Angular Rotation Rate Research Articles

Funnel Flows from Disks to Magnetized Stars

This work considers flows from an accretion disk corotating with the aligned dipole magnetic field of a rotating star. Ideal magnetohydrodynamics (MHD) is assumed with the pressure and density related as $p \propto \rho^\gamma$ and with $\rho {\bf v}^2 \ll {\bf B}^2/4\pi$, where ${\bf v}$ is the flow velocity. This limit corresponds to the Alfv\'en radius for the disk accretion larger than the corotation radius. Transonic flows, which go from subsonic motion near the disk to supersonic inflow near the star, are shown to be possible only for a narrow range of $R_d \sim r_c \equiv (GM/\Omega^2)^{1/3}$, where $R_d$ is the radius at which the dipole field line intersects the disk, $r_c$ the corotation radius, $M$ the mass of the star, and $\Omega$ its angular rotation rate. The transonic flows have very different behaviors for $\gamma > 7/5$ and $< 7/5$. In both cases, the plasma flow velocity ${\bf v}$ (which is parallel to ${\bf B}$) increases with decreasing distance $R$ from the star. However, for $\gamma >7/5$, the Mach number ${\cal M} \equiv |{\bf v}|/c_s$ (with $c_s$ the sound speed) initially increases with $R$ decreasing from $R_d$, but for $R$ decreasing from $\approx 0.22 R_d$ (for $\gamma=5/3$)the Mach number surprisingly {\it decreases}. In the other limit, $\gamma < 7/5$, ${\cal M}$ increases monotonically with decreasing $R$. Application of these results is made to funnel flows to rotating magnetized neutron stars and young stellar objects.

Stability of a Riemann S Ellipsoid with a Spheroidal Halo

The stability of Riemann S ellipsoids inside an oblate halo with respect to the second form of oscillations is investigated. It is shown that some ellipsoids with reverse internal circulation of matter, which are stable inside a spherical halo or in its absence, become unstable with respect to second “odd” forms of oscillation inside an oblate halo. Here there is asymmetry between conjugate ellipsoids from the standpoint of their stability. Only those conjugate ellipsoids that correspond to higher frequencies of reverse circulation of matter than their corresponding angular rotation rates are unstable. The domains of instability of “light” and “heavy” conjugate embedded ellipsoids are obtained as a function of the oblateness measure and relative density of the halo.

Energy cascade in a tornado wise flow generated by magnetic stirrer

The measurements of the limiting diffusion current and its fluctuations are used to study mass transfer near the stagnation region in a tornado wise flow generated by a magnetic rod stirrer. The paper aims to investigate what kind of information could be provided by the electrochemical method when the probe is submerged in the flow. The power spectral density (PSD) of the current pulsations was measured regard to three angular rotation rates of the stirrer and four different locations on a radius. The analysis of the PSD revealed that the resonance frequencies obeyed to a sub-harmonic interaction mechanism. The existence of the sub-harmonics with their odd harmonics testify the role of some entertained eddies. As for the order of magnitude of the time average value of mass transfer parameters, the diffusion layer thickness right to the electrode and the mass transfer coefficient were calculated respectively to be about 10 μm and 0.10 mm s −1. The turbulence intensity relative to the fluctuations of the limiting current, varies between 11% and 20%, in comparison with the value of 10% commonly retained in planar flows. These values seem account for the three-dimensional complexity of the flow.

Archival [ITAL]HST[/ITAL] and [ITAL]IUE[/ITAL] Study of the Dwarf Novae AH Herculis and CM Delphini: Exposed White Dwarfs?

