The trapezoidal collinear four-body problem

On the four-body problem in the Born–Oppenheimer approximation

Most stars form as part of a stellar group. These young stars are mostly surrounded by a disk from which potentially a planetary system might form. Both, the disk and later on the planetary system, may be affected by the cluster environment due to close fly-bys. The here presented database can be used to determine the gravitational effect of such fly-bys on non-viscous disks and planetary systems. The database contains data for fly-by scenarios spanning mass ratios between the perturber and host star from 0.3 to 50.0, periastron distances from 30 au to 1000 au, orbital inclination from 0∘ to 180∘ and angle of periastron of 0∘, 45∘ and 90∘. Thus covering a wide parameter space relevant for fly-bys in stellar clusters. The data can either be downloaded to perform one’s own diagnostics like for e.g. determining disk size, disk mass, etc. after specific encounters, obtain parameter dependencies or the different particle properties can be visualized interactively. Currently the database is restricted to fly-bys on parabolic orbits, but it will be extended to hyperbolic orbits in the future. All of the data from this extensive parameter study is now publicly available as DESTINY.

A study of the influence of the sun on optimal two-impulse Earth-to-Moon trajectories with moderate time of flight in the three-body and four-body models

Observational and theoretical investigations provide evidence for non-uniform spot and magnetic flux distributions on rapidly rotating stars, which have a significant impact on their angular momentum loss rate through magnetised winds. Supplementing the formalism of MacGregor & Brenner (1991) with a latitude-dependent magnetised wind model, we analyse the effect of analytically prescribed surface distributions of open magnetic flux with different shapes and degrees of non-uniformity on the rotational evolution of a solar-like star. The angular momentum redistribution inside the star is treated in a qualitative way, assuming an angular momentum transfer between the rigidly-rotating radiative and convective zones on a constant coupling timescale of 15 Myr; for the sake of simplicity we disregard interactions with circumstellar disks. We find that non-uniform flux distributions entail rotational histories which differ significantly from those of classical approaches, with differences cumulating up to 200% during the main sequence phase. Their impact is able to mimic deviations of the dynamo efficiency from linearity of up to 40% and nominal dynamo saturation limits at about 35 times the solar rotation rate. Concentrations of open magnetic flux at high latitudes thus assist in the formation of very rapidly rotating stars in young open clusters, and ease the necessity for a dynamo saturation at small rotation rates. However, since our results show that even minor amounts of open flux at intermediate latitudes, as observed with Zeeman-Doppler imaging techniques, are sufficient to moderate this reduction of the AM loss rate, we suggest that non-uniform flux distributions are a complementary rather than an alternative explanation for very rapid stellar rotation.

In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).

Even when the crystal structure and alloy composition are fixed, the arrangement of different atoms on crystal sites can significantly affect material properties and formation processes. To address this, we have been developing a research framework called Material Configurations Informatics (MCI), which focuses on the degrees of freedom in atomic configurations through computational science and machine learning approaches. With increasing computational power, large-scale first-principles calculations (DFT) have become feasible. However, the biggest challenge in MCI is the enormous number of possible atomic configurations. We tackle this problem using techniques such as efficient sampling via Bayesian optimization and interaction modeling with approaches like the Ising model. In this presentation, we introduce applications of MCI to issues such as the mixing of different surface reconstructions—an important factor in discussions of crystal growth processes—and the study of semiconductor properties in 2D alloy materials.

Context. The recent and exquisite astrometric, photometric, and radial velocity measurements of the Gaia mission resulted in a substantial advancement of the determination of the orbits for old star clusters, including the oldest Milky Way globular clusters (MW GCs). Aims. The main goal of the present paper is to use the new Gaia data release 3 (DR3) and the VISTA Variables in the Via Láctea Extended Survey (VVVX) measurements to obtain the orbits for nearly a dozen new MW GC candidates that have been poorly studied or previously unexplored. Methods. We use the Gaia DR3 and VVVX databases to identify bona fide MW GC candidates, namely VVV-CL160, Patchick 122, Patchick 125, Patchick 126, Kronberger 99, Kronberger 119, Kronberger 143, ESO 92-18, ESO 93-08, Gaia 2, and Ferrero 54. The relevant mean cluster physical parameters are derived (distances, Galactic coordinates, proper motions, radial velocities). We also measure accurate mean radial velocities for the GCs VVV-CL160 and Patchick 126 using observations acquired at the Gemini-South telescope with the Immersion GRating INfrared Spectrometer (IGRINS) high-resolution spectrograph. Orbits for each cluster are then computed using the GravPot16 model, assuming typical Galactic bar pattern speeds. Results. We reconstruct the orbits for these 11 star clusters for the first time. These include star clusters with retrograde and prograde orbital motions, both in the Galactic bulge and disk. We obtain orbital properties for this sample, such as the mean time-variations of perigalactic and apogalactic distances, eccentricities, vertical excursions from the Galactic plane, and Z-components of the angular momentum. Conclusions. Our main conclusion is that, based on the orbital parameters, Patchick 125 and Patchick 126 are genuine MW bulge or halo GCs; and Ferrero 54, Gaia 2, and Patchick 122 are MW disk GCs. In contrast, the orbits of Kronberger 99, Kronberger 119, Kronberger 143, ESO 92-18, and ESO 93-08 are more consistent with old MW disk open clusters, in agreement with previous results. VVV-CL160 falls very close to the Galactic centre, but reaches larger distances beyond the Solar orbit, and therefore its origin is still unclear.

