which approximates a long, flat strip. The experimental observations for the slope ∂H*/∂I are in good agreement with the calculations.

Aperture radiation from an axially slotted elliptical conducting cylinder using geometrical theory of diffraction

The equatorial radiation pattern of a parallel-plate TEM mode axial slot on an infinite cylinder of elliptical cross section is computed using wedge-diffraction and creeping-wave theory. The wedge-diffracted fields are obtained by the diffraction interaction from a set of infinite wedges approximating the parallel-plate-cylinder geometry. Surface-wave propagation on curved bodies commonly used in scattering is employed for the creeping-wave contribution. The total field in the lit region is approximated using superposition of wedge-diffracted and creeping-wave fields and in the shadow region solely by creeping-wave fields. The computed patterns are compared with experimental results since boundary-value solutions are not readily available. Good agreement between theory and experiment is indicated.

Thermal resistance between two long parallel cylinders of elliptical cross section

It is shown that the problem of determining the thermal resistance between two long parallel cylinders of elliptical cross section can be reduced to the corresponding problem for two infinitely thin parallel bands. The thermal resistance of the system is plotted vs the geometrical dimensions.

Attenuation in a dielectric elliptical cylinder

The problem of the propagation of electromagnetic waves along a dielectric cylinder of elliptical cross section is considered. There exist two dominant waves which possess zero cutoff frequencies. The attenuation characteristics of these dominant waves are analyzed theoretically and experimentally. Good agreements are obtained. It is shown that one of the dominant waves, with its electric fields parallel at the center of the cylinder to the minor axis of the elliptical cylinder, can propagate along a flat dielectric strip with much lower loss than can the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HE_{11}</tex> wave along a circular cylinder having the identical cross-sectional area.

Elliptical Dielectric Waveguides

The problem of electromagnetic wave propagation along a dielectric cylinder of elliptical cross section is considered. Two infinite determinants representing the characteristic equations for the two types of hybrid waves (the HEmne, and the HEmn0 waves) are derived. It is found that there exists two dominant waves which possess zero cutoff frequencies. The characteristic roots of these two dominant waves are computed for various values of eccentricity and relative dielectric constant. Theoretical propagation constants for the dominant waves are verified by experiments.

MEASURED SELF-IMPEDANCE OF A DIPOLE ANTENNA NEAR A CONDUCTING CYLINDER OF ELLIPTICAL CROSS SECTION

This paper presents the results of an experimental investigation of the impedance of an axial dipole antenna located near a conducting cylinder of elliptical cross section. Measurements were carried out for various spacings of the antenna from the cylinder along the major and minor axes, and for four different values of cylinder ellipticity.For a cylinder having a maximum dimension of 0.76 wave length it is found that the impedance (resistive and reactive components) is an oscillating function of the antenna-to-cylinder spacing, having a period of approximately one-half wave length. For spacings greater than one wave length, the impedance is within 5% of the free-space dipole impedance.

Radiation Conductance of Axial and Transverse Slots in Cylinders of Elliptical Cross Section

Expressions for the radiation field of axial and transverse slots in cylinders of elliptical cross-section are derived by a method based on diffraction theory and the principle of reciprocity. Radiation patterns of transverse slots and curves of radiation conductance are presented. It is shown that the radiation conductance is influenced considerably by the degree of curvature of the surface on which the slot is located.

The Patterns of Antennas Located near Cylinders of Elliptical Cross Section

The patterns of small dipole and loop antennas mounted on or near a perfectly conducting cylinder of elliptical cross section are calculated by determining the open-circuit terminal voltages of the antennas when receiving plane waves. The antennas are assumed to be such that they cause negligible distortion of the field when they are open-circuited, thus reducing the problem to that of calculating the diffraction of a plane wave around the cylinder. The results have applications in the design of aircraft antennas and slotted-cylinder antennas.