Change In Angular Momentum Research Articles

Destruction of star clusters due to the radial migration in spiral galaxies

Abstract Most stars in galactic discs are believed to be born as a member of star clusters or associations. Star clusters formed in discs are disrupted due to the tidal stripping and the evolution of star clusters themselves, and as a result new stars are supplied to the galactic discs. We performed N-body simulations of star clusters in galactic discs, in which both star clusters and galactic discs are modelled as N-body (‘live’) systems, and as a consequence the discs form transient and recurrent spiral arms. In such non- steady spiral arms, star clusters migrate radially due to the interaction with spiral arms. We found that the migration time-scale is a few hundred Myr and that the angular momentum changes of star clusters are at most ∼50 per cent in 1 Gyr. Radial migration of star clusters to the inner region of galaxies results in a fast disruption of the star clusters because of a stronger tidal field in the inner region of the galaxy. This effect is not negligible for the disruption time-scale of star clusters in galactic discs. Stars stripped from clusters form tidal tails which spread over 1–2 kpc. While the spatial distribution of tidal tails changes in a complicated way due to the non-steady spiral arms, the velocity distribution conserves well even if the tidal tails are located at a few kpc from their parent clusters. Tidal tails of clusters in galactic discs might be detected using velocity plots.

Extreme-mass-ratio inspiral corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole

This is the first of two papers on computing the self-force in a radiation gauge for a particle of mass $\mathfrak{m}$ moving in circular, equatorial orbit about a Kerr black hole. In the extreme-mass-ratio inspiral (EMRI) framework, with mode-sum renormalization, we compute the renormalized value of the quantity $H\ensuremath{\mathrel{:=}}\frac{1}{2}{h}_{\ensuremath{\alpha}\ensuremath{\beta}}{u}^{\ensuremath{\alpha}}{u}^{\ensuremath{\beta}}$, gauge-invariant under gauge transformations generated by a helically symmetric gauge vector; here, ${h}_{\ensuremath{\alpha}\ensuremath{\beta}}$ is the metric perturbation, ${u}^{\ensuremath{\alpha}}$ the particle's 4-velocity. We find the related order $\mathfrak{m}$ correction to the particle's angular velocity at fixed renormalized redshift (and to its redshift at fixed angular velocity), each of which can be written in terms of $H$. The radiative part of the metric perturbation is constructed from a Hertz potential that is extracted from the Weyl scalar by an algebraic inversion T. S. Keidl et al., Phys. Rev. D 82, 124012 (2010). We then write the spin-weighted spheroidal harmonics as a sum over spin-weighted spherical harmonics $_{s}Y_{\ensuremath{\ell}m}$ and use mode-sum renormalization to find the renormalization coefficients by matching a series in $L=\ensuremath{\ell}+1/2$ to the large-$L$ behavior of the expression for $H$. The nonradiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Kerr gauge.

Collision-induced stimulated photon echo at the transition 0–1

The stimulated photon echo formed by the sequence of three laser excitation pulses in a gaseous medium on the transition with the angular momentum change Ja = 0 → Jb = 1 is considered with an account of elastic depolarizing collisions. The polarization properties of this echo may be potentially interesting for the purposes of data processing. It is shown that with the polarization of the first pulse orthogonal to that of the second and third pulses, the appearance of the echo signal will be entirely determined by the action of collisions. The existence of this echo is determined by the difference in the alignment Γ(2)b and the orientation Γ(1)b relaxation rates of the excited level.

Idealized models for galactic disc formation and evolution in ‘realistic’ ΛCDM haloes

