Measured Rotation Rates Research Articles

Basic Properties of Rotary Dynamics of the Molecular Motor Enterococcus hirae V1-ATPase

V-ATPases are rotary molecular motors that generally function as proton pumps. We recently solved the crystal structures of the V1 moiety of Enterococcus hirae V-ATPase (EhV1) and proposed a model for its rotation mechanism. Here, we characterized the rotary dynamics of EhV1 using single-molecule analysis employing a load-free probe. EhV1 rotated in a counterclockwise direction, exhibiting two distinct rotational states, namely clear and unclear, suggesting unstable interactions between the rotor and stator. The clear state was analyzed in detail to obtain kinetic parameters. The rotation rates obeyed Michaelis-Menten kinetics with a maximal rotation rate (Vmax) of 107 revolutions/s and a Michaelis constant (Km) of 154 μM at 26 °C. At all ATP concentrations tested, EhV1 showed only three pauses separated by 120°/turn, and no substeps were resolved, as was the case with Thermus thermophilus V1-ATPase (TtV1). At 10 μM ATP (<<Km), the distribution of the durations of the ATP-waiting pause fit well with a single-exponential decay function. The second-order binding rate constant for ATP was 2.3 × 10(6) M(-1) s(-1). At 40 mM ATP (>>Km), the distribution of the durations of the catalytic pause was reproduced by a consecutive reaction with two time constants of 2.6 and 0.5 ms. These kinetic parameters were similar to those of TtV1. Our results identify the common properties of rotary catalysis of V1-ATPases that are distinct from those of F1-ATPases and will further our understanding of the general mechanisms of rotary molecular motors.

Multidimensional gray-wavelet processing in interferometric fiber-optic gyroscopes

A multidimensional signal processing method for a single interferometric fiber-optic gyroscope (IFOG) is proposed, to the best of our knowledge, for the first time. The proposed method, based on a novel IFOG structure with quadrature demodulation, combines a multidimensional gray model (GM) and a wavelet compression technique for noise suppression and sensitivity enhancement. In the IFOG, two series of measured rotation rates are obtained simultaneously: an in-phase component and a quadrature component. Together with the traditionally measured rate, the three measured rates are processed by the combined gray-wavelet method. Simulations show that the intensity noise and non-reciprocal phase fluctuations are effectively suppressed by this method. Experimental comparisons with a one-dimensional GM(1, 1) model show that the proposed three-dimensional method achieves much better denoising performance. This advantage is validated by the Allan variance analysis: in a low-SNR (signal-to-noise ratio) experiment, our method reduces the angle random walk (ARW) and the bias instability (BI) from 1 × 10−2 deg h−1/2 and 3 × 10−2 deg h−1 to 1 × 10−3 deg h−1/2 and 3 × 10−3 deg h−1, respectively; in a high-SNR experiment, our method reduces the ARW and the BI from 9 × 10−4 deg h−1/2 and 5 × 10−3 deg h−1 to 4 × 10−4 deg h−1/2 and 3 × 10−3 deg h−1, respectively. Further, our method increases the dimension of the state-of-the-art IFOG technique from one to three, thus obtaining higher IFOG sensitivity and stability by exploiting the increase in available information.

Rotaphone, a mechanical seismic sensor system for field rotation rate measurements and its in situ calibration

A newly developed mechanical sensor system, called a Rotaphone, for recording rotation rate components is described. The sensor system is based on measurements of the differential motions between paired low-frequency geophones attached to a rigid skeleton. The same differential velocity (and, consequently, the same rotation rate component) is obtained from more than one geophone pair, which allows for in situ calibration and matching of the individual sensors. The calibration method, which is a key point of our methodology, is explained in detail and demonstrated on synthetic examples. The instrument and the calibration technique were also subjected to laboratory testing utilizing a rotational shaking table. Some results of these tests are presented in comparison to the data from a reference sensor (fiber optic gyroscope). The new rotational seismic sensor system is characterized by a flat frequency response over a wide range from 2 to 200 Hz and sensitivity limit of the order of 10 − 8 rad/s. Its advantages are small size, portability, and easy installation and operation in the field. We present several examples of the vertical rotation rate ground motion recorded at Nový Kostel station (Czech Republic): first, a group of records of local micro-earthquakes which occurred in West Bohemia/Vogtland in May 2010 and, second, a record due to an anthropogenic source, a quarry blast at the nearby Vintiřov quarry recorded in June 2010. The measured rotation rates are of order between 10 − 6 for the local earthquakes and 10 − 7 rad/s for the blast. These measurements demonstrate that the instrument has much wider application than just prospecting measurements, for which it was originally designed.

