Angular Frequency Of Rotation Research Articles

Some observational appearances of m=1 density waves in Be star disks

One-armed (i.e., m = 1) density waves are the only global waves in nearly Keplerian disks (Kato 1983). Their frequencies are much smaller than the angular frequency of disk rotation. Based on this theory, Okazaki (1991) proposed that the long-term V/R variations of Be stars are phenomena caused by the global m = 1 oscillations in the equatorial disks. Hummel and Hanuschik (1993) showed that line profiles of disks with m = 1 perturbation patterns are in agreement with the observed V/R variability.

Overstability of nonradial pulsations in rotating early type stars

We present the result of nonadiabatic analysis for nonradial pulsations in uniformly rotating main sequence models.The angular dependence of the amplitude of a nonradial pulsation mode with an azimuthal order m in a rotating star is represented by a sum of terms proportional to spherical harmonics Ylm(θ, ø) with l = |m|, |m| + 2,… (even mode) or l = |m| + 1, |m| + 3,… (odd mode; see e.g. Saio and Lee 1991 for detail). (In this paper we consider only even modes.) This property makes the analysis complex compared with the case without rotation, in which a single Ylm expresses the angular dependence of a given mode. In our numerical analysis the summation is truncated, in which only first two terms are taken into account. Lee and Saio (1987) give the differential equations for nonadiabatic nonradial pulsations in a uniformly rotating star. Treating the angular frequency of rotation as a free parameter, we applied the nonadiabatic analysis to a main-sequence evolutionary model, for which the effect of rotation is neglected.

Rotation of the neutron-drip superfluid in pulsars: evidence for corotating vortices

The abrupt changes in the angular frequency of rotation seen in several pulsars are followed by relaxation of the angular frequency time-derivative Ω#78, assumed to be caused by angular momentum transfer to the inner-crust neutron superfluid. Quantitative calculations show that the large changes δΩ#78(t) observed in PSR 0355 + 54 and 0833 − 45 are not consistent with the relaxation of superfluid and pinned vortices, unless either the neutron star equation of state or the distribution of superfluid moment of inertia with vortex pinning energy has exceptional properties. However, a component in which the vortices are in almost exact corotation with the superfluid, and not with the solid crust, can have the appropriate relaxation

Testicular 17-ketosteroid reductase deficiency: cause of gynecomastia and hypogonadism in men

Testicular 17-ketosteroid reductase deficiency: cause of gynecomastia and hypogonadism in men

Anisotropic and gyrotropic version of Polder and van Santen's mixing formula

Abstract In order to account for the permittivity contrast between a host medium and inhomogeneities embedded in it the continuous rotating medium concept with a spatially random permittivity tensor ϵ0[ϵ(ω, r)δ ij +iα(ω, r)e ijl h l ) is introduced. Here ϵ(ω, r) is the dimensionless permittivity, α(ω, r)≡Ω (∂ϵ(ω, r)/∂ω), Ω (rad s−1) is the angular frequency of rotation of the random medium around the h axis and e ijl is the third rank antisymmetric tensor (the Levi-Civita tensor). Under this assumption and with the application of strong fluctuation theory and the bilocal approximation we find the effective permittivity tensor (EPT); in the low-frequency limit the quasistatic EPT represents the anisotropic and gyrotropic version of Polder and van Santen's mixing formula. In Nature there exists a large variety of rotating inhomogeneous media (millisecond pulsars, dust particles in air flowing in turbulent motion, polluted water in rotation). In order to demonstrate the gyrotropicity a simple laboratory expe...

Maximum rotation frequency of strange stars.

Using the MIT bag model of strange-quark matter, we calculate the maximum angular frequency of the uniform rotation of strange stars. After studying a broad range of the MIT bag-model parameters, we obtain an upper bound of 12.3 kHz.

