Showing papers on "Axial symmetry published in 1969"
TL;DR: In this article, the nuclear magnetic resonance spin resonance relaxation time was extended to include molecules which approximate an axially symmetric ellipsoid and have internal motion about an axis at any constant angle to the symmetry axis of the ellipse.
Abstract: The calculation of the nuclear‐magnetic‐resonance spin–lattice relaxation time has been extended to include molecules which approximate an axially symmetric ellipsoid and have internal motion about an axis at any constant angle to the symmetry axis of the ellipsoid. The calculation is carried out explicitly for two models of internal motion. These are, random reorientation among three equivalent positions 120° apart, and rotational diffusion.
206 citations
132 citations
TL;DR: In this paper, a method suited for numerical computation was proposed for solving the nuclear independent-particle problem for axially symmetric nuclei, and the method was used to solve the nuclear nuclear independent particle problem.
130 citations
TL;DR: In this article, it is shown that solutions for the structure of vertical free shear layers must be singular at the points where they receive fluid from a rising or spinning axisymmetric body.
Abstract: This paper considers axial motion in a rapidly rotating fluid of small viscosity. It is shown that solutions for the structure of vertical free shear layers must be allowed to be singular at the points where they receive fluid from a rising or spinning axisymmetric body. The possible types of singularities are elucidated by the use of similarity solutions and an hypothesis is introduced to limit their strength. Three particular cases of axially bounded motion are considered in detail; the split disk, the rising disk and the rising sphere. The hypothesis is shown to lead to a unique solution for the Stewartson layers. For the rising body, a Wiener-Hopf problem, which is independent of the body shape, must be solved for the central part of the Stewartson layers.
114 citations
TL;DR: In this article, a finite difference solution technique is used to solve Maxwell's equations directly in the treatment of electromagnetic pulse scattering in a time-varying inhomogeneous medium, where axial symmetry is obtained.
Abstract: A finite difference solution technique is used to solve Maxwell's equations directly in the treatment of electromagnetic pulse scattering in a time-varying inhomogeneous medium. In particular the scattering from a cylindrical rod inside a cylindrical waveguide is considered where axial symmetry is obtained.
113 citations
01 Mar 1969
TL;DR: In this paper, the representation of conical shells for axial compression was discussed and the case of axial compressions was considered. But the representation was not discussed in this paper.
Abstract: : The report concerns the representation of conical shells for the case of axial compression.
83 citations
TL;DR: In this article, asymptotic methods are employed to solve vector fields and propagation constants of modes propagating axially in a circular-cylindrical guiding system in which the dielectric constant decreases gradually and monotonically, but otherwise arbitrarily, from a maximum at the axis.
Abstract: In this paper asymptotic methods are employed to solve for the vector fields and propagation constants of modes propagating axially in a circular-cylindrical guiding system in which the dielectric constant decreases gradually and monotonically, but otherwise arbitrarily, from a maximum at the axis.
34 citations
TL;DR: In this paper, the nuclear electric field gradient tensor tensor parameters at the Fe3+ sites in Ca2Fe2O5 and Ca2AlO5 were determined to within experimental error and the z principal axis of the efg was parallel to the crystallographic b axis.
Abstract: Mossbauer spectroscopy has been used to determine the nuclear electric‐field‐gradient (efg) tensor parameters at the Fe3+ sites in Ca2Fe2O5 and Ca2FeAlO5. In all cases to within experimental error, the efg is axially symmetric and the z principal axis of the efg is parallel to the crystallographic b axis. Analytic expressions are developed for the relative transition probability of M1 radiation connecting I = 32 to I = 12 nuclear states for the situation in which the z principal axis of an axially symmetric efg is perpendicular to an internal magnetic field.
34 citations
Patent•
12 Aug 1969TL;DR: An extractor for removing a broken portion of an intramedullary nail includes an inner rod member and an outer concentric tubular member, each having a pair of axially extending fingers at one end as mentioned in this paper.
Abstract: An extractor for removing a broken portion of an intramedullary nail includes an inner rod member and an outer concentric tubular member, each having a pair of axially extending fingers at one end. The fingers are arranged in respective pairs and each finger of such pair includes a pin having a portion extending beyond the inner surface of the finger, with the projecting portions of the pins axially and circumferentially converging with respect to each other. The other end of the inner member is secured to a drum rotatably and slidably received within a housing secured to the other end of the outer member. Fixed handles on the housing have their inner ends extending into an annular groove of the drum to limit axial movement of the drum and inner member relative to the housing and outer member. A manually rotatable handle on the housing has its inner end engaging the wall of an axially extending groove in the drum to rotate the drum and housing and the inner and outer members relative to each other and bring the projecting portions of the pins into clamping engagement with a land of the cruciform cross sectionally shaped nail. The inner member also includes an end anvil which can be used to shift the broken portion of the nail within the medulla to free the nail for easier removal. A handle assembly secured to the drum permits attachment of conventional instruments which apply intermittent axial driving forces to the inner member.