We have analyzed Hubble Space Telescope (HST) archival and IUE NEWSIPS archival SWP spectra of the dwarf novae CM Del and AH Her obtained when AAVSO light-curve data indicated the occurrence of dwarf nova quiescence. We have computed synthetic, high-gravity spectra in LTE with solar composition using TLUSTY195 and SYNSPEC42 and have carried out fits of these models to the far-UV continuum and narrow absorption line spectra. For CM Del, we find that the far-UV spectrum is dominated by a hot (Teff = 22,000 K and log g = 8) white dwarf, but reliable information on the metal abundances is unavailable because of the quality of the data. For AH Her, we find evidence for a hot white dwarf with Teff = 27,000 K and log g = 8, with subsolar abundance for Si. An HST spectrum (GHRS G160M) of AH Her reveals blue-asymmetric Si IV profiles. If this is due to wind outflow, we derive a single-scattering, upper limit, mass-loss rate of 10-9 M⊙ yr-1. Synthetic profile fits to 12 co-added HST medium-resolution G160M spectra of the Si IV (1393, 1402 A) resonance doublet of CM Del yield a white dwarf rotational velocity estimate of v sin i = 400 km s-1 and Si/H = 1 times solar. The value of v sin i for CM Del is discussed in the context of angular momentum transfer and rotation rates for other cataclysmic variable, primary degenerate stars.

The motion and active deformation of India

Measurements of surface displacements using GPS constrain the motion and deformation of India and India‐Eurasia plate boundary deformation along the Himalaya. The GPS velocities of plate‐interior sites constrain the pole of the angular velocity vector of India with respect to Eurasia to lie at 25.6±1.0°N 11.1±9.0°E, approximately 6° west of the NUVEL‐1A pole of &lt;3 Ma plate motion. The angular rotation rate of 0.44 ±0.03°Myr−1 is 14% slower than the long‐term rate of 0.51° Myr−1. Insignificant velocities between plate interior sites indicate that the exposed Indian plate is stable to within 7 · 10−9 yr−1. The observed contraction vector across the Himalaya (≤20 mm/yr) veers from ∼N20°E in the northwest Himalaya to ∼N25°W in east Nepal, consistent with east‐west extension of southern Tibet.

An analytical theory of the morphology, flows, and shock compressions at corotating interaction regions in the solar wind

An analytical theory for the structure of corotating interaction regions (CIRs) in the solar wind is developed. First, an approximate stream interface is determined by mapping the curve dividing fast and slow streams at the solar wind source surface into the solar wind, at the slow solar wind speed assuming a constant angular rotation rate of the Sun. The flow of the fast wind then impinges on this surface, creating a quasi‐perpendicular reverse (forward) shock in the fast (slow) stream, deflections of the shocked fast and slow flows tangential to the interface, and a modified location of the interface. Assuming a locally planar geometry and weak shocks, analytical expressions are derived and presented for both shock compression ratios and for the north–south and east–west components of the shocked fast and slow streams. These are evaluated for two representative curves dividing fast and slow streams at the solar wind source surface. Numerical results are also presented for shocks which may not be approximated as weak. It is shown that the weak shock approximation is valid well beyond its formal limit of validity. For characteristic solar wind parameters the shock and flow parameters are presented as functions of heliocentric radial distance r and the inclination of the stream interface at the solar wind source surface. Shock and flow parameters are also shown for a simulated spacecraft observation of a CIR at r = 5 AU during a 26‐day solar rotation period. The results of the model for the shocks and flows associated with CIRs are in apparent general agreement with observations by Ulysses and other spacecraft.

Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory

In an earlier work we identi—ed a global, nonaxisymmetric instability associated with the presence of an extreme in the radial pro—le of the key function L(r) 4 (&)/i2)S2@! in a thin, inviscid, nonmagnetized accretion disk. Here &(r) is the surface mass density of the disk, )(r) is the angular rotation rate, S(r )i s the speci—c entropy, ! is the adiabatic index, and i(r) is the radial epicyclic frequency. The dispersion relation of the instability was shown to be similar to that of Rossby waves in planetary atmospheres. In this paper, we present the detailed linear theory of this Rossby wave instability and show that it exists for a wider range of conditions, speci—cally, for the case where there is a ii jump ˇˇ over some range of r in &(r) or in the pressure P(r). We elucidate the physical mechanism of this instability and its dependence on various parameters, including the magnitude of the ii bump ˇˇ or ii jump,ˇˇ the azimuthal mode number, and the sound speed in the disk. We —nd a large parameter range where the disk is stable to axisym- metric perturbations but unstable to the nonaxisymmetric Rossby waves. We —nd that growth rates of the Rossby wave instability can be high, for relative small jumps or bumps. We discuss possible D0.2) K conditions which can lead to this instability and the consequences of the instability. Subject headings: accretion, accretion diskshydrodynamicsinstabilitieswaves

