Showing papers on "Rotation published in 2019"

Slowing the spins of stellar cores

Abstract: The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler-Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.

Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects

Abstract: The properties of compact binaries, such as masses and spins, are imprinted in the gravitational waves (GWs) they emit and can be measured using parametrized waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3, which includes the effects of two independent spins in the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin frequency-dependent post-Newtonian rotation to describe precession effects, the improved model, IMRPhenomPv3, employs a double-spin rotation that is based on recent developments in the description of precessional dynamics. Besides double-spin precession, the improved model benefits from a more accurate description of precessional effects. We validate our new model against a large set of precessing numerical-relativity simulations. We find that IMRPhenomPv3 has better agreement with the inspiral portion of precessing binary-black-hole simulations and is more robust across a larger region of the parameter space than IMRPhenomPv2. As a first application we analyze the gravitational-wave event GW151226 with an efficient frequency-domain waveform model that describes two-spin precession. Within statistical uncertainty our results are consistent with published results. IMRPhenomPv3 will allow studies of the measurability of individual spins of binary black holes using GWs and can be used as a foundation upon which to build further improvements, such as modeling precession through merger, extending to higher multipoles, and including tidal effects.

Spin and orbital angular momenta of acoustic beams

Abstract: We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density caused by the local rotation of the vector velocity field. We show that the integral spin of a localized acoustic wave vanishes in agreement with the spin-0 nature of longitudinal phonons. We also show that the helicity or chirality density vanishes identically in acoustic fields. As an example, we consider nonparaxial acoustic Bessel beams carrying well-defined integer orbital angular momentum, as well as nonzero local spin density, with both transverse and longitudinal components. We describe the nontrivial polarization structure in acoustic Bessel beams and indicate a number of observable phenomena, such as nonzero energy density and purely circular transverse polarization in the center of the first-order vortex beams.

First Gaia Dynamics of the Andromeda System: DR2 Proper Motions, Orbits, and Rotation of M31 and M33

Abstract: The 3D velocities of M31 and M33 are important for understanding the evolution and cosmological context of the Local Group. Their most massive stars are detected by Gaia, and we use Data Release 2 (DR2) to determine the galaxy proper motions (PMs). We select galaxy members based on, e.g., parallax, PM, color-magnitude-diagram location, and local stellar density. The PM rotation of both galaxies is confidently detected, consistent with the known line-of-sight rotation curves: $V_{\rm rot} = -206\pm86$ km s$^{-1}$ (counter-clockwise) for M31, and $V_{\rm rot} = 80\pm52$ km s$^{-1}$ (clockwise) for M33. We measure the center-of-mass PM of each galaxy relative to surrounding background quasars in DR2. This yields that $({\mu}_{\alpha*},{\mu}_{\delta})$ equals $(65 \pm 18 , -57 \pm 15)$ $\mu$as yr$^{-1}$ for M31, and $(31 \pm 19 , -29 \pm 16)$ $\mu$as yr$^{-1}$ for M33. In addition to the listed random errors, each component has an additional residual systematic error of 16 $\mu$as yr$^{-1}$. These results are consistent at 0.8$\sigma$ and 1.0$\sigma$ with the (2 and 3 times higher-accuracy) measurements already available from Hubble Space Telescope (HST) optical imaging and VLBA water maser observations, respectively. This lends confidence that all these measurements are robust. The new results imply that the M31 orbit towards the Milky Way is somewhat less radial than previously inferred, $V_{\rm tan, DR2+HST} = 57^{+35}_{-31}$ km s$^{-1}$, and strengthen arguments that M33 may be on its first infall into M31. The results highlight the future potential of Gaia for PM studies beyond the Milky Way satellite system.

Dynamic Morphology and Swimming Properties of Rotating Miniature Swimmers With Soft Tails

Abstract: Helical microswimmers are suitable for propelling at low Reynolds numbers. To date, artificial microswimmers with rigid helical tails have been significantly developed. However, swimmers made of soft materials, which are more adaptive in confined or complex environments, are still lack of adequate investigation. In our previous studies, we demonstrated that a magnetically actuated swimmer with a plate soft tail could form a helical structure in a rotating magnetic field to propel itself at low Reynolds numbers. In this paper, we report the different dynamic morphologies formed by the soft tail of the swimmers during a simple rotation. We prove that the pitch length of the formed helical structure dynamically decreases with the rotation frequency. The formed helical structure collapses down to a cylindricallike structure, when the pitch gap of the soft tail decreases to zero. The corresponding rotation frequency is defined as a morphological step-out frequency, which is different from the magnetic step-out frequency in previous works. At the morphological step-out frequency, the swimmers performs a pure rotation without a forward propulsion, which is defined as a “dynamic stop.” The pitch length and the morphological step-out frequency increase with the rigidity of the tail. More interestingly, we found that if the rotation frequency keeps increasing, the swimmer may achieve a reverse propulsion without changing any other input parameters. The dynamic stop and reverse swimming cannot be observed if the soft tails are too long. We expect that the dynamic swimming phenomena found in the swimmers with soft tails can be used for agile and delicate motion control of soft miniature swimmers, which will be the base of numerous biomedical applications.

