Infinite Elliptic Cylinder Research Articles

Electromagnetic waves scattering from an infinite elliptical metal cylinder covered by a plasma layer in presence of external magnetic field

In this paper, scattering of the electromagnetic waves from a metal elliptical cylinder covered by a plasma layer is investigated by the Finite Element-Boundary Integral (FE-BI) method. The under study object that can be supposed as an elliptic complex antenna is located in a constant magnetic field. The inner cylinder can be rotated to plasma cover so that they are nonconfocal. Generally, elliptic antennas have azimuthal asymmetry and their response to electromagnetic waves is sensitive to incident angle of landing wave. This effect is more severe in under study antenna due to its geometrical configuration that depends on the rotating angle of the conducting core related to plasma cover. Furthermore, presence of constant magnetic field along the antenna axis causes permittivity tensor of the plasma as an influential factor in radar cross section, becomes anisotropic. Here, backscattering radar cross section (BRCS) of the antenna is calculated when irradiated by TE and TM waves under different incident angles. It will be shown how one can control BCRS of the antenna by varying its configuration and the external magnetic field intensity. Validation of numerical computations applied in this work is demonstrated by comparing it with an analytical method for a special case.

High-Frequency Diffraction of a Point Source Field by a Strongly Elongated Elliptic Cylinder

The problem of diffraction of a high-frequency point source acoustic field by an infinite elliptic cylinder with a strongly elongated cross-section is studied. At every direction of propagation, the solution is shown to be similar to those of a linear source field diffraction by a cylinder with correspondingly enlarged major semiaxis.

Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model

The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder.

A reduced physical optics model for electromagnetic scattering problem

The ultimate simplified point scatterer model contains no object's geometry informations, so a more complex prediction model containing geometrical informations is needed. The Physical Optics (PO) approximation has been widely used and considered as a good approximation of the far field electromagnetic scattering. Here, a forward model of bistatic scattering by PEC infinite elliptic cylinder based on the Physical Optics approximation is presented. The aim is to develope a simple scattering model for 2D targets illuminated by a monochromatic wave bistatic Radar. The reduced model is obtained by applying the stationary phase method to the PO integrals in both TE and TM wave cases. A parameter estimation procedure is also presented in order to examinate the efficiency of the presented model.

Electromagnetic scattering by an infinite elliptic dielectric cylinder with small eccentricity using perturbative analysis

The scattering of a plane electromagnetic wave by an infinite elliptic dielectric cylinder is examined using two alternative methods. In the first the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions while in the second, a shape perturbation method is applied by expressing the field in terms of circular-cylindrical wave functions only and the equation of the elliptical boundary in polar coordinates. Analytical expressions are obtained for the scattered electromagnetic field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = c/2a (h ¿ 1), with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> the interfocal distance of the elliptic cylinder and 2a the length of its major axis. In this case the scattered field and the scattering cross-sections expressions have the form of S(h) = S(0)[1+g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(4)</sup> h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> + O(h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> )], where the expansion coefficients g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> and g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(4)</sup> are given by exact, closed form expressions. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.

An asymptotic solution of the Schrödinger equation for the elliptic wire in the magnetic field

An asymptotic solution of the Schrödinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the ‘whispering gallery’ mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the ‘jumping ball’ modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.

Scattering by an Infinite Elliptic Metallic Cylinder

The scattering of a plane electromagnetic wave by an infinite elliptic metallic cylinder is considered. Two different methods are used for the evaluation. In the first the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions. In the second, a shape perturbation method, the field is expressed in terms of circular-cylindrical wave functions only, while the equation of the elliptical boundary is given in polar coordinates. Analytical expressions are obtained for the scattered electromagnetic field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = c/2a, (h ≪ 1), with c the interfocal distance of the elliptic cylinder and 2a the length of its major axis. In this case exact, closed form expressions are obtained for the expansion coefficients g(2) and g(4) in the relation S(h) = S(0)[1 + g(2)h2 + g(4)h4 + O(h6)] expressing the scattered field and the scattering cross-sections. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.

