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1
Chodas, Paul W., and Donald K. Yeomans. "The orbital motion and impact circumstances of Comet Shoemaker-Levy 9." International Astronomical Union Colloquium 156 (May 1996): 1–30. http://dx.doi.org/10.1017/s025292110011543x.
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Two months after the discovery of comet Shoemaker-Levy 9 came the astonishing announcement that the comet would impact Jupiter in July 1994. Computing the orbital motion of this remarkable comet presented several unusual challenges. We review the pre-impact orbit computations and impact predictions for SL9, from the preliminary orbit solutions shortly after discovery to the final set of predictions before the impacts. The final set of predicted impact times were systematically early by an average of 7 minutes, probably due to systematic errors in the reference star catalogs used in the reduction of the fragments' astrometric positions. The actual impact times were inferred from the times of observed phenomena for 16 of the impacts. Orbit solutions for the fragments were refined by using the actual impact times as additional data, and by estimating and removing measurement biases from the astrometric observations. The final orbit solutions for 21 fragments are tabulated, along with final estimates of the impact times and locations. The pre-breakup orbital history of the comet was investigated statistically, via a Monte Carlo analysis. The progenitor nucleus of SL9 was most likely captured by Jupiter around 1929 ± 9 years. Prior to capture, the comet was in a low-eccentricity, low-inclination heliocentric orbit entirely inside Jupiter's orbit, or, less likely, entirely outside. The ensemble of possible pre-capture orbits is consistent with a group of Jupiter family comets known as the quasi-Hildas.
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Yasaka, Tetsuo, and Nobuaki Ishii. "Breakup in geostationary orbit: A possible creation of a debris ring." Acta Astronautica 26, no. 7 (July 1992): 523–30. http://dx.doi.org/10.1016/0094-5765(92)90123-z.
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Anilkumar, A. K., M. R. Ananthasayanam, and P. V. Subba Rao. "A posterior semi-stochastic low Earth debris on-orbit breakup simulation model." Acta Astronautica 57, no. 9 (November 2005): 733–46. http://dx.doi.org/10.1016/j.actaastro.2005.03.068.
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Pardini, C., and L. Anselmo. "Assessment of the consequences of the Fengyun-1C breakup in low Earth orbit." Advances in Space Research 44, no. 5 (September 2009): 545–57. http://dx.doi.org/10.1016/j.asr.2009.04.014.
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Sanson, Francois, Charles Bertorello, Jean-Marc Bouilly, and Pietro M. Congedo. "Breakup prediction under uncertainty: Application to upper stage controlled reentries from GTO orbit." Aerospace Science and Technology 87 (April 2019): 340–56. http://dx.doi.org/10.1016/j.ast.2019.02.031.
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Zhang, Xiao-tian, Guang-hui Jia, and Hai Huang. "Finite element reconstruction approach for on-orbit spacecraft breakup dynamics simulation and fragment analysis." Advances in Space Research 51, no. 3 (February 2013): 423–33. http://dx.doi.org/10.1016/j.asr.2012.09.023.
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Kreilos, Tobias, Gregor Veble, Tobias M. Schneider, and Bruno Eckhardt. "Edge states for the turbulence transition in the asymptotic suction boundary layer." Journal of Fluid Mechanics 726 (May 30, 2013): 100–122. http://dx.doi.org/10.1017/jfm.2013.212.
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AbstractWe demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.
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CAPEL, P., W. HORIUCHI, Y. SUZUKI, and D. BAYE. "PROBING THE WEAKLY-BOUND NEUTRON ORBIT OF 31Ne WITH ONE-NEUTRON REMOVAL REACTIONS." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 1882–85. http://dx.doi.org/10.1142/s0217732310000551.
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A candidate of a neutron-halo nucleus, 31 Ne , contains a single neutron in the pf shell. Within Glauber and eikonal models, we analyze reactions used to study 31 Ne . We show in a 30 Ne + n model that the magnitudes of the total reaction and above all of the one-neutron removal cross sections of 31 Ne on 12 C and 208 Pb targets strongly depend on the orbital angular momentum of the valence neutron, thereby providing efficient ways to determine the structure of 31 Ne ground state. We also show that elastic-breakup observables exhibit a strong dependence upon the orbital of the valence neutron.
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Chang, T. F., C. Z. Cheng, C. Y. Chiang, and A. B. Chen. "Behavior of substorm auroral arcs and Pi2 waves: implication for the kinetic ballooning instability." Annales Geophysicae 30, no. 6 (June 4, 2012): 911–26. http://dx.doi.org/10.5194/angeo-30-911-2012.
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Abstract. We present synoptic observations of the 21 December 2006 substorm event by the THEMIS ground-based All-Sky-Imagers, the ISUAL CCD Imager aboard the FORMOSAT-2 satellite, the geosynchronous satellites and the ground-based magnetometers, and discuss the implication of the observations. There are three subsequent arc breakups with time separation of <1 min during the substorm expansion phase. In particular, we investigated the mode number of the substorm arc bead-like structure and the concurrent behavior of the arc intensity, the westward electroject intensity, and the ground Pi2 pulsation amplitude. Prior to each arc breakup there was a clear azimuthally-spaced bright spot structure along the arc with high mode number (~140–180) and the arc intensity increased together with the westward electrojet and the ground Pi2 pulsation amplitude under the arc. The Pi1 perturbations observed under the arc appeared at or after the arc breakup started. This suggests that the Pi2 pulsation is related to the arc formation. The Pi2 pulsation may be caused by the kinetic ballooning instability (KBI) that is excited in the strong cross-tail current region. The longitudinal extent of the earthward expansion front of the substorm dipolarization region at the geosynchronous orbit is estimated from timings of the energetic proton and electron injections and is roughly located between ~19.50 MLT and ~23.00 MLT, which is consistent with the corresponding longitudinal extent of the auroral substorm activity.
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Toth, I. "Impact-triggered breakup of comet C/1999 S4 (LINEAR): Identification of the closest intersecting orbits of other small bodies with its orbit." Astronomy & Astrophysics 368, no. 3 (March 2001): L25—L28. http://dx.doi.org/10.1051/0004-6361:20010182.
