Orbital Shape Research Articles

8 in 10 Stars in the Milky Way Bulge experience stellar encounters within 1000 AU in a gigayear

ABSTRACT The Galactic bulge is a tumultuous dense region of space, packed with stars separated by far smaller distances than those in the Solar neighbourhood. A quantification of the frequency and proximity of close stellar encounters in this environment dictates the exchange of material, disruption of planetary orbits, and threat of sterilizing energetic events. We present estimated encounter rates for stars in the Milky Way bulge found using a combination of numerical and analytical methods. By integrating the orbits of bulge stars with varying orbital energy and angular momentum to find their positions over time, we were able to estimate how many close stellar encounters the stars should experience as a function of orbit shape. We determined that ∼80 per cent of bulge stars have encounters within 1000 AU and that half of bulge stars will have >35 such encounters, both over a gigayear. Our work has interesting implications for the long-term survivability of planets in the Galactic bulge.

Joint dynamic optimization of the target orbit and flight trajectory of a launch vehicle based on state-triggered indices

This paper solves the problem of the on-line joint optimization of the target orbit and flight trajectory of a launch vehicle experiencing a thrust drop failure, and proposes state-triggered indices to improve the solving efficiency. The ‘highest-height index’ is triggered first to find the maximum-height circular orbit (MCO) in the orbital plane formed at the time of failure. If the orbital altitude is less than the perigee height of the prescribed target orbit, the MCO will be regarded as the optimal circular orbit to ensure safety. If not, the ‘minimal orbital plane deviations index’ is triggered to subsequently find the optimal elliptical orbit (OEO), where the orbital inclination and longitude of the ascending node are preferentially adjusted on the basis of the MCO. Furthermore, if the OEO is coplanar with the target orbit, a ‘minimal orbital shape deviations index’ is triggered to find the optimal rescue orbit, which eliminates the deviations of the perigee altitude, semi-major axis and perigee argument on the basis of the OEO. Estimation of the geocentric angle of the injection point, construction of the approximated sub-problem, and convexification processing are adopted to provide initial guesses to boost the computing. Monte Carlo simulations show that the method not only converges to the optimal or sub-optimal solution for different failure states, which avoids suspended calculations, non-convergence, and constraint violations that are common when directly solving this type of rescue problem, but also meets the basic requirements of on-line applications.

Investigation on Vibration Response for Misaligned Rotor-Bearing-Flexible Disc Coupling System—Theory and Experiment

AbstractModeling of the dynamic behavior of the rotating system when subject to misaligned shafts is an interesting subject, aiming either the selection of appropriate couplings from early stages of project or the monitoring and model-based diagnosis of such machines. This research is focused on the dynamics of the system when angular misalignment is induced. The methodology to take into account this fault is based on the structural analysis of the flexible coupling, with the consequent use of cyclic restoring forces and moments exerted by this component on the coupled shafts. Structural analysis of metallic disc coupling is conducted by means of the finite element method, in which the flexible disc component is modeled using thin shell formulation. Once misalignments are applied, the cyclic nature of coupling efforts is captured by the application of consecutive shaft spin angles. Steady-state response is simulated and then displacements spectrum are analyzed in order to highlight harmonic components rising due to misalignment. Test rig measurements are performed, and the theoretical model is discussed in terms of locus, frequency response function (FRF), orbit shape, and spectrum information. Disc coupling is regarded, as limited literature in vibration spectrums is available for this type of coupling.

In‐between: Re‐migration, orbital mobilities and emotional circulations of women from China to Taiwan and back to China

After a first labour migration from the countryside to the city in China, some Chinese migrant working women are engaged in marriage migration to Taiwan. There, they face social, gendered and economic subalternity. Therefore, some women divorce and re‐migrate to China, to the city they had been previously working in, where they remobilise social, economic and emotional resources, as well as the new competences and knowledge capitalised during mobility experiences in China and Taiwan. They oscillate between new local and global scales, and generate creative social, economic and emotional connections among spaces, places and people. Mobilities take the shape of physical and virtual, material and emotional ‘orbits’, connecting diverse spatialities, temporalities and affections. Drawing on a multi‐situated global ethnographic work tracking women's migrations from China to Taiwan and from Taiwan to China, this article contributes to the study of physical and virtual, material and emotional mobilities of migrants in a globalised social world of interconnection and hypermobility. It provides insights to apprehend, theoretically, methodologically and empirically, the link between mobilities, emotions the digitalisation of social and economic practices. Navigating through spatialities, temporalities and emotions, Chinese women produce ‘in‐between’ cosmopolitan biographies inside mutating and fluid local and global, physical and virtual, spaces. Mobilities take an orbital shape, embedded in social and affectional relations, economic practices, and emotions.