Regularities in frequency spacings of δ Scuti stars: the Kepler star KIC 9700322★

In the faint star KIC 9700322 observed by the Kepler satellite, 76 frequencies with amplitudes from 14 to 29000 ppm were detected. The two dominant frequencies at 9.79 and 12.57 c/d (113.3 and 145.5 \mu Hz), interpreted to be radial modes, are accompanied by a large number of combination frequencies. A small additional modulation with a 0.16 c/d frequency is also seen; this is interpreted to be the rotation frequency of the star. The corresponding prediction of slow rotation is confirmed by a spectrum from which v sin i = 19 \pm 1 km/s is obtained. The analysis of the spectrum shows that the star is one of the coolest {\delta} Sct variables. We also determine Teff = 6700 \pm 100 K and log g = 3.7 \pm 0.1, compatible with the observed frequencies of the radial modes. Normal solar abundances are found. An \ell = 2 frequency quintuplet is also detected with a frequency separation consistent with predictions from the measured rotation rate. A remarkable result is the absence of additional independent frequencies down to an amplitude limit near 14 ppm, suggesting that the star is stable against most forms of nonradial pulsation. The frequency spectrum of this star emphasizes the need for caution in interpreting low frequencies in {\delta} Sct stars as independent gravity modes. A low frequency peak at 2.7763 c/d in KIC 9700322 is, in fact, the frequency difference between the two dominant modes and is repeated over and over in various frequency combinations involving the two dominant modes. The relative phases of the combination frequencies show a strong correlation with frequency, but the physical significance of this result is not clear.

Control of atomic path in projectile cold atom gyroscope

Cold atoms possess low velocity, narrow velocity distribution as well as good matter wave coherence, thus they have been used to achieve cold atom interferometers. The interferometers with Sagnac effect form atom gyroscopes which can measure rotation rate accurately. Here we report our recent progress in building a projectile cold atom gyroscope. We achieve the accurate control of the bidirectional projectile cold atom motion through the use of a homemade direct digital frequency synthesizer.

A laboratory model of Saturn’s North Polar Hexagon

A hexagonal structure has been observed at ∼76°N on Saturn since the 1980s (Godfrey, D.A. [1988]. Icarus 76, 335–356). Recent images by Cassini (Baines, K., Momary, T., Roos-Serote, M., Atreya, S., Brown, R., Buratti, B., Clark, R., Nicholson, P. [2007]. Geophys. Res. Abstr. 9, 02109; Baines, K., Momary, T., Fletcher, L., Kim, J., Showman, A., Atreya, S., Brown, R., Buratti, B., Clark, R., Nicholson, P. [2009]. Geophys. Res. Abstr. 11, 3375) have shown that the feature is still visible and largely unchanged. Its long lifespan and geometry has puzzled the planetary physics community for many years and its origin remains unclear. The measured rotation rate of the hexagon may be very close to that of the interior of the planet ( Godfrey, D.A. [1990]. Science 247, 1206–1208; Caldwell, J., Hua, X., Turgeon, B., Westphal, J.A., Barnet, C.D. [1993]. Science 206, 326–329; Sánchez-Lavega, A., Lecacheux, J., Colas, F., Laques, P. [1993]. Science 260, 329–332), leading to earlier interpretations of the pattern as a stationary planetary wave, continuously forced by a nearby vortex (Allison, M., Godfrey, D.A., Beebe, R.F. [1990]. Science 247, 1061–1063). Here we present an alternative explanation, based on an analysis of both spacecraft observations of Saturn and observations from laboratory experiments where the instability of quasi-geostrophic barotropic (vertically uniform) jets and shear layers is studied. We also present results from a barotropic linear instability analysis of the saturnian zonal wind profile, which are consistent with the presence of the hexagon in the North Pole and absence of its counter-part in the South Pole. We propose that Saturn’s long-lived polygonal structures correspond to wavemodes caused by the nonlinear equilibration of barotropically unstable zonal jets.