Pulsar radio emission

A new version of the theory of pulsar radio emission is developed for the case of a coaxial rotator. It is based on the electric field that we established [G. S. Sahakian, Astrofizika, 37, 97 (1994)] for the radiation channel (the channel of open magnetic field lines) and on convenient approximations for the electron energy obtained in [G. S. Sahakian and E. S. Chubarian, Astrofizika, 37, 255 (1994)]. It is shown that, owing to the emission of photons of curvature radiation by particles, e → e+ħωc', and photon annihilation, ħωc → e+e− in the lower part of the radiation channel, a special region (the magnetic funnel) is formed in which vigorous cascade multiplication of particles occurs. The height of the magnetic funnel is h ≈ 6RΩ0.2, where R is the radius of the neutron star and Ω is its angular rotation rate. As a result of supersaturation of the plasma density in the magnetic funnel, a discharge occurs after each time intervalt≈5·10−7Ω−0.8B 12 −1.4 R 6 −0.2 , i.e., the longitudinal electric field disappears (B is the magnetic induction in the star). During the active radiative processes in the magnetic funnel, two main fluxes of particles with high ultrarelativistic energies are formed: an upward flux of electrons and a positron flux falling onto the star's magnetic cap. These fluxes are accompanied by narrow strips of positron and electron fluxes, respectively, of considerably lower energy, which are fairly powerful, coherent radio sources. The pulsar's radio luminosity is calculated to be L≈7.4·1022Ω3.8μ 30 3 R 6 −2 erg/sec, where μ=BR 3/2 is the star's magnetic moment. Comparing this result with observations, we conclude that the magnetic moment and hence the mass of the neutron star evidently must be considerably smaller, on the average, for fast pulsars than for slow ones. It is shown that the magnetic moment of the neutron star can be determined from the intervals between micropulses in the pulse profiles. The problem of the origin of the macrostructure of the radio pulse is discussed.

On the Twist of Emerging Flux Loops in the Solar Convection Zone

We perform numerical simulations of emerging flux loops in the solar convective envelope based on a weakly twisted thin flux tube model recently derived by Longcope and Klapper, generalizing the original formulation for the dynamics of untwisted thin flux tubes by Spruit. The generalized formulation includes the description of torsional Alf ven waves and takes into account the coupling of the writhing motion of the tube axis to the change in the flux tube twist based on the requirement of global helicity conservation of the closed thin flux tube. In this model, the twist of the thin flux tube is described by a quantity q defined as the angular rate of field-line rotation about the tube axis per unit length of the tube. We examine the evolution of twist along Ω-shaped emerging flux loops which are formed as a result of the non-linear growth of the Parker instability of toroidal magnetic flux tubes at the base of the solar convection zone. We find that: (1) In the northern hemisphere, a left-handed twist is generated in the flux tubes as a result of the right-handed tilt or writhe of the emerging loops induced by the Coriolis force. The generated twist increases with the latitude of emergence over the range from 0° to about 38° latitude, but then decreases when the emerging latitude exceeds 38°, because of a change in the preferred eruption pattern. The magnitude of the generated twist q is very small, ≗ 2 × 10-4 rad Mm-1, more than an order of magnitude smaller than the observed amplitude of twist (~ 0.01 rad Mm-1) in solar active regions. (2) For a toroidal flux ring with a uniform initial twist q 0 along the ring, the twist amplitude |q| at the apex of the emerging loop decrease by a factor of about 0.67 because of the stretching of the loop, as it rises from the base of the convection zone to about 20 Mm below the photosphere, at which depth the flux tube can no longer be considered thin. However, because of the more rapid increase of the tube cross-sectional radius a with height, |qa|, which corresponds to the ratio between the azimuthal field to the axial field B θ /B l of the tube, increases by a factor of about 2.5 at the apex of the loop, as it rises over the same distance. (3) Because of the effect of the Coriolis force, the distribution of twist along the emerging loop is asymmetric between the leading (in the direction of rotation) and the following sides of the loop. Both |q| and |qa| are greater at the following side than the leading at any depth. Based on the evolution of twist along emerging flux loops, we discuss possible constraints on the twist q 0 of initial toroidal flux tubes at the base of the convection zone.

