Showing papers on "Axial symmetry published in 1985"

Realization of First Order Optical Systems Using Thin Lenses

Abstract: A first order optical system is investigated in full generality within the context of wave optics. The problem is reduced to a study of the ray transfer matrices. The simplest such systems correspond to axially symmetric propagation. Realization of such systems by centrally located lenses separated by finite distances is studied. It is shown that, contrary to the commonly held view, the set of first order systems that can be realized using axially symmetric thin lenses exhausts the entire SL(2, R) group; at most three lenses are needed to realize any element of this group. In particular, the inverse of free propagation can be so realized. Among anisotropic systems it is again shown that every element of the lens group Sp(4, R) can be realized using a finite number of thin lenses.

The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

Abstract: This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

Tomographic Reconstruction Of Axially Symmetric Objects From A Single Radiograph

Abstract: In 1826 Abel presented the method of obtaining the profile of a circularly symmetric 2-D object from its projection. It is shown that the extension of Abel inversion, the reconstruction of a 3-D axially symmetric object from a single radiograph, offers significant benefits as an image analysis tool. These benefits include improved delineation of material boundaries, enhanced. display of minor deviations from axial symmetry, as produced by defects, and accurate estimation of the linear attenuation coefficients of the materials. Frequently this technique allows observation of features in the object that are too subtle to be seen in the original radiograph.

Reciprocating linear motor

Abstract: A reciprocating linear motor (10) is formed with a pair of ring-shaped permanent magnets (50, 52) having opposite radial polarizations, held axially apart by a non-magnetic yoke (20), which serves as an axially displaceable armature assembly (14) A pair of annularly wound coils (30, 32) having axial lengths which differ from the axial lengths of the permanent magnets are serially coupled together in mutual opposition and positioned with an outer cylindrical core (24) in axial symmetry about the armature assembly One embodiment includes a second pair of annularly wound coils (36, 38) serially coupled together in mutual opposition and an inner cylindrical core (26) positioned in axial symmetry inside the armature radially opposite to the first pair of coils Application of a potential difference across a serial connection of the two pairs of coils creates a current flow perpendicular to the magnetic field created by the armature magnets, thereby causing limited linear displacement of the magnets relative to the coils

Bifurcation and transition to turbulence in the gap between rotating and stationary parallel disks

Abstract: The flow in the gap between rotating and stationary parallel disks is an attractive object for studying the transition characteristics in three-dimensional internal flows. Firstly, in this case a large region of the basic motion is satisfactorily described by a self-similar solution to the Navier-Stokes equations [1]; secondly, as the parameter γ = ωh2/v (ω is the. angular velocity of rotation of one of the disks and h is the gap width) varies, there is an evolution of the basic motion, so that it is easy to produce different types of initial and subsequent instabilities. The basic steady regime for axially symmetric flow has been studied by many authors (see [1, 2]). Questions of the transition in the gap between disks have been considered [3, 4]. This paper presents a methodology and the results of experimental investigations for different types of initial and subsequent instabilities in the gap between disks enclosed by a cylindrical cover. It was found that as a result of the loss of stability of the basic regime one of two steady vortex regimes is developed depending on the value of the relative gap width. The subsequent stages of “soft” excitation of the turbulent regime are described and the corresponding boundaries established. It is shown that in very narrow gaps the excitation of turbulence has a “hard” nature of the type realized in Couette flow. The stability limit for a laminarized boundary layer on a rotating disk and the boundary for complete turbulence of the layer were determined for relatively wide gaps. A comparison was made with known data for an unenclosed rotating disk.

Magnetic drum separator

Abstract: A magnetic materials separator including an axially inclined drum disposed for axial rotation within the curvature of an arcuate magnet structure which extends axially of the drum and is disposed in close-spaced relationship with the outer surface of the drum. The magnet structure comprises an axially extending series of arcuate magnet yokes, each comprising an axially laminated array of arcuate magnet sub-assemblies which are alternately polarized in opposite axial directions. Each of the sub-assemblies comprises an arcuate magnet axially polarized and sandwiched between a arcuate pair of soft magnetic flux concentrators which have respective axial thicknesses between five and twenty percent of one-half the axial thickness of the sandwiched magnet.

Nonequilibrium phenomena in dense polyatomic fluids. I. Transport coefficients for axially symmetric (polar) molecules

Abstract: Formulas are derived for the viscosity coefficients and thermal conductivity of a dense fluid of rigid, axially symmetric molecules. The only quantities appearing in these formulas which have not been evaluated explicitly are integrals over the orientational coordinates of two interacting molecules. The theory is based on a kinetic equation which incorporates a Vlasov term, an Enskog operator specific to the short‐ranged noncentral impulsive forces, and Fokker–Planck operators associated with the longer ranged interactions. The method of moments is used to construct an approximate solution of this kinetic equation. The theory and the transport coefficients it produces are compared with those of earlier investigations.