Effect of internal gravitational coupling on Titan's non‐synchronous rotation

Variations in the spin period of Titan have been detected by the Cassini radar observations. Angular momentum exchange between Titan's surface and the atmosphere over seasonal time scales corresponding to Saturn's orbital period of 29.5 year is the most likely cause of the observed non‐synchronous rotation. The measured rotation rate can be explained if Titan's icy crust is rotationally decoupled from the interior in the presence of a subsurface ocean. However, we show that Titan is likely to rotate almost as a rigid body even when it has an internal ocean because of a substantial internal gravitational coupling between the crust and the interior. The predicted surface rotation rate will be further reduced due to Saturn's torque, but can approach to the observed value if other factors, such as larger atmospheric torque, smaller equatorial flattening or viscous relaxation of the icy crust are considered.

1145 高粘性環境におけるスピロヘータの運動効率の向上(J04-1 生物の運動機能/バイオミメティクスとバイオメカニクス/バイオロボティクスとバイオメカトロニクス(1),J04 生物の運動機能/バイオミメティクスとバイオメカニクス/バイオロボティクスとバイオメカトロニクス)

The motility of spirochete improves in viscous environments. Such phenomena cannot be observed in the macroscopic world. One of the authors has proposed a hypothesis that predicts increase of the motion efficiency with the viscosity because the polymer molecules form a quasi-rigid network. To examine the hypothesis experimentally, we simultaneously measured the swimming speeds and rotation rates of a spirochete Brachyspira pilosicoli in polymer solutions by two-directional-illuminated dark-field microscopy (2DDM), which is an originally developed method to measure rotation rate of a helical body. This experimental result illustrated increase of the motion efficiency with viscosity. Therefore, we concluded that the improvement of spirochete motility in viscous environments at least partly relates with increase of the motion efficiency caused by a quasi-rigid network of polymer molecules.

Measuring the Oblateness and Rotation of Transiting Extrasolar Giant Planets

We investigate the prospects for characterizing extrasolar giant planets by measuring planetary oblateness from transit photometry and inferring planetary rotational periods. The rotation rates of planets in the solar system vary widely, reflecting the planets' diverse formational and evolutionary histories. A measured oblateness, assumed composition, and equation of state yields a rotation rate from the Darwin-Radau relation. The light curve of a transiting oblate planet should differ significantly from that of a spherical one with the same cross-sectional area under identical stellar and orbital conditions. However, if the stellar and orbital parameters are not known a priori, fitting for them allows changes in the stellar radius, planetary radius, impact parameter, and stellar limb-darkening parameters to mimic the transit signature of an oblate planet, diminishing the oblateness signature. Thus, even if HD 209458b had an oblateness of 0.1 instead of our predicted 0.003, it would introduce a detectable departure from a model spherical light curve at the level of only one part in 105. Planets with nonzero obliquity break this degeneracy because their ingress light curve is asymmetric relative to that from egress and their best-case detectability is of order 10-4. However, the measured rotation rate for these objects is nonunique due to degeneracy between obliquity and oblateness and the unknown component of obliquity along the line of sight. Detectability of oblateness is maximized for planets transiting near an impact parameter of 0.7, regardless of obliquity. Future measurements of oblateness will be challenging because the signal is near the photometric limits of current hardware and inherent stellar noise levels.

Digitally processed, phase-reading fibre gyroscope

We present a simple digital processing method that provides a significant improvement for the performance of a phase-reading open-loop fibre-optic gyroscope. The phase-reading gyroscope measures the angular speed in terms of a phase difference between the two counter-propagating beams in the Sagnac interferometer. Instead of electronic phase meters we use a very simple PC-based digital process which computes the Sagnac phase. With this method we measure rotation rates down to 100°h −1. The errors of this scheme are studied for different signal-to-noise ratios and the number of bits of the analog-to-digital converter.