We study the dynamics of galactic disc formation and evolution in ‘realistic’ Λ cold dark matter haloes with idealized baryonic initial conditions. We add rotating spheres of hot gas at z = 1.3 to two fully cosmological dark-matter-only halo (re)simulations. The gas cools according to an artificial and adjustable cooling function to form a rotationally supported galaxy. The simulations evolve in the full cosmological context until z = 0. We vary the angular momentum and density profiles of the initial gas sphere, the cooling time and the orientation of the angular momentum vector to study the effects on the formation and evolution of the disc. The final discs show exponential radial and (double)-exponential vertical stellar density profiles, and stellar velocity dispersions that increase with age of the stars, as in real disc galaxies. The slower the cooling/accretion processes, the higher the kinematic disc-to-bulge (D/B) ratio of the resulting system. We find that the initial orientation of the baryonic angular momentum with respect to the halo has a major effect on the resulting D/B. The most stable systems result from orientations parallel to the halo minor axis. Despite the spherical and coherently rotating initial gas distribution, the orientation of the central disc and of the outer gas components, and the relative angle between the components can all change by more than 90° over several billion years. Initial orientations perpendicular to the major axis tend to align with the minor axis during their evolution, but the sign of the spin can have a strong effect. Discs can form from initial conditions oriented parallel to the major axis, but there is often strong misalignment between inner and outer material. The more the orientation of the baryonic angular momentum changes during the evolution, the lower the final D/B. The behaviour varies strongly from halo to halo. Even our very simple initial conditions can lead to strong bars, dominant bulges, massive, misaligned rings and counter-rotating components. We discuss how our results may relate to the failure or success of fully cosmological disc formation simulations.

Radial migration in disc galaxies - I. Transient spiral structure and dynamics

We seek to understand the origin of radial migration in spiral galaxies by analyzing in detail the structure and evolution of an idealized, isolated galactic disk. To understand the redistribution of stars, we characterize the time-evolution of properties of spirals that spontaneously form in the disk. Our models unambiguously show that in such disks, single spirals are unlikely, but that a number of transient patterns may coexist in the disk. However, we also show that while spirals are transient in amplitude, at any given time the disk favors patterns of certain pattern speeds. Using several runs with different numerical parameters we show that the properties of spirals that occur spontaneously in the disk do not sensitively depend on resolution. The existence of multiple transient patterns has large implications for the orbits of stars in the disk, and we therefore examine the resonant scattering mechanisms that profoundly alter angular momenta of individual stars. We confirm that the corotation scattering mechanism described by Sellwood & Binney (2002) is responsible for the largest angular momentum changes in our simulations.

How does the tennis serve technique influence the serve-and-volley?

In tennis, a high ball velocity and a fast run toward the net are key features to successful performance of “serve-and-volley” players. For the serve, tennis players can use two techniques: the foot-up (FU) or foot-back (FB) technique. The aim of this study was to determine if the running time toward the net after the serve and the ball velocity (Vball) vary between these two techniques. Moreover we analysed the angular momentum values of the trunk and of the arm holding the racquet. Fifteen expert tennis players performed six successful serve-and-volleys with both techniques. Running time to the net is significantly lower for FB, whereas Vball is significantly higher for FU. Trunk and arm angular momentums about the transverse axis are significantly higher with FU before ball impact. A significant correlation (r = 0.81, P < 0.001) exists between changes in the maximal trunk angular momentum and in running time to the net between the two serve techniques. A significant correlation (r = 0.84, P < 0.001) also exists between changes in the maximal trunk angular momentum and in Vball between the two serve techniques. According to these results, FB is the best technique for moving as quickly as possible to the net because of a lower trunk angular momentum.

A momentum-based balance controller for humanoid robots on non-level and non-stationary ground

A momentum-based balance controller controls a humanoid robot to maintain balance. The balance controller derives desired rates of change of linear and angular momentum from desired motion of the robot. The balance controller then determines desired center of pressure (CoP) and desired ground reaction force (GRF) to achieve the desired rates of change of linear and angular momentum. The balance controller determines admissible CoP, GRF, and rates of change of linear and angular momentum that are optimally close to the desired value while still allowing the robot to maintain balance. The balance controller controls the robot to maintain balance based on a human motion model such that the robot's motions are human-like. Beneficially, the robot can maintain balance even when subjected to external perturbations, or when it encounters non-level and/or non-stationary ground.