Pin-barrel extruder having adjustable pins

Abstract: A pin-barrel extruder suitable for processing rubber and thermoplastic plastics materials having pin adjustment means is disclosed. The extruder comprises a barrel having a screw rotating therein. Pins project radially inwardly into the hollow interior of the barrel. These pins are distributed both uniformly around the periphery of the barrel and in axial alignment with one another. Axially aligned pins are made adjustable, with regard to their depth of penetration into the barrel by being connected to a bar or rail. This bar or rail is disposed radially outwardly of the barrel but extends parallel to the axis thereof. Actuating means are provided for displacing the bar or rail, and hence the pins, relative to the barrel.

Damping of cylindrical phonons in extense fermion matter

Abstract: A previous model, designed so as to simulate the coupling between a one-dimensional, quantal harmonic excitation in a fermion heat bath, is extended to consider three-dimensional vibrations with axial symmetry. This investigation addresses future studies on the relaxation of collective modes in finite Fermi systems such as deformed nuclei. For this application, the equations of irreversible dynamics in the proposed model are extracted and their solutions are examined in a range of parameters appropriate for the nuclear fluid. The formulation, techniques, and discussion are far more general and can be applied to a variety of problems arising in statistical mechanics and many-body physics.

Dynamic Instability Analyses of Axially Impacted Columns

Abstract: The dynamic response and critical state of an inelastic simply supported column under an axial impact are studied. This problem is analyzed by solving the dynamic Bernoulli‐Euler equation with an axial inertia effect within the framework of finite difference approach. The influence of strain‐rate effects on the dynamic response is first examined by using an elastic‐viscoplastic theory, and then the critical values of an initial velocity and a mass of striking body for losing stability are evaluated within the context of the numerical results from different initial and boundary conditions. It is found that strain‐rate effects are important in the range of post‐dynamic instability, and that the mode of the lateral displacement after an impact depends on the initial velocity of the striking body and also on the relationship between the natural period of the first‐order lateral mode and that of the first‐order axial mode. Present study can give a basic guide to evaluate the dynamic instability of axially impa...

Bridging clutch for a hydrodynamic unit

Abstract: In a bridging clutch for a hydrodynamic unit, in particular a drive unit for a motor vehicle, a pump impeller is rotationally connected to a drive shell overlapping a turbine wheel and a clutch disc rotationally connected to the turbine wheel and holding at least one inner friction disc firmly in terms of rotation is arranged in a housing interior space formed between the drive shell and the turbine wheel. Outer friction discs held firmly in terms of rotation relative to the housing wall of the drive shell interact with the inner friction discs. In the axial direction towards the pump impeller, the friction disc assembly containing the outer and inner friction discs can be both actuated by hydraulic pressure forces via an annular axial piston arranged between the clutch disc and the housing wall and be supported via a thrust washer fixed in terms of rotation relative to the drive shell on an abutment ring held on the housing wall. To achieve an axially short construction, the axial piston is both designed as a pressed sheet-metal part and used as an outer friction disc interacting directly with an inner friction disc. The axial piston is in releasable rotational engagement with the thrust washer via positively engaging means.

On the Time-evolution of the Robinson-trautman Solutions

Abstract: An algorithm is presented for solving, by a power expansion, the field equation of the Robinson-Trautman metrics It is applied, in the linear approximation, to the line elements which evolve from an axially symmetric initial surface The special case of the ellipsoid of revolution is explicitly treated

Hydrostatic radial-piston machine

Abstract: Hitherto it has been possible, in order to determine the eccentricity, to provide as a position sensor a spring-actuated valve between the eccentric and the eccentric hoop. The force required to open the valve against the spring force is then used as a measure for the position of the eccentric. A drawback thereof is an additional rotary transmission which automatically is continuously under pressure. This further goes hand in hand with leakage and wear due to friction. To overcome these drawbacks, a sensor tappet 12 permanently bearing on the eccentric hoop 8 is now provided which, by means of a terminal section 15, dips in a piston-like manner into a radial bore 10 of the eccentric 7. The radial bore 10 is linked via a duct arrangement 20 to an axial bore 21 in the machine shaft 3 in which a spring-actuated slave piston 23 is arranged. The slave piston 23 is linked via a tappet 25 to a core 28 which can be axially displaced in a coil 29. By means of inductive pick-off it is now possible to determine at all times, both during operation and at standstill, the exact position of the eccentric hoop 8, because the sensor piston 15 and the slave piston 23 are constantly staying each other via a hydraulic column in the duct arrangement 20.

Order Parameters and Mean Field Theory for Systems of Uniaxial Molecules

Abstract: A general method is developed for finding the order parameters describing the various phases of a system of anisotropic molecules. The order parameters are introduced on the basis of the expansion of the one-particle distribution function in the generalized Fourier series, and the symmetry of the intermolecular potential. The free energy of the system is considered in the Landau form. This method is applied to a system of axially symmetrical molecules with the Kobayashi interaction potential. It is found that only three Fourier components of the interaction potential are responsible for the system's behaviour. The phase diagram of the system is discussed and the possibility of the existence of a biaxial nematic phase is established.