Heat Conduction in Infinite Elliptical Cylinder During Heating or Cooling

Heat Conduction in Infinite Elliptical Cylinder During Heating or Cooling

Implementation of Trefftz method for the solution of some elliptic boundary value problems

The purpose of this paper is to implement the well-known Trefftz method for the approximate solution of some elliptic boundary value problems for the two-dimensional Laplace's and the biharmonic operators through the use of polar harmonics as trial functions. Four applications treating four different situations are presented: the Dirichlet problem for the steady-state temperature distribution in an infinite elliptic cylinder (giving rise to Poisson's or Laplace's equations) with discontinuous boundary function for the complete and the truncated ellipses (cases 1, 2) and the first and the second fundamental problems of the plane strain theory of elastostatics for an infinite cylinder with rectangular normal cross-section (cases 3, 4). For two of the examples (cases 1, 3), the results could be checked against known exact solutions to show, in particular, that the method can sometimes give the exact solution, while for the other two (cases 2, 4) the method has provided solutions for new problems. It is shown that the use of polar harmonics, possibly together with other harmonics belonging to different coordinate systems, can handle many situations in an efficient way, i.e., by using few trial functions.

Computer Simulation on Onboard Chilling and Freezing of Albacore Tuna

ABSTRACTWe extended the application of a commercial finite‐element computer program package, PDEase, to the simulation of chilling and freezing of albacore tuna. Tuna was described as an infinite elliptical cylinder, where nonuniform boundary conditions present complications in computer simulation. Equations were developed to define the elliptical boundary. Temperature‐dependent thermal properties and time‐dependent ambient temperature conditions were used. Onboard experiments were conducted to measure the core temperature of individual tuna in slush ice tanks and in air‐blast and brine‐spray freezing systems. Measured time‐temperature profiles were compared with those of the simulation. Predicted chilling and freezing curves agreed with experiments ±3 to 6%. This program enables testing of important fish industry operation strategies.

Scattering by an infinite elliptic dielectric cylinder coating eccentrically a circular metallic or dielectric cylinder

In this paper, the scattering of a plane electromagnetic wave by an infinite elliptic dielectric cylinder, coating eccentrically a circular metallic or dielectric inner cylinder, is treated. The electromagnetic field is expressed in terms of both circular and elliptical-cylindrical wave functions, which are connected with one another by well-known expansion formulas. Translational addition theorems for circular cylindrical wave functions are also used. If the solution is specialized to small values of h=k/sub 2/c/2, where k/sub 2/ is the wavenumber of the elliptic dielectric cylinder and c its interfocal distance, semianalytical expressions of the form S(h)=S(0)[1+gh/sup 2/+O(h/sup 4/)] are obtained for the scattered field and the various scattering cross sections of this configuration. The coefficients g are independent of h. Both polarizations are considered for normal incidence. Graphical results for the scattering cross sections are given for various values of the parameters.

Heat-transfer on yawed infinite cylinders in a hypersonic stream

Nonequilibrium air flow past the nose of a yawed infinite elliptical cylinder in flight at an altitudeH=66 km and velocityV??=6500 m/s is investigated on the basis of the thin viscous shock layer equations. The ellipticity coefficient δ and the yaw angle χ are varied and calculations are carried out for both absolutely catalytic and absolutely noncatalytic body surfaces. The values of the parameter δ corresponding to the lowest maximum surface temperature are determined.