Supercritical magnetoconvection in rapidly rotating planetary cores

Planetary magnetoconvection is highly supercritical ( R≫ R crit≈ E −1/3) in the rapidly rotating ( E≪1) planetary liquid cores where, depending on the planet, the Rayleigh R number is roughly between 10 10 and 10 22, while the Ekman E number is roughly between 10 −9 and 10 −17. In the bulk of the core, balance between Archimedean and Coriolis forces can be justified in order to determine typical hydromagnetic field values and symmetries via E, 1/ R≪1 that appear as asymptotically small parameters near the highest derivatives in the fully self-consistent planetary dynamo system. Archimedean or diffusive (thickness ∼ L/ R 1/3) boundary layers control typical velocity V *= R 2/3 κ/ L ( κ: diffusivity; L: core radius), that is about maximal velocity near the inner rigid core. Ekman–Hartmann (∼ LE 1/2) boundary layers control typical magnetic field that is B *=( SρΩ/ σ) 1/2 at core–mantle boundary if S≡ μ 0 σV * LE 1/2≤1 and B *= S( ρΩ/ σ) 1/2 otherwise. Here, ρ is the liquid core density, σ the conductivity and Ω the angular rotation rate of the mantle. Effective turbulent (hereafter burred) numbers ( Ē≈ E 1/2, R̄≈ R 1/3) and especially `secondary' turbulent numbers ( E ≈E 1/4 , R ≈R 1/9 ) have moderate values that are close to each other in different planets in contrast to the initial E, R there. That could explain close values of magnetic fields at the core–mantle boundaries in Earth, Jupiter, Saturn, Uranus and Neptune. Finally, an optimal planetary dynamo system is obtained with three (only!) initial or turbulent parameters: ( E, R, S), or ( Ē, R̄, S̄), or ( E , R , S ), those parameters are defined well via available planetary core models and the observed planetary magnetic fields. The optimal system can be easy integrated and should reproduce the observed fields in contrast to the recent very expensive numerical simulations. Those were not so effective have been using unphysical hyperdiffusivity and hyperviscosity. The conditions to gain some physical usage from the hypervalues was found here.

Electropolymerization of methacrylonitrile on a rotating disk electrode at high spinning rate

Abstract The electropolymerization of methacrylonitrile has been performed under voltammetric conditions on a rotating disk electrode (RDE) spinning at high angular rotation rate ( ω =10000 rpm) in anhydrous acetonitrile. The analysis of the electrode surface by X-ray photoelectron spectroscopy (XPS) and ellipsometry reveals that a grafted film of polymethacrylonitrile is present on the surface at the end of the synthesis. In addition, the polymer known to result from a polymerization in solution, which is usually (i.e. at ω =0) found on the surface before rinsing, is not present on the electrode. Estimations provided by the Navier–Stokes equation indicate that, at such high rotation rates, considerable convection effects are to be expected at distances from the surface of the order of 1 nm. These observations, combined with the fact that acetonitrile is an excellent solvent of polymethacrylonitrile, lead us to the proposal that the grafted polymer film is initiated directly on the surface, and may not result from an a posteriori precipitation of the polymer formed in solution.