Gyroviscous momentum transfer and toroidal rotation in Tokamaks with unbalanced NBI

Gyroviscous theory for the radial transport of toroidal momentum and the related theory for the poloidal variation of the angular rotation frequency in a Tokamak with strong rotation due to NBI are reviewed. Supporting theoretical and experimental evidence are cited. Stacey confirms that gyroviscosity can account for the momentum confinement times measured in Tokamak plasmas with directed NBI. A recent paper by Connor et al. (1987, ibid., vol.29, p.919, 1987) which arrived at a different conclusion and which criticized his theory is discussed.

Effect of beam self-rotation on a Čerenkov free-electron laser

At large beam currents, the beam space charge produces a radial electric field causing E×B rotation of the beam. As the beam travels through a partially dielectric loaded waveguide, it emits coherent Čerenkov radiation at frequencies ω=βvb+l(ωα/γ0), where l is the azimuthal mode number, ωα is the angular frequency of rotation, and β is the propagation constant.

The Modulation Component of Nystagmus during Earth-horizontal Rotation: Relationship with Gaze Angle

Periodic fluctuations in gaze angle and nystagmus slow phase velocity (SPV) were characterized using 6 normal subjects rotated at constant angular velocity about their rostral-caudal body axis with that axis in the horizontal orientation. The periodicity of the fluctuations corresponded to the angular frequency of rotation. The magnitude of the SPV fluctuations was moderately well correlated with those of the gaze fluctuations. Four vector quantities were found to characterize these data fairly completely, yet compactly.

A new carrier-domain mangnetometer

A rotating-carrier-domain magnetic-field sensor with zero threshold field is presented. The device is circular lateral bipolar transistor surrounded by four voltage probing contacts. In contrast to previous carrier-domain magnetometers with four-layer, thyristor-like structures, the present sensor has three layers, the crucial circular structure being determined by a single mask. The device operates in the collector-emitter breakdown regime with short-circuited emitter and base contacts. It is based by an external constant current source. If the current supplied to the collector is above a certain threshold value, a localized current domain develops in the base region and rotates spontaneously, even at zero magnetic field, with constant tangential velocity. The angular frequency of the carrier-domain rotation is modulated by a magnetic field perpendicular to the planar device surface. Sensitivity around zero field is 250 kHz/T. The over-all plot of the rotation velocity versus the magnetic field shows a hysteresis loop. The device behaviour is explained in terms of the temperature dependence of emitter-collector breakdown phenomena and the Lorentz force acting on the current domain.

Is the light cylinder the site of emission in pulsars?

There is no agreement in reports on the oblique-rotator model of pulsars1–9 as to the site of emission within the pulsar magnetosphere. It is generally assumed, however, that the plasma-electromagnetic fields constituting the magnetosphere obey the quasistatic constraint ∂f/∂t = -ω0∂f/∂φ, where ω0 is the angular frequency of rotation of the central neutron star, t the time, and the cylindrical coordinates (r, φ, z) refer to an inertial frame whose z-axis is coincident with the axis of rotation of the star. Accordingly, the pulsar emission is attributed to a source whose distribution has a rigidly rotating pattern; though, of course, none of the charged particles which constitute the source and provide the medium for the propagation of the pattern associated with the source, are themselves constrained to be co-rotating. Here, the spectral distribution of the power emitted by such a rotating pattern is calculated and it is shown that electromagnetic radiation of frequency to ω ≫ ω0, the observed radiation from pulsars, is produced predominantly by the electric currents at the light cylinder r = c/ω0 of the magnetosphere. This is a model-independent result; it is valid irrespective of the type of emission mechanism and applies to all previously proposed models of the magnetosphere which are quasistatic and in which the radial length scale of the plasma distribution is of the order of c/ω0.