The eye of Gaia on globular clusters kinematics: internal rotation

Abstract: We derived the three-dimensional velocities of individual stars in a sample of 62 Galactic globular clusters using proper motions from the second data release of the Gaia mission together with the most comprehensive set of line-of-sight velocities with the aim of investigating the rotation pattern of these stellar systems. We detect the unambiguous signal of rotation in 15 clusters at amplitudes which are well above the level of random and systematic errors. For these clusters, we derived the position and inclination angle of the rotation axis with respect to the line of sight and the overall contribution of rotation to the total kinetic energy budget. The rotation strengths are weakly correlated with the half-mass radius, the relaxation time, and anticorrelated with the destruction rate, while no significant alignment of the rotation axes with the orbital poles has been observed. This evidence points towards a primordial origin of the systemic rotation in these stellar systems.

Observation of acoustic spin

Abstract: Unlike optical waves, acoustic waves in fluids are described by scalar pressure fields, and therefore are considered spinless. Here, we demonstrate experimentally the existence of spin in acoustics. In the interference of two acoustic waves propagating perpendicularly to each other, we observed the spin angular momentum in free space as a result of the rotation of local particle velocity. We successfully measured the acoustic spin, and spin-induced torque acting on a designed lossy acoustic probe that results from absorption of the spin angular momentum. The acoustic spin is also observed in the evanescent field of a guided mode traveling along a metamaterial waveguide. We found spin-momentum locking in acoustic waves whose propagation direction is determined by the sign of spin. The observed acoustic spin could open a new door in acoustics and its applications for the control of wave propagation and particle rotation.

Rotation Curve of the Milky Way from Classical Cepheids

Abstract: Flat rotation curves of spiral galaxies are considered as an evidence for dark matter, but the rotation curve of the Milky Way is difficult to measure. Various objects were used to track the rotation curve in the outer parts of the Galaxy, but most studies rely on incomplete kinematical information and inaccurate distances. Here, we use a sample of 773 Classical Cepheids with precise distances based on mid-infrared period-luminosity relations coupled with proper motions and radial velocities from Gaia to construct the accurate rotation curve of the Milky Way up to the distance of ~20 kpc from the Galactic center. We use a simple model of Galactic rotation to measure the rotation speed of the Sun Theta_0 = 233.6 +/- 2.8 km/s, assuming a prior on the distance to the Galactic center R_0 = 8.122 +/- 0.031 kpc from the Gravity Collaboration. The rotation curve at Galactocentric distances 4 12 kpc constructed so far.

Design of Microwave-Based Angular Displacement Sensor

Abstract: This letter presents a novel microwave-based rotation sensor having a wide dynamic range to detect and measure the angular displacement in terms of the change in resonant frequency. The proposed sensor is based on the microstrip technology, where a rotor comprised of a complementary split-ring resonator (CSRR) placed on the ground plane of the microstrip line is free to rotate around its axis. The mechanical rotation of CSRR determines a change in the cross coupling between the microstrip line and the CSRR, thus changing the overall inductance. The proposed planar unloaded microwave sensor, working around ISM band of 5.8 GHz, is quite sensitive to detect angular rotation in the wide dynamic range of 0°–90°. The linearity in dynamic range is achieved in the range of 30°–60°. Operating frequency and bandwidth can be adjusted by loading the rotor with dielectric. Depending on the type of dielectric loading of CSRR, it is possible to select the center frequency from a wide range of 4.67–5.94 GHz, with the bandwidth ranging from 116 to 250 MHz. Due to its features, the proposed sensor can be useful for various industrial applications.

A Liutex based definition and identification of vortex core center lines

Abstract: Six core issues for vortex definition and identification concern with (1) the absolute strength, (2) the relative strength, (3) the rotational axis, (4) the vortex core center, (5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the λ2 criterion and the λci criterion et al, are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.

Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold

Abstract: We review the geometric evolution of a linearly polarized light wave coupling into an optical fiber and the rotation of the polarization plane in the three dimensional semi-Riemannian manif...