MEMS inertial rate and acceleration sensor

Development of the μSCIRAS/sup TM/ (pronounced micro-Cyrus) multisensor for a period of over six years has produced a practical MEMS Inertial Measurement Unit (IMU). Using only three silicon sensors, a full-up IMU suitable for tactical grade navigation and guidance applications has been achieved. Iterative improvements in silicon sensor design and bulk micromachining processes have matured to the point where an IMU with an attractive price/performance ratio is now producible. This paper summarizes the design features and test results for an IMU with <100 deg/hr performance. Test results are shown for rate bias and acceleration bias over temperature. Production of this initial member of the μSCIRAS product family begins this year to support applications including guided artillery shells, technology insertion to decrease missile costs, navigation of remotely-piloted vehicles, dismounted soldier location devices and other navigation aids. The small size of this silicon multisensor and its ability to measure both angular rotation rate and linear acceleration provides a useful advantage in product packaging, cost, size, and system testing. The μSCIRAS Inertial Sensor Assembly (ISA) is housed in a 2 cubic inch package weighing less than 5 ounces (140 grams) requires less than 0.8 Watts of power. Continuing development will lead to greatly improved performance on the order of 1 deg/hr at low prices in high-volume production.

Energetics of galactic nuclei

A model of compact galactic nuclei in statistical equilibrium was developed in [L. Sh. Grigorian and G. S. Sahakian, Astrofizika (in press)]. It was shown that they should consist predominantly of neutron stars (pulsars) and white dwarfs. The problem of the energy reserves of galactic nuclei is discussed in terms of this concept. The mechanism of conversion of a white dwarf into a neutron star due to the accretion of interstellar matter is considered. This means that a galactic nucleus has an energy reserve of some 5·1060 N8 erg (N is the number of stars in the nucleus). It is shown that galactic nuclei are powerful sources of hard γ radiation [power L » 2·1044µ30N8(Ω/50)17/7 erg/sec, where µ is the magnetic moment and Ω is the angular rotation rate of a neutron star ] due to curvature radiation from relativistic electron fluxes flowing along channels of open magnetic field lines of pulsars. The x-ray and ultraviolet emission are due to synchrotron emission from the same electron fluxes in the magnetic field of the galactic nucleus (L » 1042-1044 erg/sec). The optical (visible and infrared) and radio emission are due to bremsstrahlung from electrons in the interstellar medium [L » 6·1046N82 (5/Rpc)3 erg/sec, where R is the radius of the galactic nucleus]. An equation is obtained for the magnetic moment of a pulsar: µ ≈ 3.4·10-5LγP17/7, where P is the pulsar’s period and L03B3; is the luminosity of the pulsar’s y radiation.

Evolution of Secondary Electron Emission Characteristics of Spacecraft Surfaces

Helical Motion In this motion, the center of gravity of the  ight vehicle traverses a helical  ight path.The longitudinalaxis of the vehicle is orientated in the same directionas the axis of the helix but displacedfrom it by a constantdistance.A Ž xed body axial spin rate equal to the angular rate of rotation of the helical  ight path is present. The resulting motion is sometimes referred to as lunar motion because the same surface of the body is always orientated toward the central axis of the maneuver; in aircraft maneuver terminology it is equivalent to a barrel roll. A three-dimensional view of the motion is given in Fig. 4. Again, with gravity neglected, we can write u D w D 0; P u D P v D P w D 0, and q D r D 0. It follows that XF D YF D 0 and that ZF D pv. Because is now 0 deg, d3⁄4=dt ; P ®, and R are all zero. This result is again consistent with that predicted by Eqs. (4–6), (10), and (11). Note that, because of the presence of axial spin, this is not the same case as that considered in Ref. 2.