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Hata, Hidehiro, Toshiya Hanada, Yasuhiro Akahoshi, Tetsuo Yasaka, and Shoji Harada. "Examining of the Collision Breakup Model between Geostationary Orbit Objects: The Second Report: Consideration of the Maximum Collision Velocity between Geostationary Earth Orbit Satellite." JOURNAL OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 53, no. 615 (2005): 160–65. http://dx.doi.org/10.2322/jjsass.53.160.
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YAMADA, T., Y. FUNAKI, H. HORIUCHI, A. TOHSAKI, G. RÖPKE, and P. SCHUCK. "DILUTE ALPHA-PARTICLE CONDENSATION IN 12C AND 16O." International Journal of Modern Physics B 22, no. 25n26 (October 20, 2008): 4545–56. http://dx.doi.org/10.1142/s0217979208050292.
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Alpha particle condensation is studied in 12 C and 16 O with the orthogonality condition model (OCM). The OCM equation is an approximation of the equation of motion of α bosons based on microscopic theories. We demonstrate that 1) the Hoyle state (the [Formula: see text] state at 7.65 MeV in 12 C ), located just above the 3α disintegration threshold has a 3α-particle condensate character, in which 3α particles occupy an identical 0S orbit with 70 % occupancy, forming a dilute gas-like configuration, and 2) the [Formula: see text] state at Ex = 15.1 MeV in 16 O , appearing above the 4α breakup threshold, is a strong candidate with dilute 4α structure of the condensate-type.
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Коробцев, И. В., М. Н. Мишина, and М. В. Еселевич. "Photometrical and trajectory observations of near-Earth space objects at Sayan solar observatory of the ISTP SB RAS." Научные труды Института астрономии РАН, no. 1 (July 22, 2022): 36–40. http://dx.doi.org/10.51194/inasan.2022.7.1.006.
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В работе приводятся результаты оптических наблюдений космического мусора, образовавшегося 28 февраля 2018 г. в области геостационарной орбиты при разрушении верхней ступени Titan 3C Transtage 17. Сбор траекторной и фотометрической информации выполнялся на телескопах Саянской солнечной обсерватории ИСЗФ СО РАН для уточнения параметров орбит фрагментов, определения характеристик их поверхностей, периодов собственного вращения. Представлены результаты анализа полученных измерений. Приведены оценки изменения площади отражающей поверхности разрушившегося объекта и размеров наиболее крупного фрагмента. The paper presents the results of optical observations of space debris formed by the breakup of the Titan 3C Transtage 17 upper stage on February 28, 2018 in the region of the geostationary orbit. The trajectory and photometrical information acquisition was performed on telescopes at the Sayan Solar Observatory of the ISTP SB RAS to improve the orbital parameters of the fragments, characteristics of their surfaces and proper rotation periods. The results of the analysis of the obtained measurements are presented. Estimates of the change in the surface reflecting area of the break-up object and the size of the largest fragment are given.
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Liu, Yongjie, Yu Jiang, and Hengnian Li. "Analytical Propagation of Space Debris Density for Collisions near Sun-Synchronous Orbits." Space: Science & Technology 2022 (September 17, 2022): 1–17. http://dx.doi.org/10.34133/2022/9825763.
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The increasing frequency of human launches has led to a dramatic increase in the amount of space debris, especially near sun-synchronous orbits. Most of the fragments are small in size, which may make tracking difficult. Therefore, characterizing the distribution, evolution, and collision risk of small debris has long been a difficult issue. This paper is aimed at investigating the orbital evolution and global dispersion behavior of debris clouds near sun-synchronous orbits. Firstly, the NASA breakup model is used to provide an initial distribution of small fragments after collision events. Secondly, the continuity equation is adopted to propagate the density variation analytically. Furthermore, we introduce some statistical quantities and the entropy of debris clouds to model the randomness and band formation. A theorem concerning the equivalence of the band formation and maximal entropy is presented. The accuracy of the band formation time estimation is also discussed. For noncatastrophic collisions at an altitude of 800 km due to a projectile with a mass of 100 g and a collision velocity of 1 km/s, we compare the analytical and numerical results of space debris density. The results show that the maximal peak error is within 0.17, and the mean square error is about 0.25 at 400 days. Additionally, the entropy of right ascension of the ascending node is 8.5% less than that for debris clouds near an orbit with the same altitude and an inclination of 30 deg. This indicates the concentrating behavior for debris clouds near sun-synchronous orbits.
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Owen, Michael P., and John M. Blondin. "3-D Hydro dynamic Simulation of Accretion Disk Formation in LMC-X4." International Astronomical Union Colloquium 163 (1997): 779. http://dx.doi.org/10.1017/s0252921100043943.
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We present preliminary results of a time-dependent, three-dimensional hydrodynamic simulation of LMC-X4, an HMXB known to be undergoing RLOF. The simulation is initialized with the collapsed companion embedded in the undisturbed primary wind. The primary is in contact with the Roche surface, although no tidal stream or accretion disk is initialed; they are allowed to form independently.Several features of general interest to disk-fed HMXBs are apparent in the simulation. First, the primary immediately develops a compressed-wind disk in the orbital plane. This may be a natural result in most disk-fed HMXBs. Fora circularized system in an orbit close enough for RLOF to take place, we may expect the primary to be in corotation. The surface velocity may then be a significant fraction of the breakup velocity, leading to a compressed-wind disk.
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Plávalová, E., and A. Rosaev. "Dynamical effect of the 9:16 resonance with Mars on some Datura asteroids, including the pair Balam and 312497." Astronomy & Astrophysics 653 (August 31, 2021): A4. http://dx.doi.org/10.1051/0004-6361/202038742.