Implementation of gravitational shocks in two-dimensional Fokker-Planck models

We derive analytical formulae for drift and dispersion terms of energy and angular momentum (� ΔE� , � (ΔE) 2 � , � ΔJ� ,a nd� (ΔJ) 2 � )a s well as their cross term (� ΔEΔJ� ) for stellar systems under an impulsive perturbation. These terms are expressed as functions of E, J, and orbit averages of powers of radius (r) and the product of radius and velocity (rv), and we confirm our formulae with a numerical simulation. Then with another numerical simulation for a time-varying (Gaussian) perturbation, we find that the adiabatic corrections suggeted by Gnedin and Ostriker can be applied not only to the energy changes (drift and dispersion) but also tothe angular momentum changes, if the changes are expressed as functions of energy only. The corrections do not describe the changes accurately when the changes are considered as functions of both energy and angular momentum. The deviations between the numerical simulation and analytical expectations are consierable only in the cluster core though, where the effect of perturbation is relatively weaker. These results are to be implemented in two-dimensional (E − J) Fokker-Planck models of the evolution of globular clusters.

Internal Flow and Axial Thrust Balancing of a Rocket Pump

Large axial thrust is produced on the rotor assembly of high-pressure rocket pumps. Thus, to ensure the reliability of bearings supporting the high rotational speed rotor, precise axial thrust balancing is essential. To realize complete axial thrust balancing, the back shroud of the main impeller is employed as the balance piston of a self-balancing type axial thrust balancing system in which the rotor assembly moves axially to compensate unbalance axial force. In this balancing system, which is often applied, complicated internal flow characteristics and pressure distributions are very important for predicting the precise characteristics of the axial thrust produced by the system. In the present study, a calculation method for analyzing the internal flow system taking into account effects of boundary layer conditions and angular momentum change in the impeller side-chambers is applied to the system combining the balance piston and grooves on the casing wall of the balance piston chamber. The analysis program is able to detect phenomena which could not be captured in past calculations and is effective for calculating internal flow characteristics much faster than possible with CFD analysis. A combination of balance piston and grooves on the casing wall of the balance piston chamber was confirmed to be suitable for extending the dynamic range of axial thrust balancing although installation of the grooves increased the leakage flow rate and friction torque at the same time.

Radial migration in galactic thick discs

We present a study of the extent to which the Sellwood & Binney radial migration of stars is affected by their vertical motion about the midplane. We use both controlled simulations in which only a single spiral mode is excited, as well as slightly more realistic cases with multiple spiral patterns and a bar. We find that rms angular momentum changes are reduced by vertical motion, but rather gradually, and the maximum changes are almost as large for thick disc stars as for those in a thin disc. We find that particles in simulations in which a bar forms suffer slightly larger angular momentum changes than in comparable cases with no bar, but the cumulative effect of multiple spiral events still dominates. We have determined that vertical action, and not vertical energy, is conserved on average during radial migration.

Intersystem Crossing Involving Strongly Spin Exchange-Coupled Radical Ion Pairs in Donor–bridge–Acceptor Molecules

Intersystem crossing involving photogenerated strongly spin exchange-coupled radical ion pairs in a series of donor-bridge-acceptor molecules was examined. These molecules have a 3,5-dimethyl-4-(9-anthracenyl)-julolidine (DMJ-An) donor either connected directly or connected by a phenyl bridge (Ph), to pyromellitimide (PI), 1 and 2, respectively, or naphthalene-1,8:4,5-bis(dicarboximide) (NI) acceptors, 3 and 4, respectively. Femtosecond transient optical absorption spectroscopy shows that photodriven charge separation produces DMJ(+•)-PI(-•) or DMJ(+•)-NI(-•) quantitatively in 1-4 (τ(CS) ≤ 10 ps), and that charge recombination occurs with τ(CR) = 268 and 158 ps for 1 and 3, respectively, and with τ(CR) = 2.6 and 10 ns for 2 and 4, respectively. Magnetic field effects (MFEs) on the neutral triplet state yield produced by charge recombination were used to measure the exchange coupling (2J) between DMJ(+•) and PI(-•) or NI(-•), giving 2J > 600 mT for 1-3 and 2J = 170 mT for 4. Time-resolved electron paramagnetic resonance (TREPR) spectroscopy revealed that the formation of (3)*An upon charge recombination occurs by spin-orbit charge transfer intersystem crossing (SOCT-ISC) and/or radical-pair intersystem crossing (RP-ISC) mechanisms with the magnitude of 2J determining which triplet formation mechanism dominates. SOCT-ISC is the exclusive triplet formation mechanism in 1-3, whereas both RP-ISC and SOCT-ISC are active for 4. The triplet sublevels populated by SOCT-ISC in 1-4 depend on the donor-acceptor geometry in the charge separated state. This is consistent with the fact that the SOCT-ISC mechanism requires the relevant donor and acceptor orbitals to be nearly perpendicular, so that electron transfer results in a large orbital angular momentum change that must be compensated by a fast spin flip to conserve overall system angular momentum.