Deformation across the forearc of the Cascadia subduction zone at Cape Blanco, Oregon

Over the interval 1992–1999 the U.S. Geological Survey measured the deformation of a geodetic array extending N80°E (approximate direction of plate convergence) from Cape Blanco on the Oregon coast to the volcanic arc near Newberry Crater (55 and 350 km, respectively, from the deformation front). Within about 150 km from the deformation front, the forearc is being compressed arcward (N80°E) by coupling to the subducting Juan de Fuca plate. Dislocation modeling of the observed N80°E compression suggests that the main thrust zone (the locked portion of the Juan de Fuca‐forearc interface) is about 40 km wide in the downdip direction. The transverse (N10°W) velocity component of the forearc measured with respect to the fixed interior of North America decreases with distance from the deformation front at a rate of about 0.03 mm yr−1 km−1. That gradient appears to be a consequence of rigid rotation of the forearc block relative to fixed interior North America (Euler vector of 43.4°±0.1°N, 120.0°±0.4°W, and −1.67±0.17 ° (m.y.)−1; quoted uncertainties are standard deviations). The rotation rate is similar to the paleomagnetically measured rotation rate (−1.0±0.2 °(m.y.)−1) of the 15 Ma lava flows along the Columbia River 250 km farther north. The back arc does not appear to participate in this rotation but rather is migrating at a rate of about 3.6 mm yr−1 northward with respect to fixed North America. That migration could be partly an artifact of an imperfect tie of our reference coordinate system to the interior of North America.

Presupernova Evolution of Rotating Massive Stars. I. Numerical Method and Evolution of the Internal Stellar Structure

The evolution of rotating stars with zero-age main-sequence (ZAMS) masses in the range 8-25 M☉ is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70% of breakup. The stars rotate rigidly on the ZAMS as a consequence of angular momentum redistribution during the pre-main-sequence evolution. Redistribution of angular momentum and chemical species are then followed as a consequence of Eddington-Sweet circulation, Solberg-Hoiland instability, the Goldreich-Schubert-Fricke instability, and secular and dynamic shear instability. The effects of the centrifugal force on the stellar structure are included. Convectively unstable zones are assumed to tend toward rigid rotation, and uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (nonmagnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlying material of 1016-1017 cm2 s-1. These values are insensitive to the initial angular momentum and to uncertainties in the efficiencies of rotational mixing. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to breakup. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.

Solar Rotation Measurements at Mount Wilson over the Period 1990–1995

One of the most fundamental properties of the Sun is its rate of rotation. Kinetic energy of large-scale circulation might interact with rotation and cause the surface rate to vary throughout the solar cycle. The solar wind carries off angular momentum from the Sun, and the coupling between the outer and inner parts of the heliosphere might produce effects that are evident in the photosphere and chromosphere. The quadrapole moment of Sun's gravitational potential depends on the rotation rate. The interaction between rotation, convection, and solar magnetic fields forms the solar dynamo which governs the solar cycle of activity. Although the rate of solar rotation has been measured for decades, several key questions remain: What is the rotation rate, and what is the uncertainty in this value? Does the rotation rate depend on the solar cycle? Can the gradient of rotation rate as a function of distance from the solar center be detected within the solar atmosphere? The synoptic program of solar observations carried out at the 150 foot tower of the Mount Wilson Observatory has long been a source of measurements which address these questions. Improvements in the facilities of this program over the past decade have led to a reduction in the errors of measurement which now permit a new examination of these questions. Key improvements were: 12/81?installation of a fiber-optic image reformattor to select the spectral sampling of the absorption lines; 2/86?multiple daily observations were begun; 12/87?the Cr II line at ?5237.3 was added to the regular program of observation; 9/90?the grating mount and alignment system were replaced; 7/91?the polarization analysis optics were placed in a new alignment box and index matching fluid was introduced around the KDP variable retarder; 11/95?antireflection optics were installed for the KDP end windows to reduce interference fringes. Each of these changes resulted in a noticeable reduction in the rms error in the measured rotation rate which is now at the level of 7 m s-1. Within this error we find that there is no solar cycle variation in the rotation rate and the rate is the same for both ?5250 and ?5237. We find that the synodic rotation rate is 2.84 ? 0.01 ?rad s-1. This value agrees well with most recent determinations.