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Context. We studied the effect of the mean motion 9:16 resonance with Mars (9:16M) on the dynamics of the very young asteroid family Datura and the young pair (3749) Balam and (312497) 2009 BR60. Aims. We aim to understand the mechanism of dynamical interaction of the members of a family that are subjected to mean motion resonance in order to precisely estimate the age of an asteroid family or pair and to reconstruct their breakup processes. Methods. We calculated the expected (9:16M) resonance position, its boundaries, and multiplet fine structure and their time evolution under the effect of Mars orbit variations. We used the Lyapunov characteristic exponent and Euclid algorithm in our analytical calculations. We compared these results with backward numerical integrations of some Datura asteroids to check for consistency. Results. We explain the strong variations in the semi-major axis of some Datura asteroids as caused by the variations in the orbit of Mars. Using the Datura family as an example, we show that the distance from resonance may be a better measure of chaos than the widely accepted Lyapunov exponent. Additionally, we find that asteroid (3749) Balam exhibits the conspicuous effects of dynamical perturbations that are likely induced by the 9:16M resonance. Conclusions. Focusing on one of the most robust and well-established young asteroid families, the Datura family, we show that mean motion resonances play an important role as drivers of the dynamical evolution of asteroid families.
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Jewitt, David, Yoonyoung Kim, Michael Mattiazzo, Max Mutchler, Jing Li, and Jessica Agarwal. "Disintegration of Long-period Comet C/2021 A1 (Leonard)." Astronomical Journal 165, no. 3 (February 22, 2023): 122. http://dx.doi.org/10.3847/1538-3881/acb53b.
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Abstract We present imaging observations of the disintegrating long-period comet C/2021 A1 (Leonard). High-resolution observations with the Hubble Space Telescope show no evidence for surviving fragments, and place a 3σ upper limit on their possible radius of ∼60 m (albedo 0.1 assumed). In contrast, wide-field observations from the Swan Hill Observatory, Australia, show an extensive debris cloud, the cross section and estimated mass of which are consistent with complete disintegration of the nucleus near 2021 mid-December (at about 0.8 au). Two methods give the pre-disruption radius of the nucleus, r n = 0.6 ± 0.2 km. Tidal, collisional, sublimation, and pressure-confined explosion models provide implausible explanations of the disintegration. However, rotational instability driven by outgassing torques has a very short timescale (∼0.1 yr) given the orbit and size of the nucleus of C/2021 A1, and offers the most plausible mechanism for the disruption. Initial rotational breakup is accelerated by the exposure and strong sublimation of previously buried volatiles, leading to catastrophic destruction of the nucleus.
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Michaely, Erez, and Michael M. Shara. "White dwarf–main sequence star collisions from wide triples in the field." Monthly Notices of the Royal Astronomical Society 502, no. 3 (February 9, 2021): 4540–46. http://dx.doi.org/10.1093/mnras/stab339.
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ABSTRACT Multiple star systems interact strongly with galactic field stars when the outer semi-major axis of a triple or multiple star is >103 AU. Stable triples composed of two white-dwarfs (WD) and a low-mass main sequence (MS) star in a wide outer orbit can thus be destabilized by gravitational interactions with random field stars. Such interactions excite the eccentricity of the distant third star sufficiently so that it begins to interact significantly with the inner binary. When this occurs, the triple undergoes multiple binary-single resonant encounters. These encounters may result either in a collision between the non-degenerate component and a WD, or the breakup of the triple into a compact binary and a third object which is ejected. The compact binary can be either a MS–WD pair which survives, or collides or a double WD (DWD), which may inspiral through gravitational wave emission. We calculate the collision rate between a MS and WD star, and the merger rate of DWDs. Additionally, we describe the prospects of detectability of such a collision, which may resemble a sub-luminous supernovae event.
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Jackson, Pierce M., Ryota Nakano, Yaeji Kim, and Masatoshi Hirabayashi. "Active Main-belt Asteroid (6478) Gault: Constraint on Its Cohesive Strength and the Fate of Ejected Particles in the Solar System." Planetary Science Journal 3, no. 1 (January 1, 2022): 16. http://dx.doi.org/10.3847/psj/ac4031.
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Abstract Active asteroid (6478) Gault sheds mass independent of location along its orbit. Rotational instability is considered to induce the observed activities. If this is the case, because Gault’s breakup event has not been detected, surface failure is likely, implying that its surface materials are constantly ejected while its major body remains intact. Given this scenario, we first constrain Gault’s bulk cohesive strength. We then characterize heliocentric trajectories of ejected particles over thousands of years. The results show that Gault may be sensitive to structural failure at the current spin period (∼2.5 hr). Gault’s bulk density needs to be below 1.75 g cm−3 in order for particles on the equatorial surface to be shed owing to centrifugal forces. In this case, Gault requires cohesive strength of at least ∼200 Pa to maintain the structure at the center, whereas the surface strength needs to be less than ∼100 Pa to induce mass shedding. This suggests that Gault’s structure may consist of a weak surface layer atop a strong core. The trajectories of dust ejected from Gault depend on how efficiently they are accelerated by solar radiation pressure. Escaped particle clouds with sizes of < ∼100 μm could collide with Gault after ∼700–5300 yr with speeds of ∼0.2 km s−1. This implies a temporal increase in the impact flux and complex interactions between the ejected particles and their host body.
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Wang, H. S., and X. Y. Hou. "On the secondary’s rotation in a synchronous binary asteroid." Monthly Notices of the Royal Astronomical Society 493, no. 1 (February 14, 2020): 171–83. http://dx.doi.org/10.1093/mnras/staa133.
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ABSTRACT This article studies the secondary’s rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem, composed of a spherical primary plus a triaxial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) influence of the secondary’s rotation on the mutual orbit is considered and (2) instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find the following. (1) The genealogy of the two families of periodic orbits is the same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates on to a short-period orbit travelling N times. (2) In the limiting case where the secondary’s mass is negligible, our results can be reduced to classical spin-orbit theory, by equating the long-period orbit with free libration and the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary’s mass is non-negligible. (3) By studying the stability of periodic orbits for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°) and the maximum mutual orbit eccentricity that does not break the secondary’s synchronous state. We also find an anti-correlation between the secondary’s libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.
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Yan, Duokui, Rongchang Liu, Xingwei Hu, Weize Mao, and Tiancheng Ouyang. "New Phenomena in the Spatial Isosceles Three-Body Problem with Unequal Masses." International Journal of Bifurcation and Chaos 25, no. 12 (November 2015): 1550169. http://dx.doi.org/10.1142/s0218127415501692.