Modeling of Cross-Coupling Responses on Hingeless Helicopters via Gyroscopic Effect

The perplexing cross-coupled responses between the control axes on hingeless helicopters have puzzled researchers for years. Unlike previous studies, which introduced a physically meaningless phase-lag to account for the cross-couplings, this paper proposes a new method to relate both on-axis and off-axis responses by the gyroscopic moments through the actuation mechanism of hingeless helicopters. This new method allows investigators to directly and analytically quantify the debatable cross-coupling due to the complex actuation of the rotor. This method is based on the fact that when the angular momentum of the spinning rotor is disturbed by an incremental lift along the main blades due to the varying cyclic pitch angle controlled by the servo mechanisms, off-axis moments are induced to counteract the changes in angular momentum according to the principles of the gyroscope, and hence these gyroscopic moments directly exhibit on-axis responses. This new method yields a parametric framework for examining the previously unexplained cross-coupled responses of hingeless helicopters and demonstrates that, in addition to aerodynamics, intricate dynamic nonlinearities also occur due to non-intuitive actuation mechanisms on the rotor of hingeless helicopters. Finally, simulations and experiments were performed to validate the proposed modeling method.

Changes in angular momentum during curved sprinting in Track and Field

Changes in angular momentum during curved sprinting in Track and Field

GPDs AND TMDs

For transversely polarized nucleons the distribution of quarks in the transverse plane is transversely shifted and that shift can be described in terms of Generalized Parton Distributions (GPDs). This observation provides a 'partonic' derivation of the Ji-relation for the quark angular momentum in terms of GPDs. Wigner distributions are used to show that the difference between the Jaffe-Manohar definiton of quark orbital angular momentum and that of Ji is equal to the change of orbital angular momentum due to the final state interactions as the struck quark leaves the target in a DIS experiment.

Seasonal excitation of polar motion

We estimate geophysical excitations (χ1 and χ2) of polar motion using multiple sources of data, including recent atmospheric, oceanic, and hydrological models, satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE), and compare geophysical excitations with observed polar motion excitations from space geodetic techniques. At seasonal time scales, both model-estimated excitations from the geophysical fluids envelope (i.e., atmosphere, ocean, and hydrosphere) and GRACE-observed excitations agree remarkably well with polar motion observations in the χ2 component, and in the χ1 component, model estimates and observed geodetic excitations show significant discrepancies. However, mass excitations estimated from GRACE show significantly better agreement with observed excitations than those from models, especially in χ1, due to better quantification of terrestrial water storage and oceanic mass changes using GRACE data. Furthermore, GRACE satellite gravity measurements offer a unique means for quantifying contributions from cryospheric angular momentum (CAM) change, a component mostly neglected in previous studies due to the lack of adequate observations or reliable ice sheets models. Based on GRACE estimates, CAM excitations appear a minor, but not negligible contributor to seasonal excitations of polar motion. The significantly better agreement in χ2 (than that in χ1) between observations and model excitations is related to the higher sensitivity of χ2 excitations to atmospheric pressure and terrestrial water changes over the Eurasia and North American continents, because of the special relationship between the ΔS21 spherical harmonic coefficient (proportional to χ2) mass model and the locations of the two continents.