The complexity of upper extremity control of the paralyzed patient offers a great challenge to the rehabilitation engineer, orthotist/prosthetist, or others. However, researchers can approach the problem of disabled arm motion, for the sake of simplicity, as a series of links with minimum pivots and minimum gravitational forces. In addition, when the degrees of freedom are reduced from four to three as in the case of this study, then some daily functions can be achieved by using simple braces and splints that are powered externally and internally. In our design of a hybrid arm orthosis (HAO), we emphasized simplicity and active contribution of the user. The orthosis takes full advantage of the wheelchair frame without changing its profile. The HAO offers body powered shoulder abduction and elbow flexion of one degree of freedom. A motor-powered wrist supination and three-joint jaw chuck pinch offer the remaining two degrees of freedom.

The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. This unexpected conclusion can be explained assuming the presence of a non-vanishing yet extremely fine tuned cosmological constant, or invoking the existence of an exotic source of energy, dark energy, which is not observed in laboratory experiments yet seems to dominate the energy budget of the Universe. On the other hand, it may be that these observations are just signalling the fact that Einstein's General Relativity is not the correct description of gravity when we consider distances of the order of the present horizon of the universe. In order to study if the latter explanation is correct, we have to formulate new theories of the gravitational interaction, and see if they admit cosmological solutions which fit the observational data in a satisfactory way. Quite generally, modifying General Relativity introduces new degrees of freedom, which are responsible for the different large distance behaviour. On one hand, often these new degrees of freedom have negative kinetic energy, which implies that the theory is plagued by ghost instabilities. On the other hand, for a modified gravity theory to be phenomenologically viable it is necessary that the extra degrees of freedom are efficiently screened on terrestrial and astrophysical scales. One of the known mechanisms which can screen the extra degrees of freedom is the Vainshtein mechanism, which involves derivative self-interaction terms for these degrees of freedom. In this thesis, we consider two different models, the Cascading DGP and the dRGT massive gravity, which are candidates for viable models to modify gravity at very large distances. Regarding the Cascading DGP model, we consider the minimal (6D) set-up and we perform a perturbative analysis at first order of the behaviour of the gravitational field and of the branes position around background solutions where pure tension is localized on the 4D brane. We consider a specific realization of this set-up where the 5D brane can be considered thin with respect to the 4D one. We show that the thin limit of the 4D brane inside the (already thin) 5D brane is well defined, at least for the configurations that we consider, and confirm that the gravitational field on the 4D brane is finite for a general choice of the energymomentum tensor. We also confirm that there exists a critical tension which separates background configurations which possess a ghost among the perturbation modes, and background configurations which are ghost-free. We find a value for the critical tension which is different from the value which has been obtained in the literature; we comment on the difference between these two results, and perform a numeric calculation in a particular case where the exact solution is known to support the validity of our analysis. Regarding the dRGT massive gravity, we consider the static and spherically symmetric solutions of these theories, and we investigate the effectiveness of the Vainshtein screening mechanism. We focus on the branch of solutions in which the Vainshtein mechanism can occur, and we truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all non-linearities of the mode which is involved in the screening. We determine analytically the number and properties of local solutions which exist asymptotically on large scales, and of local (inner) solutions which exist on small scales. Moreover, we analyze in detail in which cases the solutions match in an intermediate region. We show that asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while non asymptotically flat solutions can connect both with inner solutions which display the Vainshtein mechanism, or with solutions which display a self-shielding behaviour of the gravitational field. We show furthermore that there are some regions in the parameter space of the theory where global solutions do not exist, and characterize precisely in which regions the Vainshtein mechanism takes place.