Electromagnetic scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one

The scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one is considered. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions, which are connected with one another by well-known expansion formulas. In the special case of small h=ka/2 (a being the interfocal distance of the elliptic conductor and k the wavenumber of the dielectric coating), exact, closed-form expressions of the form S (h)=S(0)(1+g"h/sup 2/+O(h/sup 4/)) are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane

It is demonstrated by specific examples that eigenvalues of the electric field integral equation (EFIE) operator for finite extent objects in lossless media can have branch points in the complex frequency s -plane. Specifically, it is shown from the analysis of the spheroidal wave equation in the s -plane that branch points are present in the eigenvalues of the integral operator associated with the scalar scattering problem from a perfectly conducting spheroid. Similarly, it is concluded from the analysis of the Mathieu's differential equation that branch points, besides that associated with the infinite extent of the object, exist in the s -plane behavior of the eigenvalues of the EFIE operator for a perfectly conducting infinite elliptic cylinder. A proof is given that branch point singularities cannot occur in the eigenvalues of EFIE operators for structures in which geometrical symmetry completely determines the eigenfunctions (and hence they are frequency independent). It is conjectured that branch points may always be present when sufficient object symmetry is lacking. This conjecture is supported by the fact that branch points appear when a sphere is deformed into a spheroid or when a circular cylinder is deformed into an elliptic one. An analogous phenomenon has been observed in circuit and transmission line problems. For example, it is shown that when the taper parameter of an exponential transmission line goes to zero (the line becomes uniform and thus a symmetrical structure), the branch points in the eigenvalues of the impedance matrix move away to infinity.

The parameters of an infinite homogeneous elliptical cylinder determined from its gravity effects

The Fourier transform of the vertical component of the attraction of a homogeneous horizontal infinite elliptical cylinder is computed. By comparing this function with the Fourier transform of the vertical component, determined experimentally, it is possible to determine the mass of the cylinder per unit length, as well as the position of the centre and of both the foci of the ellipse representing the cross-section of the cylinder.

Die Schwerewirkungen eines elliptischen Zylindersegmentes

A method has been derived for computing the gravity effect of a segment of an infinite homogeneous elliptical cylinder. The initial data was represented by formulae expressing the components of the field of gravity of a homogeneous two-dimensional body by means of line integrals. The method is based on the integration of theln R function over the boundary of the cross-section of the attracting body, R being the distance from a fixed point in which the gravity effect is determined. The problem was solved in confocal co-ordinates.

INTERPRETATION OF THE ALERT ANOMALY IN GEOMAGNETIC VARIATIONS

The theoretical basis for the interpretation of the Alert anomaly in geomagnetic variations has been reexamined. Under the uniform horizontal inducing field approximation, the electromagnetic response of an infinite elliptical cylinder of infinite conductivity has been derived, and from this the response for the upheaval of a half-elliptical conductor from a highly conducting mantle. The results have been extended to an asymmetric upheaval of the conducting mantle. A theory has also been developed of the electromagnetic response of an elliptic cylinder which is useful for application to the finite conductivity case.The electromagnetic coupling between an infinite circular cylinder and an underlying conducting layer has been investigated as far as the second-order approximation. An exact solution has then been obtained for the infinite conductivity approximation, and useful examples calculated.The situation at Alert has been reexamined following this work which reduces one of the difficulties of the earlier interpretation. An upheaval of about 100 km of the 1400–1500 °C isotherm to within 25–30 km of the surface appears capable of accounting for the gross characteristics of the response but the solution is certainly not unique and may be in error by as much as 60%. The asymmetry in the response is difficult to explain quantitatively. The response parameters thought to be most useful have been clearly defined and the ambiguity in the electromagnetic response solutions illustrated. Suggestions for further progress are made. Brief mention is made of preliminary magnetotelluric and gravitational studies at Alert.

Scattering from an infinite elliptical cylinder

Scattering from an infinite elliptical cylinder

Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers

SummaryWild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β&gt;0 (accelerated flow) but not so good for β&lt;0 (retarded flow).)

Note on the motion of an infinite elliptic cylinder in fluids having a constant shear motion

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 18, Issue 4 p. 223-226 Hauptaufsätze Note on the motion of an infinite elliptic cylinder in fluids having a constant shear motion Manohar Ray, Manohar Ray Lahore, IndiaSearch for more papers by this author Manohar Ray, Manohar Ray Lahore, IndiaSearch for more papers by this author First published: 1938 https://doi.org/10.1002/zamm.19380180403AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume18, Issue41938Pages 223-226 RelatedInformation