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This work studies periodic orbits as action minimizers in the spatial isosceles three-body problem with mass [Formula: see text]. In each period, the body with mass [Formula: see text] moves up and down on a vertical line, while the other two bodies have the same mass [Formula: see text], and rotate about this vertical line symmetrically. For given [Formula: see text], such periodic orbits form a one-parameter set with a rotation angle [Formula: see text] as the parameter. [Formula: see text]Two new phenomena are found for this set. First, for each [Formula: see text], this set of periodic orbits bifurcate from a circular Euler (central configuration) orbit to a Broucke (collision) orbit as [Formula: see text] increases from [Formula: see text] to [Formula: see text]. There exists a critical rotation angle [Formula: see text], where the orbit is a circular Euler orbit if [Formula: see text]; a spatial orbit if [Formula: see text]; and a Broucke (collision) orbit if [Formula: see text]. The exact formula of [Formula: see text] is numerically proved to be [Formula: see text]. Second, oscillating behaviors occur at rotation angle [Formula: see text] for all [Formula: see text]. Actually, the orbit with [Formula: see text] runs on its initial periodic shape for only a few periods. It breaks the first periodic shape and becomes irregular in a moment. However, it runs close to a different periodic shape after a while. In a short time, it falls apart from the second periodic shape and runs irregularly again. Such oscillation continues as time [Formula: see text] increases. Up to [Formula: see text], the orbit is bounded and keeps oscillating between periodic shapes and irregular motions. Further study implies that, for each [Formula: see text], the angle between any two consecutive periodic shapes is a constant. When [Formula: see text], similar oscillating behaviors are expected.
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Chen, Lei, Ke Zhang, Xiangwei Zhu, Yangbo Huang, Gang Ou, and Huicui Liu. "BeiDou Satellites Assistant Determination by Receiving Other GNSS Downlink Signals." International Journal of Antennas and Propagation 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/1413401.
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GNSS’s orbit determinations always rely on ground station or intersatellite links (ISL). In the emergency of satellite-to-ground links and ISL break-off, BeiDou navigation satellite system (BDS) satellites cannot determine their orbits. In this paper, we propose to add a spaceborne annular beam antenna for receiving the global positioning system (GPS) and global navigation satellite system (GLONASS) signals; therefore, the BDS satellites may be capable of determining their orbits by GPS/GLONASS signals. Firstly, the spectrum selection, the power isolation, the range of Doppler frequency shift, and changing rate are taken into account for the feasibility. Specifically, the L2 band signals are chosen for receiving and processing in order to prevent the overlapping of the receiving and transmitting signals. Secondly, the minimum number of visible satellites (MNVS), carrier-to-noise ratio (C/N0), dilution of precision (GDOP), and geometric distance root-mean-square (gdrms) are evaluated for acquiring the effective receiving antennas’ coverage ranges. Finally, the scheme of deploying 3 receiving antennas is proved to be optimal by analysis and simulations over the middle earth orbit (MEO), geostationary earth orbit (GEO), and the inclined geosynchronous satellite orbit (IGSO). The antennas’ structures and patterns are designed to draw a conclusion that installing GPS and GLONASS receivers on BDS satellites for emergent orbits determination is cost-effective.
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Hamers, Adrian S. "Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure – III. Suborbital effects: hybrid integration techniques and orbit-averaging corrections." Monthly Notices of the Royal Astronomical Society 494, no. 4 (April 22, 2020): 5492–506. http://dx.doi.org/10.1093/mnras/staa1084.
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ABSTRACT The secularmultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the formalism underlying secularmultiple, we previously averaged over all orbits in the system. This approximation significantly speeds up numerical integration of the equations of motion, making large population synthesis studies possible. However, the orbit averaging approximation can break down when the secular evolution time-scale of the system is comparable to or shorter than any of the orbital periods in the system. Here, we present an update to secularmultiple in which we incorporate hybrid integration techniques, and orbit-averaging corrections. With this update, the user can specify which orbits should be integrated directly (without averaging), or assuming averaged orbits. For orbits that are integrated directly, we implemented two integration techniques, one which is based on the regularized Kustaanheimo–Stiefel equations of motion in element form. We also implemented analytical orbit-averaging corrections for pairwise interactions to quadrupole order. The updates presented here provide more flexibility for integrating the long-term dynamical evolution of hierarchical multiple systems. By effectively combining direct integration and orbit averaging the long-term evolution can be accurately computed, but with significantly lower computational cost compared to existing direct N-body codes. We give a number of examples in which the new features are beneficial. Our updated code, which is written in c++ supplemented with a user-friendly interface in python, is freely available.
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Henderson, M. G. "Observational evidence for an inside-out substorm onset scenario." Annales Geophysicae 27, no. 5 (May 8, 2009): 2129–40. http://dx.doi.org/10.5194/angeo-27-2129-2009.
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Abstract. We present observations which provide strong support for a substorm expansion phase onset scenario in which a localized inner magnetospheric instability developed first and was later followed by the development of a Near Earth Neutral Line (NENL) farther down-tail. Specifically, we find that the onset began as a localized brightening of an intensified growth phase arc which developed as a periodic series of arc-aligned (i.e. azimuthally arrayed) bright spots. As the disturbance grew, it evolved into vortical structures that propagated poleward and eventually morphed into an east-west aligned arc system at the poleward edge of the auroral substorm bulge. The evolution of the auroral intensity is consistent with an exponential growth with an e-folding time of around 188 s (corresponding to a linear growth rate, γ of 5.33×10−3 s−1). During the initial breakup, no obvious distortions of auroral forms to the north were observed. However, during the expansion phase, intensifications of the poleward boundary of the expanding bulge were observed together with the equatorward ejection of auroral streamers into the bulge. A strong particle injection was observed at geosynchronous orbit, but was delayed by several minutes relative to onset. Ground magnetometer data also shows a two phase development of mid-latitude positive H-bays, with a quasi-linear increase in H between the onset and the injection. We conclude that this event provides strong evidence in favor of the so-called "inside-out" substorm onset scenario in which the near Earth region activates first followed at a later time by the formation of a near-to-mid tail substorm X-line. The ballooning instability is discussed as a likely mechanism for the initial onset.
