Circular Cylinder Of Infinite Length Research Articles

Electromagnetic response of an anisotropic conducting cylinder to an external source

A novel analytical solution is obtained for the boundary value problem of a circular cylinder of infinite length that is excited by a prescribed external field. The cylinder is anisotropic in the sense that the complex conductivity and magnetic permeability are diagonal uniaxial tensors with generally unequal elements. The solution involves Bessel functions of nonintegral order. Known special cases are recovered.

Values of Diffusion Coefficients Deduced from the Closing Times of Helicopter-Produced Clearings in Fog

Abstract Values of diffusion coefficients determined from the observed closing times of nine conical-shaped clearings in fog produced by hovering helicopters at Lewisburg, WV, in September 1969 are presented. The values were established following the method of Elliott (1970) assuming that the geometric and diffusive properties of the clearings and surroundings could be approximated by theoretical equations of the type governing the diffusion of heat and water substance in a bounded, circular cylinder of infinite length, with appropriate specification of the condensation conditions. The coefficient values for the nine experiments were found to range from 0.7 × 105 to 1.9 × 105 cm2 s−1. The physical, thermal and kinematic characteristics of the Lewisburg fog were investigated that might explain the variation of the coefficient values across this range. These efforts revealed that the values varied primarily, and inversely, with 1) the depth of the fog and 2) the Richardson number within the fog layer. Secon...

A study of the flux density distribution in type II superconductors rotating in a magnetic field

Torque measurements on type II superconductors rotating in a magnetic field H 0 directed perpendicular to the rotational axis can be used to determine pinning and viscous friction of vortices. The exact analysis of these measurements requires a knowledge of the vortex configuration in the rotating specimen, which is studied for the case of a circular cylinder of infinite length. A method is developed to calculate numerically the vortex configuration if the dependence of critical current density J c and flux flow conductivity Σ f on flux density B and if the equilibrium magnetization curve are known. An inverse procedure also allows us to determine these material parameters from the measured torque and magnetization of the rotating sample. Results obtained by applying this procedure to different materials are reported.

Steady State Temperature Distribution in a Solid Cylinder Moving in the Direction of its Axis Through a Cross-Flow of Hot Gas

A range of boundary value problems is solved that describe the steady state temperature distribution in a solid circular cylinder of infinite length, moving in the direction of its axis. The cylinder is heated by a hot gas flowing perpendicularly to the cylinder. The problems differ in complexity depending on whether or not the cylinder is radially isothermal and the gas temperature uniform. Dimensionless charts are presented. This work pertains to the “moving wire techniques” for studying polymer flammability and measuring heat transfer from gases.

Scattering by a lossy dielectric circular cylindrical multilayer numerical values

The theoretical scattering solution for a plane wave incident normally on a lossy dielectric multilayer circular cylinder of infinite length is outlined. Numerical values of the modal scattering coefficient for TE and TM modes are given for several single and multilayer cylinders. Verifications of the results are described. The values may serve as reference data.

Vibration analysis of axisymmetric resonators

A brief description is given of results obtained from a finite element analysis for axisymmetric resonators based on the Clough-Felippa triangular element rotated about the axis of symmetry. The method is tested against exact results for circular cylinders of infinite length and is shown to be very accurate. It is applied to give design curves for tapered horns, and to analyse two basic resonator designs.

Field descriptions for a steady, developing tube flow of vanishing Reynolds number

Numerical solutions for the stream function, vorticity, velocity, and pressure fields are presented for the case of a steady, laminar, isothermal, Newtonian flow developing from an initial slug flow in a circular cylinder of infinite length at zero Reynolds number.

Correction Devisors for the Four-Point Probe Resistivity Measurement on Cylindrical Semiconductors

Using the Neumann function, this paper gives the expressions of the correction devisors for the equally spaced and linearly arrayed four-point probes on the same generating line of a circular cylinder of infinite length. Also for the cylinder of semi-infinite and finite length, the effects of the non-conducting and conducting edges are considered. The correction devisors are given as the function of the ratio of the radius of the cylinder to the probe spacing with the parameter of the edge effect. Several special cases obtained using our idea coincide with other results already calculated by the method of images hitherto used.

A contribution to the electromagnetic theory of the unmyelinated axon

The unmyelinated axon of negligibly thin axolemma is idealized as a right circular cylinder of infinite length imbedded in an unbounded aqueous electrolyte. The scalar wave equation is solved in this geometry subject to the boundary conditions (i) that the electric scalar potential vanish at infinity and be a known function along the cylinder axis, and (ii) that the radial current be continuous across the axolemma. Exact solutions for the infinite reluctivity limit are obtained for the interior potential, the total axial current, and the radial current at the axolemma; an approximate solution is obtained for the exterior potential. These solutions are compared with predictions of the classical transmission line theory commonly employed in describing the electrical properties of axons.