GNSS-RO LEO satellite orbit optimization for Egypt and the Middle East region

The “Radio Occultation (RO)” method is one from the simple, accurate and high resolution methods that produces a complete atmosphere model. Each region/country optimizes a “Low Earth Orbiter (LEO)” satellite orbit that covers its climate requirements by processing the “Global Navigation Satellite System (GNSS)” received signal. Orbit optimization includes the six Keplerian parameters that define the orbit shape. The optimum values of the Keplerian parameters are based up on the number and the distribution of the observations located in the country or the case study region. In the present research, a GNSS-LEO orbit optimization is made for Egypt and the Middle East region. The research objective is to feed the case study region by an adequate and uniform distributed number of observations. Both of time and spatial distributions are taken in consideration in deferent orbits comparison. Two GNSS constellations, “Global Positioning System (GPS)” (29 satellites) and “Global Navigation Satellite System (GLONASS)” (24 satellites), data are used in the analysis. More than hundred orbit cases are used for analysis to find the optimum one.Research demonstrated that the proposed orbit parameters for Egypt area are: altitude = 1500 km, inclination = 0°, initial value of mean anomaly = 300° and the other parameters are set to 0 values. The average expected number of observations due to this orbit is 8 observations per day in Egypt. Results also showed that the proposed orbit parameters for Middle East region are: altitude = 1500 km, inclination = 0°, initial value of mean anomaly = 330° and the other parameters are set to 0 values. The average expected number of observations due to this orbit is 854 observations per day in the Middle East region. These orbits insure obtaining the maximum number of observations with the best spatial and time distribution. The only deference between the two orbits is the angle of the initial value of the mean anomaly. If it is set to 300°, the observations distribution is expected to be distorted over the Middle East region by a small value. And if it is set to 330°, the number of observations through Egypt will be reduced to 7 instead of 8 observations per day.

Identifying invariant ergodic subsets and barriers to mixing by cutting and shuffling: Study in a birotated hemisphere

Mixing by cutting and shuffling can be mathematically described by the dynamics of piecewise isometries (PWIs), higher dimensional analogs of one-dimensional interval exchange transformations. In a two-dimensional domain under a PWI, the exceptional set, E[over ¯], which is created by the accumulation of cutting lines (the union of all iterates of cutting lines and all points that pass arbitrarily close to a cutting line), defines where mixing is possible but not guaranteed. There is structure within E[over ¯] that directly influences the mixing potential of the PWI. Here we provide computational and analytical formalisms for examining this structure by way of measuring the density and connectivity of ɛ-fattened cutting lines that form an approximation of E[over ¯]. For the example of a PWI on a hemispherical shell studied here, this approach reveals the subtle mixing behaviors and barriers to mixing formed by invariant ergodic subsets (confined orbits) within the fractal structure of the exceptional set. Some PWIs on the shell have provably nonergodic exceptional sets, which prevent mixing, while others have potentially ergodic exceptional sets where mixing is possible since ergodic exceptional sets have uniform cutting line density. For these latter exceptional sets, we show the connectivity of orbits in the PWI map through direct examination of orbit position and shape and through a two-dimensional return plot to explain the necessity of orbit connectivity for mixing.

Character of Frontier Orbitals of Antiviral Drugs: Candidate Drugs against Covid-19

We performed density functional theory (DFT) calculations for ribonucleotides and active triphosphate metabolites of candidate drugs against Coronavirus disease 2019 (Covid-19). Frontier orbitals (highest occupied molecular orbital and lowest unoccupied molecular orbital) at optimized structure of each molecule were obtained. T-705RTP (active triphosphate metabolite of favipiravir) and cytidine triphosphate (CTP) have similar shapes of frontier orbitals. We also obtained similar shapes of frontier orbitals among dihydroxy GS-441524 triphosphate (GS-441524 is an active triphosphate metabolite of remdesivir) and adenosine triphosphate (ATP). From a theoretical viewpoint, we suggest T-705RTP is a CTP analogue and dihydroxy GS-441524 triphosphate is an ATP analogue.

WITHDRAWN

The document associated with this DOI has been withdrawn.