Experimental study of linear magnetic dichroism in photoionization satellite transitions of atomic rubidium

Laser orientation in the initial state has been used to study the properties of satellite transitions in inner-shell photoionization of rubidium atoms. The linear magnetic dichroism in the angular distribution (LMDAD) has been utilized to probe the continuum waves of orbital angular momentum conserving monopole, and angular momentum changing conjugate satellites, accompanying the $4p$ ionization of atomic Rb. We show experimentally that LMDAD of both types of satellite transitions is nonzero and that LMDAD of monopole satellites, measured as a function of photon energy, mimics the LMDAD of direct photoionization, whereas the LMDAD of conjugate transitions deviates drastically from that trend. The results indicate that conjugate transitions cannot be described theoretically without explicit inclusion of electron-electron interaction. The present data can thus be used as a very precise test of current models for photoionization.

Transitions in Zr, Hf, Ta, W, Re, Hg, Ac, and U ions with high sensitivity to variation of the fine-structure constant

We study transitions between ground and low-energy excited states of heavy ions corresponding to $s\ensuremath{-}d$ single-electron transitions or ${s}^{2}\ensuremath{-}{d}^{2}$ double-electron transitions. The large nuclear charge $Z$ and significant change in angular momentum of electron orbitals make these transitions highly sensitive to a potential variation in the fine-structure constant $\ensuremath{\alpha}$. The transitions may be considered as candidates for laboratory searches for space-time variation of $\ensuremath{\alpha}$.

Dynamic switching of the chiral beam on the spiral plasmonic bull’s eye structure [Invited

A polarization-dependent switchable plasmonic beaming structure composed of metallic hole surrounded by double spiral dielectric gratings is proposed. The main mechanism of the proposed structure is based on the angular momentum change of surface plasmon caused by the spiral geometry. On- and off-states of the proposed device are determined by the condition whether the rotating direction of incident polarization is the same as or opposite of the direction of the spiral rotations. Qualitative analytical expressions of the switching mechanisms and full-vectorial numerical results are presented.

Ensemble Kalman-Filtering of Earth rotation observations with a global ocean model

We study the changes in ocean angular momentum which lead to changes in the Earth's rotation. The focus lies on the consistency of model, model-forcing and observations. To check this consistency an ensemble-based Kalman-Filter approach was applied to ocean angular momentum time series which we derived from Earth rotation observations. The filter propagates a reduced rank error-covariance matrix with an optimal ensemble. This way, a complex system like the utilized global ocean circulation model can be assimilated with 32 ensemble members only. The Kalman-Filter improved the ocean-model's trajectory with respect to the observations, i.e., the observed ocean angular momentum was better reproduced by our model. A subsequent analysis of the changes which were induced by the filter revealed that the utilized atmospheric forcing is insufficient. When the filter is not entitled to change the forcing fields no improvement in the model trajectory was possible.

Lateral Friction in Reduced-Gravity Models: Parameterizations Consistent with Energy Dissipation and Conservation of Angular Momentum

AbstractThe f-plane reduced-gravity model has been extended with the parameterization of lateral friction in the momentum equations. The parameterization should preferably fulfill some requisites. One of them is that in the absence of external torques the change in angular momentum should be determined by boundary conditions alone. Internal torques should balance in the angular momentum budget. This requirement is fulfilled when the parameterization in the vertically integrated momentum equations is the divergence of a symmetric stress tensor. These equations solve for the mean transport, which includes implicitly the eddy-induced contribution. Another requirement on the parameterization of lateral stress follows from considering that it should imply kinetic energy dissipation. Both requirements fail with a commonly used parameterization and are fulfilled with the one proposed by C. Schär and R. B. Smith, which also is in near agreement with derivations of the shallow-water equations via vertical integrations of the Navier–Stokes equations. Here, the authors show two other parameterizations that are consistent with the angular momentum and energy requirements. One of the parameterizations follows from the symmetric component of a stress tensor in agreement with the parameterization shown by P. R. Gent to be energetically consistent. The other parameterization is related to the so-called biharmonic dissipation. In general, the difficulty for friction parameterizations is on the energy dissipation requirement, because the one on angular momentum is easily fulfilled.