Surface Rotation and Photometric Activity for Kepler Targets. I. M and K Main-sequence Stars

Abstract: Brightness variations due to dark spots on the stellar surface encode information about stellar surface rotation and magnetic activity. In this work, we analyze the Kepler long-cadence data of 26,521 main-sequence stars of spectral types M and K in order to measure their surface rotation and photometric activity level. Rotation-period estimates are obtained by the combination of a wavelet analysis and autocorrelation function of the light curves. Reliable rotation estimates are determined by comparing the results from the different rotation diagnostics and four data sets. We also measure the photometric activity proxy Sph using the amplitude of the flux variations on an appropriate timescale. We report rotation periods and photometric activity proxies for about 60 per cent of the sample, including 4,431 targets for which McQuillan et al. (2013a,2014) did not report a rotation period. For the common targets with rotation estimates in this study and in McQuillan et al. (2013a,2014), our rotation periods agree within 99 per cent. In this work, we also identify potential polluters, such as misclassified red giants and classical pulsator candidates. Within the parameter range we study, there is a mild tendency for hotter stars to have shorter rotation periods. The photometric activity proxy spans a wider range of values with increasing effective temperature. The rotation period and photometric activity proxy are also related, with Sph being larger for fast rotators. Similar to McQuillan et al. (2013a,2014), we find a bimodal distribution of rotation periods.

Period spacings of γ Doradus pulsators in the Kepler field: Rossby and gravity modes in 82 stars

Abstract: Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $\gamma$\,Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is seen. For each pattern, the mean pulsation period, the mean period spacing, and the slope are measured. We find that the slope correlates with the mean period for Rossby mode patterns. The traditional approximation of rotation is used to measure the near-core rotation rate, assuming the star rotates rigidly. We report the near-core rotation rates, the asymptotic period spacings, and the radial orders of excited modes of these 82 main-sequence stars. The near-core rotation rates lie between $0.6\,\mathrm{d^{-1}}$ and $2.3\,\mathrm{d^{-1}}$. Six stars show surface rotation modulations, among which only KIC\,3341457 shows differential rotation while the other five stars have uniform rotations. The radial orders of excited modes show different distributions for the dipole and quadrupole gravity modes versus the Rossby modes.

Inverse kinematics of a 5-axis hybrid robot with non-singular tool path generation

Abstract: This paper deals with non-singular tool path generation of a 5-axis hybrid robot named TriMule, which is designed for large part machining in situ. It is observed that at a singularity pose sudden changes occur in rotation of the C-axis and lengths of three telescopic legs. It is found that when the tool axis rotates about the axis normal to the plane expanded by the tool axis and the singular axis, the singular axis itself is forced to rotate simultaneously about the same axis in the opposite direction. This exploration enables the minimum rotation angle of the tool axis to be determined accurately for avoiding singularity and reducing machined surface errors caused by tool axis modification, leading to the development of an algorithm for non-singular tool path generation by modifying a partial set of the control points of B-splines. Both simulation and experiment on a prototype machine are carried out to verify the effectiveness of this approach.

Acoustical boundary hologram for macroscopic rigid-body levitation.

Abstract: In previous studies, acoustical levitation in the far-field was limited to particles. Here, this paper proposes the “boundary hologram method,” a numerical design technique to generate a static and stable levitation field for macroscopic non-spherical rigid bodies larger than the sound wavelength λ. This paper employs boundary element formulation to approximate the acoustic radiation force and torque applied to a rigid body by discretizing the body surface, which is an explicit function of the transducer's phase and amplitude. Then, the drive of the phased array is numerically optimized to yield an appropriate field that stabilizes the body's position and rotation. In experiments, this paper demonstrates the levitation in air of an expanded polystyrene sphere with a diameter of 3.5 λ and a regular octahedron with diagonal length of 5.9 λ, both located 24 λ from the acoustic elements, by a 40 kHz (λ = 8.5 mm) ultrasonic phased array. This method expands the variety of objects that can be levitated in the far-field of an ultrasonic phased array.

How to control single-molecule rotation.

Abstract: The orientation of molecules is crucial in many chemical processes. Here, we report how single dipolar molecules can be oriented with maximum precision using the electric field of a scanning tunneling microscope. Rotation is found to occur around a fixed pivot point that is caused by the specific interaction of an oxygen atom in the molecule with the Ag(111) surface. Both directions of rotation are realized at will with 100% directionality. Consequently, the internal dipole moment of an individual molecule can be spatially mapped via its behavior in an applied electric field. The importance of the oxygen-surface interaction is demonstrated by the addition of a silver atom between a single molecule and the surface and the consequent loss of the pivot point. The orientation of a molecule on a surface affects many processes, so the ability to control single-molecule rotation could be powerful. Here, the authors use the electric field from a scanning tunneling microscope tip to precisely induce unidirectional rotation of a polar molecule, allowing visualization of the molecule’s internal dipole moment.