29 citations
TL;DR: In this paper, the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered, and a valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region.
Abstract: The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas‐vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.
26 citations
TL;DR: In this article, a linear theory is presented for the steady, axially symmetric motion of a stratified fluid in a narrow, rotating spherical annulus with a spherically symmetric gravitational field.
Abstract: A linear theory is presented for the steady, axially symmetric motion of a stratified fluid in a narrow, rotating spherical annulus with a spherically symmetric gravitational field.The fluid is driven by a combination of differential rotation of the two shells and differential heating applied at the surfaces of the spheres.It is shown that the effect of stratification becomes increasingly important at lower latitudes with the Ekman layers on the spheres’ surfaces fading in strength as the geostrophic interior velocities themselves tend toward the shell speeds at lower latitudes.The Singularities In The Geostrophic Solutions At The Equator Are Removed By A Boundary Layer Whose Detailed Structure Depends On The Ratio Of Horizontal To Vertical Mixing Coefficients Of Momentum And Heat.
TL;DR: Vibration characteristics of circular cylindrical shells containing water under axial excitation, investigating bubble formation and shell-fluid interaction are investigated in this paper, where the authors consider the case of a single shell.
Abstract: Vibration characteristics of circular cylindrical shells containing water under axial excitation, investigating bubble formation and shell-fluid interaction
TL;DR: In this article, integral constraints are derived for steady recirculating flows of nearly incompressible fluids, arising from the action of a small amount of viscosity and heat conduction.
Abstract: Integral constraints are derived for steady recirculating flows of nearly incompressible fluids, arising from the action of a small amount of viscosity and heat conduction. These constraints are then combined with the inviscid nondiffusive incompressible flow equations to show that two-dimensional flows containing closed nested streamlines, or three-dimensional flows with closed nested stream surfaces, are isothermal. In the former case it is shown that the vorticity is constant, and in the latter case there is an analogous result when the flow is axially symmetric and confined to axial planes. For a circular cell free convection problem, the interior temperature and vorticity are determined from the boundary conditions by an approximate integration of the boundary layer equations.
TL;DR: In this paper, the solution of the equations representing the shape of an axially symmetric sheet of fluid is given, and the effect of gravity on the stability of a water bell is also considered.
Abstract: The solution of the equations representing the shape of an axially symmetric sheet of fluid is given. It is shown that under certain conditions gravity can greatly influence the shape of these sheets (or water bells as they are commonly known). The calculated shape is compared with a photograph of a water bell and it is shown that there is good agreement between the theory and experiment. The effect of gravity on the stability of a water bell is also considered.
TL;DR: In this article, a theory of nuclear magnetic relaxation in solution was developed for situations in which the molecules of interest can tumble in a way that resembles their rotation in the gas phase, and the equations were constructed heuristically from the exact correlation function for the free axially symmetric top and the classical limit of the quantum-mechanical equation is obtained.
Abstract: A theory of nuclear magnetic relaxation in solution is developed for situations in which the molecules of interest can tumble in a way that resembles their rotation in the gas phase. The equations are constructed heuristically from the exact correlation function for the free axially symmetric top and the classical limit of the quantum-mechanical equation is obtained. In the limit when the symmetric top becomes a spherical top the equations are identical to these obtained on a classical model by Steele.
TL;DR: In this paper, it was shown that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes, and the asymptotic behavior of the stability criterion was considered in the limit of very large radial Reynolds number, and also in a limit where both the radial Reynolds numbers and the Hartmann numbers are large.
Abstract: In considering the onset of instability of an electrically conducting fluid between rotating permeable perfectly conducting cylinders in an applied axial magnetic field, it is found that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes. Results are presented showing the effect of the oscillatory modes on the criterion of onset of instability.The asymptotic behaviour of the stability criterion is considered in the limit of very large radial Reynolds number, and also in the limit where both the radial Reynolds number and the Hartmann number are large.
TL;DR: In this article, the condition for instability of an isotropic elastic-plastic cylinder under pressure p and independent axial load P is examined and it is shown that the boundary value problem admits different loading conditions, each condition leading to a different result.
TL;DR: In this article, 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.
Abstract: 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.
TL;DR: In this paper, the radiation pattern of an axial slot on a circular conducting cylinder is computed using the wedge-diffraction theory in combination with the creeping wave theory, and the total field in the "lit" region is obtained by the superposition of the wedgediffracted and creeping wave fields.
Abstract: The wedge-diffraction theory in combination with the creeping wave theory is used to compute the radiation pattern of an axial slot on a circular conducting cylinder. The slot is excited by a parallel-plate waveguide operating in the TEM-mode. The total field in the "lit" region is obtained by the superposition of the wedge-diffracted and creeping wave fields. The total field in the "shadow" region is obtained solely from the creeping wave contribution.