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Saillenfest, M., J. Laskar, and G. Boué. "Secular spin-axis dynamics of exoplanets." Astronomy & Astrophysics 623 (February 26, 2019): A4. http://dx.doi.org/10.1051/0004-6361/201834344.
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Context. Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are therefore in heavy contrast with the uncertain nature of the available data. Aims. We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still giving precise quantitative results if the parameters are well known. Together with bounds for the poorly constrained parameters of exoplanets, this analysis is designed to enable a quick and straightforward exploration of the spin-axis dynamics. Methods. The long-term orbital solution is decomposed into quasi-periodic series and the spin-axis Hamiltonian is expanded in powers of eccentricity and inclination. Chaotic zones are measured by the resonance overlap criterion. Bounds for the poorly known parameters of exoplanets are obtained from physical grounds (rotational breakup) and dynamical considerations (equipartition of the angular momentum deficit). Results. This method gives accurate results when the orbital evolution is well known. The detailed structure of the chaotic zones for the solar system planets can be retrieved from simple analytical formulas. For less-constrained planetary systems, the maximal extent of the chaotic regions can be computed, requiring only the mass, the semi-major axis, and the eccentricity of the planets present in the system. Additionally, some estimated bounds of the precession constant allow to classify which observed exoplanets are necessarily out of major spin-orbit secular resonances (unless the precession rate is affected by the presence of massive satellites).
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Shilin, V. D., V. N. Lagutkin, A. P. Lukyanov, A. M. Starostenko, and M. M. Ibragimov. "APPLICATION ISSUES OF SPACE INFORMATION FACILITIES FOR SPACE OBJECTS MONITORING." Issues of radio electronics, no. 3 (March 20, 2018): 85–89. http://dx.doi.org/10.21778/2218-5453-2018-3-85-89.
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Complex of computer models for study of effectiveness of application of space information facilities was developed for solution the tasks of orbits monitoring and space objects recognition. It is shown, that space information facilities provide minimal breaks in observations and can make a significant informational contribution to the solution of the problem of reducing the required time of orbits determination of space objects, including maneuvering ones on both low and high orbits. Comparative assessments of required time for estimation of space objects orbits parameters for various orbits of space information facilities were obtained. It is also shown, that space systems allow carrying out recognition and control of space objects state more effectively, due to the possibility of their observation from short distances in the optical waveband. Methods of space objects image processing are developed and estimates of their effectiveness are presented. Proposals are given for use of small spacecrafts for monitoring low-Earth-orbit space objects when flying on cross courses.
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CHOLAK, PETER A., PETER GERDES, and KAREN LANGE. "-MAXIMAL SETS." Journal of Symbolic Logic 80, no. 4 (December 2015): 1182–210. http://dx.doi.org/10.1017/jsl.2015.3.
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AbstractSoare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits.
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NITTA, MUNETO. "MODULI SPACE OF GLOBAL SYMMETRY IN N=1 SUPERSYMMETRIC THEORIES AND THE QUASI-NAMBU–GOLDSTONE BOSONS." International Journal of Modern Physics A 14, no. 15 (June 20, 1999): 2397–430. http://dx.doi.org/10.1142/s0217751x99001202.
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We derive the moduli space of the global symmetry in N=1 supersymmetric theories. We show that, at the generic points, it coincides with the space of quasi-Nambu–Goldstone (QNG) bosons, which appear besides the ordinary Nambu–Goldstone (NG) bosons when the global symmetry G breaks down spontaneously to its subgroup H with preservation of N=1 supersymmetry. At the singular points, most of the NG bosons change to QNG bosons and the unbroken global symmetry is enhanced. The G orbits parametrized by the NG bosons are the fiber at the moduli space and the singular points correspond to the point where the H orbit (in the G orbit) shrinks. We also show that the low energy effective Lagrangian is the arbitrary function of the moduli parameters.
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Riyopoulos, Spilios. "Nonlinear Landau damping of purely perpendicular Bernstein modes." Journal of Plasma Physics 36, no. 1 (August 1986): 111–25. http://dx.doi.org/10.1017/s0022377800011612.
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The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.
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Sergeev, V. A., M. V. Kubyshkina, W. Baumjohann, R. Nakamura, O. Amm, T. Pulkkinen, V. Angelopoulos, et al. "Transition from substorm growth to substorm expansion phase as observed with a radial configuration of ISTP and Cluster spacecraft." Annales Geophysicae 23, no. 6 (September 15, 2005): 2183–98. http://dx.doi.org/10.5194/angeo-23-2183-2005.
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Abstract. Transition from the growth phase to the substorm expansion during a well-isolated substorm with a strong growth phase is investigated using a unique radial (THEMIS-like) spacecraft constellation near midnight, including the probing of the tail current at ~16 RE with Cluster, of the transition region at ~9 RE with Geotail and Polar, and of the inner region at 6.6 RE with two LANL spacecraft. The activity development on both a global scale and near the spacecraft footpoints was monitored with global auroral images (from the IMAGE spacecraft) and the ground network. Magnetospheric models, tuned using in-situ observations, indicated a strong tail stretching and plasma sheet thinning, which included the growth of the near-Earth current (approaching 30 nA/m2) and possible formation of a local B minimum in the neutral sheet (~5 nT) at ~10–12 RE near the substorm onset. However, there were no indications that the substorm onset was initiated just in this region. We emphasize the rather weak magnetic and plasma flow perturbations observed outside the thinned plasma sheet at Cluster, which could be interpreted as the effects of localized earthward-contracting newly-reconnected plasma tubes produced by the impulsive reconnection in the midtail plasma sheet. In that case the time delays around the distinct substorm onset are consistent with the activity propagation from the midtail to the inner magnetosphere. A peculiar feature of this substorm was that 12min prior to this distinct onset, a clear soft plasma injection to the GEO orbit was recorded which has little associated effects both in the ionosphere and in the transition region at ~9 RE. This pseudo-breakup was probably due to either a localized ballooning-type activity or due to the braking of a very narrow BBF whose signatures were also recorded by Cluster. This event manifested the (previously unknown) phenomenon, a strong tail overloading (excessive storage of magnetic energy) contrasted to the modest energy dissipation and plasma acceleration, which are both discussed and interpreted as the consequences of cold/dense and thick pre-substorm plasma sheet which often occurs after the long quiet period. The lessons of using the radial spacecraft configurations in substorm onset studies are also discussed. Keywords. Magnetospheric physics (Auroral phenomena, plasma sheet, storms and substorms)
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Saha, Prasenjit. "The breakup of quasiperiodic orbits near Jovian resonances." Icarus 87, no. 1 (September 1990): 103–9. http://dx.doi.org/10.1016/0019-1035(90)90023-3.