Most field stars will have encountered the highest stellar density and hence the largest number of interactions in their birth environment. Yet the stellar dynamics during this crucial phase are poorly understood. Here we analyze the radial velocities measured for 152 out of 380 observed stars in the 2?6 Myr old star cluster IC 348 as part of the SDSS-III APOGEE. The radial velocity distribution of these stars is fitted with one or two Gaussians, convolved with the measurement uncertainties including binary orbital motions. Including a second Gaussian improves the fit; the high-velocity outliers that are best fit by this second component may either (1) be contaminants from the nearby Perseus OB2 association, (2) be a halo of ejected or dispersing stars from IC 348, or (3) reflect that IC 348 has not relaxed to a Gaussian velocity distribution. We measure a velocity dispersion for IC 348 of 0.72 ? 0.07 km s?1 (or 0.64 ? 0.08 km s?1 if two Gaussians are fitted), which implies a supervirial state, unless the gas contributes more to the gravitational potential than expected. No evidence is found for a dependence of this velocity dispersion on distance from the cluster center or stellar mass. We also find that stars with lower extinction (in the front of the cloud) tend to be redshifted compared with stars with somewhat higher extinction (toward the back of the cloud). This data suggest that the stars in IC 348 are converging along the line of sight. We show that this correlation between radial velocity and extinction is unlikely to be spuriously caused by the small cluster rotation of 0.024 ? 0.013 km s?1 arcmin?1 or by correlations between the radial velocities of neighboring stars. This signature, if confirmed, will be the first detection of line of sight convergence in a star cluster. Possible scenarios for reconciling this convergence with IC 348's observed supervirial state include: (a) the cluster is fluctuating around a new virial equilibrium after a recent disruption due to gas expulsion or a merger event, or (b) the population we identify as IC 348 results from the chance alignment of two sub-clusters converging along the line of sight. Additional measurements of tangential and radial velocities in IC 348 will be important for clarifying the dynamics of this region and informing models of the formation and evolution of star clusters. The radial velocities analyzed in this paper have been made available online.

Bidirectional Human-Robot Learning: Imitation and Skill Improvement

This article presents a novel method for enabling energy-efficient and orientation-independent gravity compensation in active vibration isolation systems by taking advantage of the inherent negative stiffness of a hybrid reluctance actuator (HRA). Counteracting the gravitational force acting on the mover of an HRA with the position dependent force of the actuator’s integrated permanent magnet, the gravitational force can be compensated without the need for an additional actuation. An HRA-system with two translational degrees of freedom (DOF) is developed, comprising a permanent magnet for generating a constant biasing flux for both system axes and two actuator coils per axis for actively controlling the position of the mover. The system prototype has an actuation range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.7 mm in both DOF, while enabling energy efficient gravity compensation of payloads up to 500 g by an additional current feedback control loop. Experiments demonstrate that the current consumption for compensation of a 500 g payload is reduced from 1.58 A to 10 mA, which corresponds to a reduction of the power consumption by a factor of 25 000.

We present an extension of the formalism recently proposed by Pepper & Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high mass end which, when considered jointly with the radial velocity requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide field surveys may detect hot Neptunes whose radial velocity signal can be measured with present-day instrumentation in very nearby (<100 pc) clusters.

The post-starburst region B in M82 and its massive star cluster component have been the focus of multiple studies, with reports that there is a large population of coeval clusters of age ∼1 Gyr, which were created with a Gaussian initial mass distribution. This is in disagreement with other studies of young star clusters, which invariably find a featureless power-law mass distribution. Here, we present Gemini-North optical spectra of seven star clusters in M82-B and show that their ages are all between 10 and 300 Myr (a factor of 3–100 younger than previous photometric results) and that their extinctions range between near zero and 4 mag (A V ). Using new HST ACS-HRC U-band observations we age date an additional ∼30 clusters whose ages/extinctions agree well with those determined from spectroscopy. Completeness tests show that the reported ‘turn-over’ in the luminosity/mass distributions is most likely an artefact, due to the resolved nature of the clusters. We also show that the radial velocities of the clusters are inconsistent with them belonging to a bound region.

Comets are a remarkable feature in our night sky, visible on their passage through the inner Solar system as the Sun's energy sublimates ices and liberates surface material, generating beautiful comae, dust, and ion tails. Comets are also thought to orbit other stars, and are the most promising interpretation of sporadic absorption features (i.e. transits) seen in spectra of stars such as $\beta$ Pictoris and 49 Ceti. These `exocomets' are thought to form and evolve in the same way as in the Solar system, and as in the Solar system we may gain insight into their origins by deriving their orbits. In the case of $\beta$ Pictoris, orbits have been estimated indirectly, using the radial velocity of the absorption features coupled with a physical evaporation model to estimate the stellocentric distance at transit $d_{\rm tr}$. Here, we note that the inferred $d_{\rm tr}$ imply that some absorption signatures should accelerate over several hours, and show that this acceleration is indeed seen in HARPS spectra. This new constraint means that orbital characteristics can be obtained directly, and the pericentre distance and longitude constrained when parabolic orbits are assumed. The results from fitting orbits to 12 accelerating features, and a handful of non-accelerating ones, are in broad agreement with previous estimates based on an evaporation model, thereby providing some validation of the exocomet hypothesis. A prediction of the evaporation model, that coma absorption is deeper for more distant transits, is also seen here.