Main stages of evolution of matter in the universe. I

A possible scenario for the evolution of the universe following the big bang at t > 10-5 sec is considered. The necessary conditions that must be present for the formation of stars and stellar systems to be possible are formulated. As a condition for the formation of stars we take kTs≤ GMsmp(3R), and for stellar systems HR ≲ (GM/R)1/2, where Ts is the temperature of the cosmic plasma, mp is the mass of a proton, Ms is the mass of a star, M is the mass of a stellar cluster, R is the radius of these celestial bodies, and H is the bubble parameter for the corresponding time. In accordance with these criteria, we assume that in the course of cosmological expansion, neutron stars should have been formed first (times 2.10-4 ≲ t ≲ 1 sec, densities 0.07 ≲ ρB≲ 2.104 g/cm3) and then, in chronological order, appeared white dwarfs (t ≈ 102 sec, ρB ≲ 5.10-3 g/cm3), ordinary stars (t ≈ 4.106 sec, ≲B ≈ 10-11 g/cm3), galactic nuclei (t ≈ 3.1011 sec, ≲B ≈ 5.10-19 g/cm3, globular clusters (t ≈ 1013 sec, ≲B ≈ 4.10-21 g/cm3), and galaxies (t ≈ 1015 sec, ≲B ≈ 10-24 g/cm3), where ≲B is the average density of ordinary (baryon) matter in the universe. It is shown that a galactic nucleus is a stellar system in statistical equilibrium and consists mainly of neutron stars and white dwarfs. The formation of some pulsars (neutron stars with angular rotation rates 1 v0, where v0 is the velocity corresponding to the work function 2GMMs/R, M being the mass and R the radius of the Galaxy’s nucleus.

Efficient streamline, streamribbon, and streamtube constructions on unstructured grids

Streamline construction is one of the most fundamental techniques for visualizing steady flow fields. Streamribbons and streamtubes are extensions for visualizing the rotation and the expansion of the flow. The paper presents efficient algorithms for constructing streamlines, streamribbons, and streamtubes on unstructured grids. A specialized Runge-Kutta method is developed to speed up the tracing of streamlines. Explicit solutions are derived for calculating the angular rotation rates of streamribbons and the radii of streamtubes. In order to simplify mathematical formulations and reduce computational costs, all calculations are carried out in the canonical coordinate system instead of the physical coordinate system. The resulting speed up in overall performance helps explore large flow fields.

Pulsar radio emission. I. Oblique rotator

The problem of pulsar radio emission for the case of a coaxial rotator was investigated in our preceding paper [G. S. Sahakian, Astrofizika,38, 143 (1995)]. In this paper it is solved for the realistic case in which the star's magnetic axis does not coincide with its rotational axis (an inclined rotator). It is shown that above the star's magnetic cap a special region, called a magnetic funnel, is formed in which vigorous processes of particle multiplication occur. The height of this region is h ≈ 8·106Ω0.2μ301/3R61.3 cm and its radius r(Ωr/c)0.5 depends little on the inclination angle a (Ω is the angular rotation rate, μ is the magnetic moment, R is the star's radius, and r is distance from the center of the star). It is shown that the pulsar radio emission is produced in the magnetic funnel. Here, in the course of active radiative processes, two main particle fluxes with a high ultrarelativistic energy are formed: an upward electron flux and a positron flux falling onto the star's magnetic cap. These main fluxes are accompanied by individual narrow strips of positron and electron fluxes with a relatively low energy, which are fairly powerful, coherent radio sources. Such secondary fluxes are formed immediately after the annihilation of photons of curvature radiation emitted by particles of the main fluxes. The pulsar's radio luminosity is estimated to be L≈7.4·1023Ω3.52μ308/3 ψ(a), where ψ(a) is a known function (ψ≈1 for a<50°). Equating the theoretical and observed radio luminosities L and L0, we obtain the formula μ30≈P1.32R60.4(2.1·10−27L0/ψ)3/8 for the magnetic moment of the pulsar's neutron star, where P is the pulsar's period. The magnetic moments of slow pulsars calculated from this formula turn out to be considerably larger than those of fast pulsars. This means that the masses of slow pulsars are larger, on the average, than those of fast pulsars. The magnetic funnel operates with interruptions, periodically undergoing a discharge, so that the production of pulsar radio emission operates with interruptions. The durations of the production of radio emission and of the interruptions between those processes are on the order of h/c≈2.7·10−4Ω0.2μ301/3 sec, i.e., pulsar radio emission has a microstructure. Consequently, a study of the microstructure of the profiles of observed radio pulses enables one to obtain additional information about the magnetic moments of the neutron stars.