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Melikov, Agassi, Sevinj Aliyeva, and Janos Sztrik. "Retrial Queues with Unreliable Servers and Delayed Feedback." Mathematics 9, no. 19 (September 28, 2021): 2415. http://dx.doi.org/10.3390/math9192415.
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In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.
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Arora, Bharti, J. C. Pandey, and M. De Becker. "Long-term soft and hard X-ray investigation of the colliding wind WN+O binary WR 25." Monthly Notices of the Royal Astronomical Society 487, no. 2 (May 28, 2019): 2624–38. http://dx.doi.org/10.1093/mnras/stz1447.
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ABSTRACT We investigated the long-term behaviour in X-rays of the colliding wind binary WR 25, using archival data obtained with Suzaku, Swift, XMM–Newton, and NuSTAR spanning over ∼16 yr. Our analysis reveals phase-locked variations repeating consistently over many consecutive orbits, in agreement with an X-ray emission fully explained by thermal emission from the colliding winds in the 208-d orbit. We report on a significant deviation of the X-ray flux with respect to the 1/D trend (expected for adiabatic shocked winds) close to periastron passage. The absence of a drop in post-shock plasma temperature close to periastron suggests this break in trend cannot be explained in terms of reduced pre-shock velocities in this part of the orbit. Finally, NuSTAR data reveal a lack of hard X-ray emission (above 10.0 keV) above the background level. Upper limits on a putative non-thermal emission strongly suggest that the sensitivity of present hard X-ray observatories is not sufficient to detect non-thermal emission from massive binaries above 10 keV, unless the wind kinetic power is large enough to significantly feed particle acceleration in the wind–wind interaction.
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Barker, Adrian J., and Gordon I. Ogilvie. "Internal wave breaking and the fate of planets around solar-type stars." Proceedings of the International Astronomical Union 6, S271 (June 2010): 363–64. http://dx.doi.org/10.1017/s1743921311017807.
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AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.
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Hinse, Tobias C., and Jae Woo Lee. "Synthetic modelling of the light-travel time effect of circumbinary planets." Proceedings of the International Astronomical Union 8, S299 (June 2013): 289–90. http://dx.doi.org/10.1017/s1743921313008636.
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AbstractIn recent years several multi-body, circumbinary planets have been proposed to orbit short-period eclipsing binaries. In light of the recent discoveries based on the Kepler data, the existence of such systems seems plausible. However, performing a detailed dynamical analysis reveals that the majority of the proposed planetary systems follow highly unstable orbits. In order to solve the origin of this problem, we have started to model synthetic light-travel time signals of stable planetary systems. In particular, we aim to study the response of the model in various circumstances (e.g red/white noise level, various sampling frequencies, in-homogeneous data sets, baseline dependency.) This work will significantly increase the confidence with which model work is carried out for future systems and help towards an understaning when models break down (e.g resulting in unstable systems).
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El-Mowafy, Ahmed. "Predicting orbit and clock corrections during their outage in real-time positioning using GPS, GLONASS and QZSS for natural hazard warning systems." Journal of Applied Geodesy 13, no. 2 (April 26, 2019): 69–79. http://dx.doi.org/10.1515/jag-2018-0043.
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Abstract Real-time Precise Point Positioning (RT PPP) is a primary positioning method used in natural hazard warning systems (NHWS) such as monitoring tsunami and earthquakes. The method relays on precise orbit and clock corrections to eliminate satellite-related errors and its performance can be significantly improved by using measurements from multi-GNSS constellations compared with using only one system, such as GPS. The Japanese Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) provides these corrections for GPS, GLONASS and QZSS satellites enabling a multi-GNSS RT-PPP. However, the accuracy of RT PPP will suffer a major decline in case of presence of an outage in receiving these corrections, for instance due to a temporary failure of the user modem. For that reason, a method is proposed to maintain RT PPP when such a break takes place. For short outages less than 30 minutes we predict MADOCA orbits using a Holt-Winters’ auto-regressive model, and for longer outages up to 1 hr, the most recent International GNSS Service (IGS) ultra-rapid orbits can be used, but only for GPS. In addition, the clock corrections are predicted as a time series using a linear model with sinusoidal terms. The best regression period to estimate the required model parameters is discussed based on analysis of the autocorrelation of the corrections. The prediction model parameters are estimated using a sliding time window. Evaluation of the proposed method showed that positioning accuracy of 15 cm was maintained during the prediction period, which is twice better than using IGS ultra-rapid predicted products. For NHSW, the displacement errors due to prediction errors were generally within ±6 cm with one min interval and ±10 cm with five min interval.
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Almenara, J. M., R. F. Díaz, G. Hébrard, R. Mardling, C. Damiani, A. Santerne, F. Bouchy, et al. "SOPHIE velocimetry of Kepler transit candidates." Astronomy & Astrophysics 615 (July 2018): A90. http://dx.doi.org/10.1051/0004-6361/201732500.