Finite element analysis of flow in a gas filled rotating annulus

Abstract: Linearized multidimensional flow in a gas centrifuge can be described away from the ends by Onsager's pancake equation. However a rotating annulus results in a slightly different set of boundary conditions from the usual symmetry at the axis of rotation. The problem on an annulus becomes ill-posed and requires some special attention. Herein we treat axially linear inner and outer rotor temperature distributions and velocity slip. An existence condition for a class of non-trivial, one-dimensional solutions is given. New exact solutions in the infinite bowl approximation have been derived containing terms that are important at finite gap width and non-vanishing velocity slip. The usual one-dimensional, axially symmetric solution is obtained as a limit. Our previously reported finite element algorithm has been extended to treat this new class of problems. Effects of gap width, temperature and slip conditions are illustrated. Lastly, we report on the compressible, finite length, circular Couette flow for the first time.

Axially symmetric Kaluza-Klein dyons and nonlinear sigma-models

Abstract: We show that the main part of the field equations for axially symmetric Kaluza-Klein dyons reduces to that of a nonlinear sigma-model on symmetric spaces when these models are generalized in a suitable way. As a result, we derive Lax pairs of the Belinskii-Zakharov type as well as the Pohlmeyer-Eichenherr-Forger type. The well-known four-dimensional axially symmetric stationary fields of Einstein and Einstein-Maxwell equations become special cases of ours.

Spontaneous breaking of axial symmetry in v-vortices in superfluid /sup 3/He-B

Abstract: A new, axially asymmetric state of a broken-parity vortex in /sup 3/He-B has been found. At low pressures, this state has an energy lower than that of an axisymmetric state. Only a first-order phase transition can occur between these two states. The properties of a rotating liquid, which are associated with the breaking of axial symmetry in a vortex, are discussed.

Electron spin polarization ratio detector

Abstract: PURPOSE:To measure a polarization ratio almost without being affected by a change of the surface condition of an electron beam-radiated object by changing the radiation direction to the object with the polarization direction kept constant. CONSTITUTION:An electron beam 1 to be measured is fed between two pairs of deflection electrodes 3, 3' arranged at a right angle to each other applied with sinusoidal wave voltage Vr, Vr' out of phase by 90 deg. from a generator 7 through a collimator 2, and it is rotated around a center axis 9 as shown by an arrow R while the angle alpha between the center axis 9 and the electron beam 1 is kept constant. Furthermore, the electron beam 1 is fed through the axial symmetry DC electric field Er generated by ringlike deflection electrode systems 4, 4' while the angle alpha with the center axis 9 on a metal polycrystal target 6 with a surface vertical to the center axis 9 is kept constant and the incidence direction is rotated. The absorbed current is synchronously detected by a signal processor 8 with a signal from the generator, the polarization direction is calculated, and the spin polarization ratio is calculated based on the ratio between the secondary electron current from the target collected by a collector 5 and the sum of the absorbed current.

On a particular solution of the equation of Ernst with n fields, parametrized by an arbitrary harmonic function

Abstract: We determine a particular solution, dependent upon an arbitrary harmonic function in cylindrical coordinates, of the system of n partial differential equations, which characterizes both the axially symmetric field solution of the Einstein (n−1)–Maxwell equations and one class of axially symmetric static self‐dual SU(n+1) Yang–Mills fields.

Fields and permeances of flat rectangular and cylindrical dc electromagnetic structures

Abstract: Analytical solutions to the field problem of flat rectangular and axially symmetric cylindrical dc electromagnetic systems are presented. It is shown that the fiat configuration is a special case of the general solution. The results are presented in normalized forms as permeance functions. Calculated results are compared with those obtained experimentally.

Coaxial reel assembly apparatus

Abstract: A reel assembly apparatus for coaxial magnetic tape reels is provided in which both an inboard reel and an outboard reel may be reliably clamped to their respective drive spindles from the outboard side of the assembly apparatus with ease and convenience. For the purpose of clamping the inboard reel, an internal locking nut extends radially in the plane of the inboard reel from its drive spindle into threading engagement with a hub of the inboard reel. A linkage, extending axially through the outboard drive spindle, rotates in response to turning movement of a bail accessible to an operator. The locking nut, in response to the rotation of the linkage, (1) initially causes the inboard hub to rotate, relative to the inboard reel, a limited amount into a reel-clamping position, and (2) then causes an axial movement of the inboard hub. This latter movement drives the inboard reel axially, to clamp it against a radially extending member of the inboard drive spindle. A second locking nut, coupling a second bail to the outboard hub, serves similarly for clamping the outboard reel to its drive spindle. With the locking nuts in the planes of their respective reels, the reels can be positioned axially immediately adjacent each other, thereby conserving space for a compact design.