Gravitational, Inertial and Toroidal Oscillations of the Outer Core and Their Related Free Wobbles

According to the respective restoring forces of self-gravitation, Coriolis force, and inertial coupling at the boundaries, the free oscillations of a contained fluid can be classified into gravitational, inertial, and toroidal oscillations. For the outer core of the Earth, however, due to the interplay of rotation, elasticity, and self-gravitation, the gravitational undertones and inertial oscillations are not distinguishable. Both have eigenfunctions consisting of spheroidal and toroidal parts of about equal amplitude, and exist in alternating allowed and forbidden zones depending on the gravitational stability of the outer core. The forbidden zones for a stable core correspond to the allowed zones for an unstable core, while for a neutrally stratified core there appear to be no forbidden zones. The eigenfunction of a toroidal mode consists essentially of a primary toroidal field and a secondary spheroidal component of the order of ellipticity, coupled at the outer core-mantle or outer core-inner core boundary. Therefore, in general, toroidal core modes appear in doublets Sn+1m Tnm and Sn−1m Tn−1m with degenerate frequency equal to 2m/n(n+1) times the angular frequency of rotation of the Earth. The ellipticities of the outer core boundaries are responsible for the removal of the degeneracy. It is shown that the primary toroidal and secondary spheroidal fields constitute the “generalized Poincare motion” which, for the fundamental mode S21T11, reduces to the “simple motion” defined by Poincare in 1910. Numerical solutions have been obtained for all three types of free core modes. While those for gravitational undertones and inertial oscillations are obtained by arbitrarily truncating the hydrodynamic equations, it is shown that the eigensolutions for toroidal modes are correct to first order in ellipticity due to the particular geometry of the outer core of the Earth.

Electrodynamics of rotating relativistic electron beams

On the basis of the Minkowski formulation, this paper discusses the basic laws governing the small-signal fields propagated along an electron beam which is rotating around its axis with constant angular frequency of rotation and drifting in the axial direction at constant relativistic velocity. In the first preliminary section are described the dc conditions for getting a stable relativistic electron beam in the presence of neutralizing ions with arbitrary number density and externally applied static magnetic field. Then, after a brief discussion of the ac-field equations, the constitutive relations for small-signal fields are obtained in both the laboratory frame, which is assumed to be an inertial frame, and the rest frame of the electron beam, which is not an inertial but a rotating frame. The rotating relativistic electron beam is found to be a nonuniformly moving dispersive medium or, more specifically, an inhomogeneous bianisotropic medium with space and time dispersion. With the use of the constitutive relations derived above, the following sections consider the energy and momentum for the small-signal fields, and their conservation relations, together with their transformation laws between the laboratory frame and the rest frame of the electron beam. Our discussion includes, as the special cases, all the important cases of an ion-neutralized or axially confined beam and the Brillouin beam.

NIRSE: Normal-incidence rotating-sample ellipsometer

We describe a normal-incidence rotating-sample ellipsometer (NIRSE) which is capable of measuring the ratio of the complex amplitude reflection coefficients ϱ of an anisotropic sample for incident light that is linearly polarized along two orthogonal principal axes in its surface. In the NIRSE, ϱ is derived from the normalized amplitudes of the Fourier components of a photoelectric signal at double and four times the angular frequency of sample rotation. The application of PIE (perpendicular-incidence ellipsometry) to anisotropic film-substrate systems is also discussed.

A Theory of Toroidal Core Oscillations of the Earth

A rotating incompressible fluid bounded by two concentric spherical rigid surfaces can exhibit purely toroidal free oscillations. The eigenfrequencies are fractions of the angular frequency of rotation. If the bounding surfaces are slightly ellipsoidal, secondary spheroidal fields become existent, and in general, a free mode splits into a doublet with one of which exists only when the inner bounding surface is present. For the real earth, the compressibility of the outer core, the elasticity of the solid earth, and the self-gravitation of the entire earth modify the toroidal core oscillations. The present treatment gives explicitly the effects of these parameters on the eigenfrequencies.

Stationary thread glow discharge

On the basis of new experimental results showing that a uniformly and slowly rotating regular thread is almost quasi-neutral and is difficult to influence by an external magnetic field, relations were derived which explain these phenomena. The angular frequency of rotation of a thread, derived from the equation of continuity, the equation for the momentum and from Poisson's equation, is dependent on the axial macroscopic velocity of negative ions, as has already been proved. At the same time conditions were obtained for the distribution of the space charge in the thread. It is seen that the quasi-neutrality is only very slightly disturbed.

Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation

THE nuclear magnetic resonance spectrum of a solid rotated at high speed consists of a narrowed central line and a set of side-spectra spaced at integral multiples of the rotation rate of either side1,2. The interaction energy between each pair on nuclear magnets in the solid contains the angular factor (3 cos2θ – 1), where θ is the angle between the internuclear vector and the applied field. When the solid rotates about an axis making an angle α with the applied field, the angular factor may be expressed3 as the sum of its mean value ½ (3 cos2 α – 1) (3 cos2 γ – 1), where γ is the angle between the internuclear vector and the axis of rotation, and two time-dependent terms, (3/2) sin 2α sin 2γ cos ωr t, and (3/2) sin2 α sin2 γ cos 2 ωr t, where ωr is the angular frequency of rotation. The two time-dependent terms lead to the formation of the side-spectra. It should be noted that when α is 90°, as in our earlier experiments1,2, the first of these terms is absent, so that side-spectra occur in this case at even multiples of ωr only ; for general α, the side-spectra occur at odd and even multiples of ωr. The form of the mean value of the angular factor for each nuclear pair leads to the conclusion that the central spectrum should have the shape found for the static crystal when the applied field is directed along the axis of rotation, but reduced in width by the factor ½ (3 cos2 α – 1), and having a second moment4 reduced by a factor ¼ (3 cos2 α – 1)2. Thus, in particular, when α has the value cos−1 (1/√3) = 54° 44′, the dipolar broadening of the central line should be removed5. With a speed of rotation large compared with the static line-width, the side-spectra will be displaced far from the centre and will be weak, leaving only a sharp central line broadened by residual non-dipolar causes.

On eddy currents in a rotating disk

A DEVICE which often occurs in electric machines and instruments consists of a relatively thin conducting disk rotating between the pole pieces of a permanent magnet or electromagnet. The author has received inquiries as to the method of calculating the paths of the eddy currents and the torque in such cases. The following rather simple method, which is quite accurate for a permanent magnet, seems not to be described in the literature. It assumes that the disk is so thin that the skin effect can be neglected. This is true for all frequencies that can be produced mechanically. To facilitate calculation in the special case of circular poles it is also assumed that 2πωabγ=εa is much less than one where ω is the angular frequency of rotation in radians per second, a the pole-piece radius, b the disk thickness, and γ the electric conductivity, all in centimeter-gram-second electromagnetic units. This produces a fractional error of less than εa in the eddy current densities and of less than (εa) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in the torque. In the case of the electromagnet the situation is complicated by the presence of the permeable pole pieces in the magnetic field of the eddy currents. This may send a large demagnetizing flux through the electromagnet. An approximate solution for this case will be considered.

On Eddy Currents in a Rotating Disk

A DEVICE which often occurs in electric machines and instruments consists of a relatively thin conducting disk rotating between the pole pieces of a permanent magnet or electromagnet. The author has received inquiries as to the method of calculating the paths of the eddy currents and the torque in such cases. The following rather simple method, which is quite accurate for a permanent magnet, seems not to be described in the literature. It assumes that the disk is so thin that the skin effect can be neglected. This is true for all frequencies that can be produced mechanically. To facilitate calculation in the special case of circular poles it is also assumed that 2πωabγ=ea is much less than one where ω is the angular frequency of rotation in radians per second, a the pole-piece radius, b the disk thickness, and γ the electric conductivity, all in centimeter-gram-second electromagnetic units. This produces a fractional error of less than ea in the eddy current densities and of less than (ea)2 in the torque. In the case of the electromagnet the situation is complicated by the presence of the permeable pole pieces in the magnetic field of the eddy currents. This may send a large demagnetizing flux through the electromagnet. An approximate solution for this case will be considered.