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Kepler-419 is a planetary system discovered by the Kepler photometry which is known to harbour two massive giant planets: an inner 3 MJ transiting planet with a 69.8-day period, highly eccentric orbit, and an outer 7.5 MJ non-transiting planet predicted from the transit-timing variations (TTVs) of the inner planet b to have a 675-day period, moderately eccentric orbit. Here we present new radial velocity (RV) measurements secured over more than two years with the SOPHIE spectrograph, where both planets are clearly detected. The RV data is modelled together with the Kepler photometry using a photodynamical model. The inclusion of velocity information breaks the MR−3 degeneracy inherent in timing data alone, allowing us to measure the absolute stellar and planetary radii and masses. With uncertainties of 12 and 13% for the stellar and inner planet radii, and 35, 24, and 35% for the masses of the star, planet b, and planet c, respectively, these measurements are the most precise to date for a single host star system using this technique. The transiting planet mass is determined at better precision than the star mass. This shows that modelling the radial velocities and the light curve together in systems of dynamically interacting planets provides a way of characterising both the star and the planets without being limited by knowledge of the star. On the other hand, the period ratio and eccentricities place the Kepler-419 system in a sweet spot; had around twice as many transits been observed, the mass of the transiting planet could have been measured using its own TTVs. Finally, the origin of the Kepler-419 system is discussed. We show that the system is near a coplanar high-eccentricity secular fixed point, related to the alignment of the orbits, which has prevented the inner orbit from circularising. For most other relative apsidal orientations, planet b’s orbit would be circular with a semi-major axis of 0.03 au. This suggests a mechanism for forming hot Jupiters in multiplanetary systems without the need of high mutual inclinations.
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Li, Daohai, Alexander J. Mustill, and Melvyn B. Davies. "Flyby encounters between two planetary systems II: exploring the interactions of diverse planetary system architectures." Monthly Notices of the Royal Astronomical Society 496, no. 2 (June 9, 2020): 1149–65. http://dx.doi.org/10.1093/mnras/staa1622.
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ABSTRACT Planetary systems formed in clusters may be subject to stellar encounter flybys. Here, we create a diverse range of representative planetary systems with different orbital scales and planets’ masses and examine encounters between them in a typical open cluster. We first explore the close-in multisuper Earth systems ≲0.1 au. They are resistant to flybys in that only ones inside a few au can destabilize a planet or break the resonance between such planets. But these systems may capture giant planets on to wide orbits from the intruding star during distant flybys. If so, the original close-in small planets’ orbits may be tilted together through Kozai–Lidov mechanism, forming a ‘cold’ system that is significantly inclined against the equator of the central host. Moving to the intermediately placed planets around solar-like stars, we find that the planets’ mass gradient governs the systems’ long-term evolution post-encounter: more massive planets have better chances to survive. Also, a system’s angular momentum deficit, a quantity describing how eccentric/inclined the orbits are, measured immediately after the encounter, closely relates to the longevity of the systems – whether or not and when the systems turn unstable in the ensuing evolution millions of years post-encounter. We compare the orbits of the surviving planets in the unstable systems through (1) the immediate consequence of the stellar fly or (2) internal interplanetary scattering long post-encounter and find that those for the former are systematically colder. Finally, we show that massive wide-orbit multiplanet systems like that of HR 8799 can be easily disrupted and encounters at a few hundreds of au suffice.
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MacLeod, Morgan, Michelle Vick, and Abraham Loeb. "Tidal Wave Breaking in the Eccentric Lead-in to Mass Transfer and Common Envelope Phases." Astrophysical Journal 937, no. 1 (September 1, 2022): 37. http://dx.doi.org/10.3847/1538-4357/ac8aff.
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Abstract The evolution of many close binary and multiple star systems is defined by phases of mass exchange and interaction. As these systems evolve into contact, tidal dissipation is not always sufficient to bring them into circular, synchronous orbits. In these cases, encounters of increasing strength occur while the orbit remains eccentric. This paper focuses on the outcomes of close tidal passages in eccentric orbits. Close eccentric passages excite dynamical oscillations about the stars’ equilibrium configurations. These tidal oscillations arise from the transfer of orbital energy into oscillation mode energy. When these oscillations reach sufficient amplitude, they break near the stellar surface. The surface wave-breaking layer forms a shock-heated atmosphere that surrounds the object. The continuing oscillations in the star’s interior launch shocks that dissipate into the atmosphere, damping the tidal oscillations. We show that the rapid, nonlinear dissipation associated with the wave breaking of fundamental oscillation modes therefore comes with coupled mass loss to the wave-breaking atmosphere. The mass ratio is an important characteristic that defines the relative importance of mass loss and energy dissipation and therefore determines the fate of systems evolving under the influence of nonlinear dissipation. The outcome can be rapid tidal circularization (q ≪ 1) or runaway mass exchange (q ≫ 1).
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Johnson, N. L. "History and consequences of on-orbit break-ups." Advances in Space Research 5, no. 2 (January 1985): 11–19. http://dx.doi.org/10.1016/0273-1177(85)90382-5.
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Pfeffer, Joel L., Sebastian Trujillo-Gomez, J. M. D. Kruijssen, Robert A. Crain, Meghan E. Hughes, Marta Reina-Campos, and Nate Bastian. "Predicting accreted satellite galaxy masses and accretion redshifts based on globular cluster orbits in the E-MOSAICS simulations." Monthly Notices of the Royal Astronomical Society 499, no. 4 (October 10, 2020): 4863–75. http://dx.doi.org/10.1093/mnras/staa3109.
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ABSTRACT The ages and metallicities of globular clusters (GCs) are known to be powerful tracers of the properties of their progenitor galaxies, enabling their use in determining the merger histories of galaxies. However, while useful in separating GCs into individual accretion events, the orbits of GC groups themselves have received less attention as probes of their progenitor galaxy properties. In this work, we use simulations of galaxies and their GC systems from the MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE project to explore how the present-day orbital properties of GCs are related to the properties of their progenitor galaxies. We find that the orbits of GCs deposited by accretion events are sensitive to the mass and merger redshift of the satellite galaxy. Earlier mergers and larger galaxy masses deposit GCs at smaller median apocentres and lower total orbital energy. The orbital properties of accreted groups of GCs can therefore be used to infer the properties of their progenitor galaxy, though there exists a degeneracy between galaxy mass and accretion time. Combining GC orbits with other tracers (GC ages, metallicities) will help to break the galaxy mass/accretion time degeneracy, enabling stronger constraints on the properties of their progenitor galaxy. In situ GCs generally orbit at lower energies (small apocentres) than accreted GCs, however they exhibit a large tail to high energies and even retrograde orbits (relative to the present-day disc), showing significant overlap with accreted GCs. Applying the results to Milky Way GCs groups suggests a merger redshift z ∼ 1.5 for the Gaia Sausage/Enceladus and z > 2 for the ‘low-energy’/Kraken group, adding further evidence that the Milky Way had two significant mergers in its past.