Relation between the spatial shape of excited molecular orbital and molecular-frame electron scattering cross section

SynopsisWe report the molecular-frame electron scattering cross sections of the 2σg→1πg excitation in O2 and N2, obtained using an electron-ion coincidence technique. The vector correlation between the scattered electron and the fragment ion has been measured at incident electron energy of 1.4 keV. The results exhibit clear molecular-orientation dependence reflecting the nodal structure of the 1πg orbital. It strongly suggests that the electron-ion coincidence technique can provide a powerful tool to investigate spatial shapes of unoccupied molecular orbitals.

Third components with elliptical orbits in the eclipsing binaries

In our research, we studied 9 eclipsing binary stars: AR Lac, U CrB, S Equ, SU Boo, VV UMa, WW Gem, YY Eri, V0404 Lyr, HP Aur. We collected large sets of moments of minima from BRNO and observational data from AAVSO databases. Then, we obtained moments of minima for AAVSO observations (totally - 397 minima) using method of approximation with symmetric polynomial, realized in software MAVKA. This software was provided by Kateryna D. Andrych and Ivan L. Andronov. After we combined obtained moments of minima with data taken from BRNO and plotted O-C diagrams. For all stars these diagrams represented sinusoidal-like oscillations with superposition of linear (for SU Boo, VV UMa, WW Gem, V0404 Lyr and HP Aur) or parabolic trend (for AR Lac, U CrB, S Equ and YY Eri). The oscillations could be described as presence of the third component, which does not take part in eclipses, but causes the well-known light-time effect (LTE). That effect could be easily detected using long data series of observations. However, the oscillations have clear asymmetry, which we interpreted as elliptical shape of the third components orbit. Parabolic trend we explained as mass transfer between components of binary system. For all stars we computed minimal possible mass of the third component. In addition, we developed our own code in computed language Python and using it we computed orbital elements of the third component. Moreover, for stars with parabolic trend we calculated rate of the mass transfer. Finally, for all computed values we estimated errors.

Ancestry estimation using image analysis of orbital shapes from Thai and Japanese skulls

Ancestry estimation using image analysis of orbital shapes from Thai and Japanese skulls

Orbital wall restoring surgery with primary orbital wall fragments in blowout fracture

Most orbital surgeons believe that it’s difficult to restore the primary orbital wall to its previous position and that the orbital wall is so thin that cannot be firmly its primary position. Therefore, orbital wall fractures generally have been reconstructed by replacing the bony defect with a synthetic implant. Although synthetic implants have sufficient strength to maintain their shape and position in the orbital cavity, replacement surgery has some drawbacks due to the residual permanent implants. In previous studies, the author has reported an orbital wall restoring technique in which the primary orbital wall fragment was restored to its prior position through a combination of the transorbital and transantral approaches. Simple straight and curved elevators were introduced transnasally to restore the orbital wall and to maintain temporary extraorbital support in the maxillary and ethmoid sinus. A transconjunctival approach provided sufficient space for implant insertion, while the transnasal approach enabled restoration of the herniated soft tissue back into the orbit. Fracture defect was reduced by restoring the primary orbital wall fragment to its primary position, making it possible to use relatively small size implant, furthermore, extraorbital support from both sinuses decreased the incidence of implant displacement. The author could recreate a natural shape of the orbit with the patient’s own orbital bone fragments with this dual approach and effectively restored the orbital volume and shape. This procedure has the advantages for retrieving the orbital contents and restoring the primary orbital wall to its prior position.

The Electron Affinity as the Highest Occupied Anion Orbital Energy with a Sufficiently Accurate Approximation of the Exact Kohn-Sham Potential.

Negative ions are not accurately represented in density functional approximations (DFAs) such as (semi)local density functionals (LDA or GGA or meta-GGA). This is caused by the much too high orbital energies (not negative enough) with these DFAs compared to the exact Kohn–Sham values. Negative ions very often have positive DFA HOMO energies, hence they are unstable. These problems do not occur with the exact Kohn–Sham potential, the anion HOMO energy then being equal to minus the electron affinity. It is therefore desirable to develop sufficiently accurate approximations to the exact Kohn–Sham potential. There are further beneficial effects on the orbital shapes and the density of using a good approximation to the exact KS potential. Notably the unoccupied orbitals are not unduly diffuse, as they are in the Hartree–Fock model, with hybrid functionals, and even with (semi)local density functional approximations (LDFAs). We show that the recently developed B-GLLB-VWN approximation [Gritsenko et al. J. Chem. Phys.2016, 144, 204114] to the exact KS potential affords stable negative ions with HOMO orbital energy close to minus the electron affinity.