Eigenschaften der L�sungen der nichtlinearisierten Ginsburg-Landau-Gleichungen in Zylindersymmetrie

Solutions of the nonlinear Ginzburg-Landau equations in cylindrical symmetry have been computed for a type I superconductor. From these solutions the behaviour of a circular cylinder of infinite length in a magnetic field parallel to its axis has been deduced. For a series of values of the magnetic field solutions are given in two cases. The first case was calculated with the assumption of no fluxoid frozen in (fluxoid quantum number n=0), whereas in the second case a vortex with fluxoid quantum numbern=1 was assumed on the axis of the cylinder. For both series of solutions investigation of the thermodynamic stability was carried out. This and further thermodynamic considerations led to the result that in a gedankenexperiment the transition from the normal to the superconducting state and vice versa can be performed in a reversible manner. The expulsion of the magnetic field from the sample during the reversible transition to the superconducting state (Meissner-Effect) is also described by the solutions. Further results are the existence of a supercooled state down to a magnetic fieldHc2=κ√2Hcb and of a superheated state up to a fieldHc1>Hcb. The value ofHc1 depends on the radius of the cylinder. If a condensation to the superconducting state takes place at a fieldH0 whereHc2<H0<Hcb, condensation withn=0 seems to be preferred in comparison to that withn=1.

Excitation of a conducting cylindrical surface of large radius of curvature

Approximate expressions are obtained for the magnetic field induced by slots on conducting circular cylinders of infinite length and of radius large compared to the signal wavelength. The approximations are derived from the formal solution of the cylinder problem and are valid for all distances from the slot. The expression for a short slot dipole, at any orientation, is expressed in terms of the field of the slot on a flat conducting sheet multiplied by a curvature term. The latter is a function of the ray path length and radius of curvature, making the results applicable to other convex surfaces. Corresponding expressions for half wavelength axial and transverse slots are also obtained and the results compared with experimental measurements.

SCATTERING OF A PLANE WAVE FROM A CIRCULAR DIELECTRIC CYLINDER AT OBLIQUE INCIDENCE

A solution is given for the problem of a plane wave incident obliquely on a circular cylinder of infinite length. The electric properties of the cylinder are taken to be homogeneous and isotropic but otherwise arbitrary. It is shown that in the general case the scattered field contains a significant cross-polarized component which vanishes at normal incidence. While the solution is derived for the magnetic vector of the incident wave transverse to the axis of the cylinder, the corresponding result for the other polarization can be obtained from symmetry.

Sound Diffraction by Rigid Spheres and Circular Cylinders

The results of calculations of the pressure distribution on the surface of a stationary rigid sphere and a stationary rigid circular cylinder of infinite length, when exposed to a plane progressive sound wave, are compared with experiment. A small probe microphone was used to measure the sound pressures on the surface of the obstacles in a room essentially free from acoustic wall reflections under a variety of experimental conditions. The sound pressures p on the surface are conveniently expressed relative to the free-field pressure p0 in the undisturbed incident wave. In the case of the sphere, reasonably good agreement was obtained between theory and experiment in the range of 13 &amp;lt;ka &amp;lt; 10, where k is the wave number of the incident wave and a the radius of the obstacle. In particular, the existence of the “bright” spot diametrically opposite the point nearest the sound source was verified experimentally. This comparison of experiment with theory affords a valuable means of estimating the validity of the experimental procedure. In the case of the cylinder whose axis was oriented parallel to the wave front of the incident wave and whose length was chosen to equal its diameter, the pressures were measured for the most part in the median plane. There is a marked similarity between the results obtained for this finite cylinder and the results obtained for a sphere. The pressure at the point in the median plane farthest away from the source of sound (θ = 180°) is substantially equal to the free-field pressure only for ka &amp;lt; 5. As the frequency is increased further, the sound pressure near θ = 180° drops rapidly up to and most likely beyond ka = 10 at an approximately constant rate, in decibels per frequency octave. A small microphone located on the surface of such a cylinder at θ = 180° will exhibit a low pass filter action with a cut-off at k ≈ 5. Tables are furnished of the ratio p/p0 computed for a rigid circular cylinder of infinite length. This ratio is tabulated in magnitude and phase in the range of 12 ⩽ ka 10, for azimuths θ varying from 0 to 180° in 10-degree steps. The results are very similar to the spherical case for θ not exceeding about 150 degrees. There is only an insignificant trace of the bright spot at θ = 180°.