Rotation Measurement and Control of Optically Trapped Particles

When a particle of isotropic shape is trapped by a convergent laser beam, it begins to rotate around itself. This self-rotation is caused by the torque resulting from total forces acting on the particle surface. We have developed a method to quickly and automatically measure the rotation rate from temporal variation of the light scattered from the particle. The rotation rate is derived from the period of the intensity variation. The rotation rate can be measured up to 3000rpm. The rotation rate that has been proportional to the trapping beam power is feedback controlled by a loop connecting the measured rotation rate and the trapping beam power.

Measurement and Control of Optically Induced Rotation of Anisotropic Shaped Particles

When a particle of anisotropic shape is trapped by a laser beam, it generally begins to rotate around itself. This self-rotation is caused by the torque resulting from total forces acting on the particle surface. We have measured the rotation rate rapidly and automatically from temporal variation of light scattered from the rotating particle. The rotation rate, which could be measured up to 2200 rpm, has been shown to be linearly dependent on the power of the trapping beam. We controlled the rotation rate by a feedback loop connecting the measured rotation rate and the trapping beam power.

Effect of a depolarizer in a fibre-optic gyroscope with a 3 × 3 coupler

We present a simple digital processing method that provides a significant improvement for the performance of a phase-reading open-loop fibre-optic gyroscope. The phase-reading gyroscope measures the angular speed in terms of a phase difference between the two counter-propagating beams in the Sagnac interferometer. Instead of electronic phase meters we use a very simple PC-based digital process which computes the Sagnac phase. With this method we measure rotation rates down to 100°h−1. The errors of this scheme are studied for different signal-to-noise ratios and the number of bits of the analog-to-digital converter.

Rotation rates of small magnetic features from two- and one-dimensional cross-correlation analyses

We present results of an analysis of 628 high-resolution magnetograms taken daily with the NSO Vacuum Telescope on Kitt Peak from 1975 to 1991. Motions in longitude on the solar surface are determined by a two-dimensional cross-correlation analysis of consecutive day pairs. We find that the measured rotation rate of small magnetic features, i.e., excluding active regions, is in excellent agreement with the results of the previous one-dimensional analysis of the same data (Komm, Howard, and Harvey, 1993). The polynomial fits show magnetic torsional oscillations, i.e., a more rigid rotation during cycle maximum and a more differential rotation during cycle minimum, but with smaller amplitudes than the one-dimensional analysis. The full width at half maximum of the cross-correlations is almost constant over latitude which shows that the active regions are effectively excluded. The agreement between the one- and two-dimensional cross-correlation analyses shows that the two different techniques are consistent and that the large-scale motions can be divided into rotational and meridional components that are not affected by each other.

Rotational dating of middle-aged stars

By the age of about 100 million years, the rotational velocity of solar mass stars becomes independent of the initial rotation rate on the main sequence, due to the strong dependence of the angular momentum loss rate on the rotation rate; once this common value is reached, the rotation velocity depends only on time and the mass of the star. Thus, the measured rotation rate of a low-mass star provides an estimate of its age when its mass is known. The observed rotation periods of low-mass stars in the Hyades are used to test this conclusion and to check the validity of the theoretical angular momentum loss rates. Adapting the magnetic braking model of Kawaler (1988), the angular momentum loss rate is integrated to derive a relation between rotation period and age, and this relation is converted to a period-age-color relation using simple stellar models. Using this method, a mean rotational age for the Hyades is obtained which is in close agreement with the age determined by isochrone fitting.

THE SYNCHRONOUS ROTATION OF IOTA PEGASI.

ABSTRACT Measured rotation rates of the spectroscopic binary stars ι Peg A (6.5±0.3 km s-1) and B(5±1 km s-1) are found to be equal to the orbital synchronization values. The question of whether synchronization has actually occurred is discussed and the evidence is found to favor the hypothesis.

Solar rotation results at Mount Wilson

We publish here rotation results from Doppler velocity measurements made at Mount Wilson over a period of more than 14 years. Altogether data from 188 rotations are presented. These results are displayed in various tables and figures. Measurements of scattered light along with its effect on the measured rotation rate are shown.