Расчет периодов просвечивания венерианской атмосферы радиосигналом между двумя космическими аппаратами в задаче изучения её состава

The paper considers calculating the periods of radio signal transmission through the atmosphere of Venus between a small spacecraft placed in a limited orbit in the vicinity of the collinear libration point of the Sun-Venus system and a Venus orbiter. The problem arises in the framework of the project under discussion to study the atmosphere of Venus. The possibility of transfers of these spacecrafts to the required orbits under various initial conditions is also studied. The impulses required for transferring to the specified orbits at the selected initial state vector, the most suitable for solving this problem are calculated. The duration and the number of transmission periods depending on the location of one of the spacecrafts in a limited orbit in the vicinity of the libration point L1 or L2 of the Sun-Venus system are analyzed. The influence of the shape of the orbiter near-Venusian orbit on the character and duration of the periods of transmission through the atmosphere of Venus is investigated. It is concluded that the location of a small spacecraft in a limited orbit in the vicinity of the L1 libration point of the Sun-Venus system is more advantageous compared to L2 both in terms of the duration and the number of the transmission periods as well as terms of the necessary energy costs.

Machine Learning Optimization of the Collocation Point Set for Solving the Kohn–Sham Equation

The rectangular collocation approach makes it possible to solve the Schrödinger equation with basis functions that do not have amplitude in all regions in which wave functions have significant amplitude. Collocation points can be restricted to a small region of space. As no integrals are computed, there are no problems due to discontinuities in the potential, and there is no need to use integrable basis functions. In this paper, we show, for the Kohn-Sham equation, that machine learning can be used to drastically reduce the size of the collocation point set. This is demonstrated by solving the Kohn-Sham equations for CO and H2O. We solve the Kohn-Sham equation on a given effective potential which is a critical part of all DFT calculations, and monitor orbital energies and orbital shapes. We use a combination of Gaussian process regression and a genetic algorithm to reduce the collocation point set size by more than an order of magnitude (from about 51 000 points to 2000 points) while retaining mhartree accuracy.

Structural and dynamical modeling of WINGS clusters

The orbital shapes of galaxies of different classes are a probe of their formation and evolution. The Bayesian MAMPOSSt mass-orbit modeling algorithm is used to jointly fit the distribution of elliptical, spiral-irregular, and lenticular galaxies in projected phase space, on three pseudo-clusters (built by stacking the clusters after re-normalizing their positions and velocities) of 54 regular clusters from the Wide-field Nearby Galaxy-clusters Survey (WINGS), with at least 30 member velocities. Our pseudo-clusters (i.e., stacks) contain nearly 5000 galaxies with available velocities and morphological types. Thirty runs of MAMPOSSt with different priors are presented. The highest MAMPOSSt likelihoods are obtained for generalized Navarro-Frenk-White (NFW) models with steeper inner slope, free-index Einasto models, and double NFW models for the cluster and the brightest cluster galaxy. However, there is no strong Bayesian evidence for a steeper profile than the NFW model. The mass concentration matches the predictions from cosmological simulations. Ellipticals usually best trace the mass distribution while S0s are close. Spiral galaxies show increasingly elongated orbits at increasing radii, as do S0s on two stacks, and ellipticals on one stack. The inner orbits of all three types in the three stacks are consistent with isotropy. Spiral galaxies should transform rapidly into early-types given their much larger extent in clusters. Elongated outer orbits are expected for the spirals, a consequence of their recent radial infall into the cluster. The less elongated orbits we find for early-types could be related to the longer time spent by these galaxies in the cluster. We demonstrate that two-body relaxation is too slow to explain the inner isotropy of the early types, which suggests that inner isotropy is the consequence of violent relaxation during major cluster mergers or dynamical friction and tidal braking acting on subclusters. We propose that the inner isotropy of the short-lived spirals is a selection effect of spirals passing only once through pericenter before being transformed into early-type morphologies.

Ascent trajectory optimization for air‐breathing vehicles in consideration of launch window

SummaryThis paper studies the optimal ascent trajectory for a one‐stage‐to‐orbit, air‐breathing vehicle. This kind of vehicle allows endoatmospheric lateral maneuver and thus can extend the launch window. To obtain the optimal orbit‐insertion trajectory in consideration of launch time, a novel optimization model is proposed by designing longitudinal and lateral profiles separately. The longitudinal flight aims to meet the orbital shape that contains the eccentricity and the angular momentum, which are transformed to boundary constrains in altitude, path angle, and velocity. For lateral motion, the orbit inclination and right ascension of ascending node are designed to vary simultaneously as the range. By designing an altitude profile, the terminal altitude and path angle are naturally met and removed from the constraints and accurate orbit insertion is realized by searching the total range and the initial azimuth. Then, the original problem is converted to a parameter optimization problem and solved by a hybrid optimization algorithm, in which the solution is first searched by a particle swarm optimization method and then refined by a modified golden section method. Simulation tests the proposed method with various scenarios. Compared to traditional launch vehicles, a launch window over 1.5 hours is derived without consuming the propellant in the upper stage.