Patent•
01 May 1969TL;DR: In this article, the authors describe a constroLLed Fusion Reactor of the stron type having a MAGNETIC CONTAINMENT ZONE created by the interaction of a high energy CYlinDRICAL LAYER of CHARGED PARTICLES ROTATING in an AXIALLY SYMMETRIC MAGnetic FIELD region.
Abstract: CONTROLLED FUSION REACTOR OF THE STRON TYPE HAVING A MAGNETIC CONTAINMENT ZONE CREATED BY THE INTERACTION OF THE MAGNETIC FIELD OF A HIGH ENERGY CYLINDRICAL LAYER OF CHARGED PARTICLES ROTATING IN AN AXIALLY SYMMETRIC MAGNETIC FIELD REGION IN WHICH AN ADDITIONAL AXIAL CONDUCTOR INTRODUCES A SHEAR MAGENTIC FIELD COMPOENENT TO SUPPRESS INSTABILITIES WHICH CAUSE PLASMA LOSS.
TL;DR: In this article, the propagation coefficients and field configurations of an axially magnetized, plasma-filled waveguide are treated by the Rayleigh-Ritz variational technique, and the results are placed in the form of a matrix eigenvalue problem.
Abstract: Propagation coefficients and field configurations of the normal modes of an axially magnetized, plasma‐filled waveguide are treated by the Rayleigh‐Ritz variational technique. The results are placed in the form of a matrix eigenvalue problem. The eigenvalues are approximations to the propagation coefficients, and the eigenvectors contain Fourier coefficients of the electric fields of the normal modes expanded in terms of fundamental functions. This form is well suited to computer calculation and is used in a following paper to compute reflection and transmission coefficients of waveguide sections of finite length. The axially symmetric normal modes are examined in detail and are found to possess certain interesting properties that have not been fully recognized. First of all, these modes are reciprocal. Furthermore, under certain conditions they can, like ``helicon'' waves, be divided into ``ordinary'' (``cut off'') and ``extraordinary'' (``lossless'') modes. The axially symmetric modes are not circularly polarized, however, but instead change shape in a rather remarkable manner as they propagate.
Patent•
01 Oct 1969
TL;DR: In this paper, a wrench assembly including a series of axially overlapping telescoping wrench segments which are maintained axially relative to one another by an integral spiral spring interconnecting all of the segments.
Abstract: A wrench assembly including a series of axially overlapping telescoping wrench segments which are maintained axially relative to one another by an integral spiral spring interconnecting all of the segments. Each segment has a substantially constant wall thickness from one end to the other end with diametrically opposed tabs struck out of the side walls and extending toward one another, about which the spring is spiraled.
TL;DR: Edge diffraction effects in TEM axially slotted finite ground plane on radiation pattern in waveguides of different geometries as discussed by the authors were studied in the context of TEM.
Abstract: Edge diffraction effects in TEM axially slotted finite ground plane on radiation pattern in waveguides of different geometries
TL;DR: In this article, a variational principle is used to extract states of good angular momentum from intrinsic wavefunctions which are not axially symmetric, and a diagonalization between bands on top of the usual projections is generated.
TL;DR: In this paper, the nucleon wave functions and energy eigenvalues in a deformed Woods-Saxon potential are calculated approximately by diagonalizing the Hamiltonian in a finite subspace of Hilbert space.
TL;DR: In this paper, the creep deformations of a circular cylindrical shell are calculated under the action of uniform axial compression and the solution is obtained in the form of trigonometric series for the stresses and displacements.
Abstract: The creep deformations of a circular cylindrical shell are calculated under the action of uniform axial compression. The edges of the shell of finite length are simply supported and the deformations are assumed to be axially symmetric. Such axisymmetric deformations have been observed to occur when the shell is moderately thin-walled. The solution is obtained in the form of trigonometric series for the stresses and displacements.
TL;DR: In this article, a general expression for the change in electrostatic energy that occurs when an axially symmetric, deformed conducting sphere (i.e., a closed surface which can be represented in terms of a Legendre polynomial expansion) is inserted in an axial electric field is derived.
TL;DR: In this article, a thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically, and the residual stresses in the ring are analyzed.
Abstract: A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed.The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method.The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic.An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are ...
01 Jan 1969
01 Jul 1969
TL;DR: In this paper, the equations describing transverse propagation of electromagnetic waves in a cylindrically stratified plasma, in which a static magnetic field is imposed parallel to the axis of cylindrical symmetry, are examined.
Abstract: The equations describing transverse propagation of electromagnetic waves in a cylindrically stratified plasma, in which a static magnetic field is imposed parallel to the axis of cylindrical symmetry, are examined. A systematic method developed previously for isotropic media, Heading (3), Westcott (6) is adapted to yield generalized proffles relating to the plasma properties. These proffles are capable of producing exact solutions for the field distribution in terms of standard transcendental functions. Previously known proffles appear as special cases of the analysis.