Micromachined rate and acceleration sensor having vibrating beams

Apparatus is disclosed for measuring the specific force and angular rotation rate of a moving body. A silicon substrate has first and second substantially planar and substantially parallel surfaces. An accelerometer is formed of the substrate and has a force sensing axis. An output signal is provided which is indicative of the moving body along the force sensing axis. The accelerometer is mounted so as to be movable along a vibration axis perpendicular to the force sensing axis. The accelerometer is driven so as to impart a dithering motion thereto of a predetermined frequency along the vibration axis. The accelerometer includes a frame, a proof mass and a hinge interconnected between the frame and the proof mass for rotating the proof mass about a hinge axis when the moving body is subjected to a force along the force sensing axis. The accelerometer further includes at least one vibrating beam having first and second ends respectively coupled to the frame and the proof mass, a longitudinal axis disposed perpendicular to the force sensing axis and the vibration axis, and a conductive path disposed along the vibrating beam. The hinge axis is substantially parallel to the vibration axis. A signal generator applies a periodic drive signal to the conductive path. The periodic drive signal has a resonant frequency that is a function of the force applied along the force sensing axis to the moving body.

Micromachined rate and acceleration sensor

A sensor (10) is disclosed for measuring the specific force and angular rotation rate of a moving body and is micromachined from a silicon substrate (16). First and second accelerometers (32a and b) are micromachined from the silicon substrate (16), each having a force sensing axis (38) and producing an output signal of the acceleration of the moving body along its force sensing axis (38). The first and second accelerometers (32a and b) are mounted within the substrate (16) to be moved along a vibration axis (41). The first and second accelerometers (32a and b) are vibrated or dithered to increase the Coriolis component of the output signals from the first and second accelerometers (32a and b). A sinusoidal drive signal of a predetermined frequency is applied to a conductive path (92) disposed on each of the accelerometers. Further, magnetic flux is directed to cross each of the conductive paths (92), whereby the interaction of the magnetic flux and of the drive signal passing therethrough causes the desired dithering motion. A link (72) is formed within the silicon substrate (16) and connected to each of the accelerometers (32a and b), whereby motion imparted to one results in a like, but opposite motion applied to the other accelerometer (32). Further, a unitary magnet (20) and its associated flux path assembly direct and focus the magnetic flux through the first and second accelerometers (32a and b) formed within the silicon substrate (16).

Spin-up/spin-down of magnetized stars with accretion discs and outflows

An investigation is made of disk accretion of matter onto a rotating star with an aligned dipole magnetic field. A new aspect of this work is that when the angular velocity of the star and disk differ substantially we argue that the $\bf B$ field linking the star and disk rapidly inflates to give regions of open field lines extending from the polar caps of the star and from the disk. The open field line region of the disk leads to the possibility of magnetically driven outflows. An analysis is made of the outflows and their back affect on the disk structure assuming an ``$\ap$" turbulent viscosity model for the disk and a magnetic diffusivity comparable to this viscosity. The outflows are found to extend over a range of radial distances inward to a distance close to $r_{to}$, which is the distance of the maximum of the angular rotation rate of the disk. We find that $r_{to}$ depends on the star's magnetic moment, the accretion rate, and the disk's magnetic diffusivity. The outflow regime is accompanied in general by a spin-up of the rotation rate of the star. When $r_{to}$ exceeds the star's corotation radius $r_{cr} = (GM/\om_*^2)^{1\ov 3}$, we argue that outflow solutions do not occur, but instead that ``magnetic braking" of the star by the disk due to field-line twisting occurs in the vicinity of $r_{cr}$. The magnetic braking solutions can give spin-up or spin-down (or no spin change) of the star depending mainly on the star's magnetic moment and the mass accretion rate. For a system with $r_{to}$ comparable to $r_{cr}$, bimodal behavior is possible where extraneous perturbations cause the system to flip between spin-up and spin-down.