Diels-Alder Cycloaddition on Nonisolated-Pentagon-Rule C2v(19 138)-C76 and YNC@C2v(19 138)-C76: The Difference in Regioselectivity Caused by the Inner Metallic Cluster.

Diels-Alder reactions of cyclopentadiene to C2v(19 138)-C76 and YNC@C2v(19 138)-C76 violating the isolated pentagon rule have been systematically studied by means of density functional theory calculations. As for the free fullerene, the pentalene-type [5,5]-bond in the adjacent pentagon pair is the most favorable from thermodynamic and kinetic viewpoints, which is attributed to the highly strained carbon atoms accompanied by the suitable lowest unoccupied molecular orbital shape with a large distribution to interact with cyclopentadiene. Upon encapsulating the YNC cluster, a corannulene-type [5,6]-bond and a pyracylene-type [6,6]-bond become the two most reactive addition sites under thermodynamic and kinetic conditions, which possess similar reaction energies and energy barriers. Especially, the [5,6]-bond exhibits a larger reaction energy and a lower energy barrier than that on the free fullerene, which should be ascribed to its shorter bond length and larger π-orbital axis vector value after trapping the metallic cluster. The suitable unoccupied molecular orbital lobes with large distributions on the [5,6]- and [6,6]-bonds are also an advantage of cycloadditions. This work presents the first example that the most favorable addition site is remote from the adjacent pentagon pair in the fullerene cage after encapsulating a metallic cluster.

Three-dimensional computer modeling of standard orbital mean shape in Asians

Although some data for western norms in orbit shape were reported, the standard norms for Asian orbits were not established yet. The data would be very valuable for the various surgical procedures as well as the production of the appropriate instruments and implants. Therefore, we suggest a Korean orbit mean shape model based on the three-dimensional computer modeling, which includes the analysis of the various parameters with the calculated average value, thereby providing a standard mean shape orbital model that could be used for the Asian patients' orbital surgeries. This paper would be the first literature that provides the standard orbit model for Asians. We developed orbit-specific computer software (AMC-SWUⓇ) for the production of an orbit mean shape model. The production steps included semi-automatic segmentation, shape reconstruction, statistical shape model generation, and mean shape and variance model production. The study included records of 48 male and 48 female patients who met the inclusion criteria. Three-dimensional facial bone computed tomography (CT) images of 96 patients were obtained, and these images were used to produce a representative mean shape model. The mean models had vertical dimensions of 36.93 and 35.11 mm, horizontal dimensions of 38.49 and 36.79 mm, and rim dimensions of 45.76 and 42.90 mm for males and females, respectively. We developed a realistic, visualized three-dimensional Korean orbit mean shape model and compared its parameters with calculated values. There is a variance in orbital dimensions between the sexes and the orbital changes with age. We also demonstrated orbital anatomic differences between ethnic groups.

Description of learning difficulties on atomic structure and periodic table topics of tenth grade students in SMAN 7 Padang

This descriptive research was done on atomic structure and periodic table topics in SMAN 7 Padang. On these topics, students had difficulties on achieving learning goals where only 38% students could achieve the minimum defined criteria. This research aims to determine percentage of learning difficulties in all learning indicators and find factors that cause learning difficulties. 57 tenth grade students as research sample were obtained through cluster sampling technique. Research instruments used were diagnostic test and questionnaire and data were then analyzed descriptively. Analysis showed that learning difficulties were 91.2%, 13.2%, 88.3%, 51.5%, 70%, 64%, 84%, 84%, and 74.9% in the indicator of describing subatomic particles and their discovery; determining atomic number and mass number of elements and isotopes; describing atomic model according to Dalton, Thomson, Rutherford, Bohr, and wave mechanics; explaining electron configuration and orbital diagrams; determining quantum number and orbital shape; describing development of periodic system; modern periodic system; periods and groups in periodic table; and periodic trends of elements respectively. Students’ learning difficulties were influenced by school factors including teaching methods 35.8%, curriculum 47.5%, teacher relation with students 49.1 %, relation among students 41.7%, time and school discipline 33.3%, teaching tools 39.4% and school building condition 17.7%.