Gravity-mode period spacings and near-core rotation rates of 611 γ Doradus stars with Kepler

Abstract: We report our survey of $\gamma$\,Doradus stars from the 4-yr \textit{Kepler} mission. These stars pulsate mainly in g modes and r modes, showing period-spacing patterns in the amplitude spectra. The period-spacing patterns are sensitive to the chemical composition gradients and the near-core rotation, hence they are essential for understanding the stellar interior. We identified period-spacing patterns in 611 $\gamma$\,Dor stars. Almost every star pulsates in dipole g modes, while about 30\% of stars also show clear patterns for quadrupole g modes and 16\% of stars present r mode patterns. We measure periods, period spacings, and the gradient of the period spacings. These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the Traditional Approximation of Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes. Most stars have a near-core rotation rate around $1$\,$\mathrm{c/d}$ and an asymptotic spacing around 4000\,s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. 11 stars show rotational splittings with fast rotation rates. We compared the observed slope--rotation relation with the theory and find a large spread. We detected rotational modulations in 58 stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5\%.

Autonomous Vehicles: Autodriver Algorithm and Vehicle Dynamics

Abstract: A given road can be expressed mathematically in a global (or world) coordinate frame. Following the road can be substituted by following the loci of its curvature center and turning at the right circle of curvature. Considering that a vehicle in motion is always in turn about an instantaneous rotation center relative to the ground, an autonomous vehicle capable of following a given path by coinciding the rotation center of vehicle at every moment on the curvature center of the road could be designed. The dynamic reactions of the vehicle influence its path of motion and make its rotation center to depart from the desired path of the curvature center of the road. In this study, the Autodriver algorithm control strategy to front-wheel-steering vehicles has been developed and a control loop is introduced to compensate the present errors generated by the differences of the desired locating on the road and the real position of the vehicle.

A chiral molecular propeller designed for unidirectional rotations on a surface.

Abstract: Synthetic molecular machines designed to operate on materials surfaces can convert energy into motion and they may be useful to incorporate into solid state devices. Here, we develop and characterize a multi-component molecular propeller that enables unidirectional rotations on a material surface when energized. Our propeller is composed of a rotator with three molecular blades linked via a ruthenium atom to a ratchet-shaped molecular gear. Upon adsorption on a gold crystal surface, the two dimensional nature of the surface breaks the symmetry and left or right tilting of the molecular gear-teeth induces chirality. The molecular gear dictates the rotational direction of the propellers and step-wise rotations can be induced by applying an electric field or using inelastic tunneling electrons from a scanning tunneling microscope tip. By means of scanning tunneling microscope manipulation and imaging, the rotation steps of individual molecular propellers are directly visualized, which confirms the unidirectional rotations of both left and right handed molecular propellers into clockwise and anticlockwise directions respectively. Controlling the rotation direction of individual molecular machines requires precise design and manipulation. Here, the authors describe a surface-adsorbed molecular propeller that, upon excitation with a scanning tunneling microscope tip, can rotate clockwise or anticlockwise depending on its chirality, and directly visualize its stepwise rotation with STM images.

A Nonlocal Shallow-Water Model Arising from the Full Water Waves with the Coriolis Effect

Abstract: In the present study a mathematical model of the equatorial water waves propagating mainly in one direction with the effect of Earth’s rotation is derived by the formal asymptotic procedures in the equatorial zone. Such a model equation is analogous to the Camassa–Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the Riccati-type differential inequality.

Asteroseismology of evolved stars to constrain the internal transport of angular momentum. I. Efficiency of transport during the subgiant phase

Abstract: Context: The observations of solar-like oscillations in evolved stars have brought important constraints on their internal rotation rates. To correctly reproduce these data, an efficient transport mechanism is needed in addition to meridional circulation and shear instability. Aims: We study the efficiency of the transport of angular momentum during the subgiant phase. Results: The precise asteroseismic measurements of both core and surface rotation rates available for the six Kepler targets enable a precise determination of the efficiency of the transport of angular momentum needed for each of these subgiants. These results are found to be insensitive to all the uncertainties related to the modelling of rotational effects before the post-main sequence phase. An interesting exception in this context is the case of young subgiants (typical values of log(g) close to 4), because their rotational properties are sensitive to the degree of radial differential rotation on the main sequence. These young subgiants constitute therefore perfect targets to constrain the transport of angular momentum on the main sequence from asteroseismic observations of evolved stars. As for red giants, we find that the efficiency of the additional transport process increases with the mass of the star during the subgiant phase. However, the efficiency of this undetermined mechanism decreases with evolution during the subgiant phase, contrary to what is found for red giants. Consequently, a transport process with an efficiency that increases with the degree of radial differential rotation cannot account for the core rotation rates of subgiants, while it correctly reproduces the rotation rates of red giant stars. This suggests that the physical nature of the additional mechanism needed for the internal transport of angular momentum may be different in subgiant and red giant stars.