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Zhang, Zhengwu, Jinting Wang, and Feng Zhang. "Equilibrium Customer Strategies in the Single-Server Constant Retrial Queue with Breakdowns and Repairs." Mathematical Problems in Engineering 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/379572.
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We consider a single-server constant retrial queueing system with a Poisson arrival process and exponential service and retrial times, in which the server may break down when it is working. The lifetime of the server is assumed to be exponentially distributed and once the server breaks down, it will be sent for repair immediately and the repair time is also exponentially distributed. There is no waiting space in front of the server and arriving customers decide whether to enter the retrial orbit or to balk depending on the available information they get upon arrival. In the paper, Nash equilibrium analysis for customers’ joining strategies as well as the related social and profit maximization problems is investigated. We consider separately the partially observable case where an arriving customer knows the state of the server but does not observe the exact number of customers waiting for service and the fully observable case where customer gets informed not only about the state of the server but also about the exact number of customers in the orbit. Some numerical examples are presented to illustrate the effect of the information levels and several parameters on the customers’ equilibrium and optimal strategies.
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Udagawa, T., Y. J. Lee, and T. Tamura. "Breakup-fusion analyses of single-nucleon stripping to bound and unbound orbits." Physical Review C 39, no. 1 (January 1, 1989): 47–55. http://dx.doi.org/10.1103/physrevc.39.47.
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Bhowmik, Debanjan, and Sayeef Salahuddin. "Deterministic Spin–Orbit Torque Switching of a Perpendicularly Polarized Magnet Using Wedge Shape of the Magnet." SPIN 06, no. 02 (June 2016): 1640008. http://dx.doi.org/10.1142/s2010324716400087.
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Spin–orbit torque provides an efficient way to switch magnets for low power memory applications by reducing the current density needed to switch the magnetization. Perpendicularly polarized magnets are preferred for high density data storage applications because of their high thermal stability in scaled dimensions. However, spin–orbit torque cannot switch a perpendicularly polarized magnet deterministically from up to down and down to up in the absence of an external magnetic field because spin–orbit torque alone cannot break the symmetry of the system. This poses a severe challenge to the applicability of spin–orbit torque for memory devices. In this paper, we show through micromagnetic simulations that when spin–orbit torque is applied on a magnet with a wedge shape, the moments of the magnet are aligned in-plane. On removal of the spin–orbit torque the moments deterministically evolve to vertically upward or downward direction because the anisotropy axis of the magnet is tilted away from the vertical direction owing to the wedge shape of the magnet. Thus, spin–orbit torque driven deterministic switching of the magnet in the absence of an external magnetic field is possible.
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ADOUANI, ABDELHAMID, and HABIB MARZOUGUI. "Singular measures for classP-circle homeomorphisms with several break points." Ergodic Theory and Dynamical Systems 34, no. 2 (April 2012): 423–56. http://dx.doi.org/10.1017/etds.2012.133.
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AbstractLetfbe a classP-homeomorphism of the circle with break point singularities, that is, differentiable except at some singular points where the derivative has a jump. Letfhave irrational rotation number andDfbe absolutely continuous on every continuity interval ofDf. We prove that if the product of thef-jumps along any subset of break points is distinct from 1 then the invariant measureμfis singular with respect to the Haar measure. This result generalizes previous results obtained by Dzhalilov and Khanin, Dzhalilov, Akhadkulov, Dzhalilov–Liousse and Mayer. Moreover, we prove that if the rotation numberρ(f) is irrational of bounded type then (a) if the product of thef-jumps on some orbit is distinct from 1 then the invariant measureμfis singular with respect to the Haar measurem, and (b) if the product of thef-jumps on each orbit is equal to 1 andD2f∈Lp(S1) for somep>1 thenμfis equivalent to the Haar measure.
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Pan, Shanshan, and Xiyun Hou. "Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem." Applied Sciences 12, no. 18 (September 6, 2022): 8952. http://dx.doi.org/10.3390/app12188952.
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Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter μ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented.
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Souza, Leonardo C., Amanda C. Mathias, Pedro Haerter, and Ricardo L. Viana. "Basin Entropy and Shearless Barrier Breakup in Open Non-Twist Hamiltonian Systems." Entropy 25, no. 8 (July 30, 2023): 1142. http://dx.doi.org/10.3390/e25081142.
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We consider open non-twist Hamiltonian systems represented by an area-preserving two-dimensional map describing incompressible planar flows in the reference frame of a propagating wave, and possessing exits through which map orbits can escape. The corresponding escape basins have a fractal nature that can be revealed by the so-called basin entropy, a novel concept developed to quantify final-state uncertainty in dynamical systems. Since the map considered violates locally the twist condition, there is a shearless barrier that prevents global chaotic transport. In this paper, we show that it is possible to determine the shearless barrier breakup by considering the variation in the escape basin entropy with a tunable parameter.
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Gardner, Tyler, John D. Monnier, Francis C. Fekel, Jean-Baptiste Le Bouquin, Adam Scovera, Gail Schaefer, Stefan Kraus, et al. "ARMADA. II. Further Detections of Inner Companions to Intermediate-mass Binaries with Microarcsecond Astrometry at CHARA and VLTI." Astronomical Journal 164, no. 5 (October 11, 2022): 184. http://dx.doi.org/10.3847/1538-3881/ac8eae.
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Abstract We started a survey with CHARA/MIRC-X and VLTI/GRAVITY to search for low-mass companions orbiting individual components of intermediate-mass binary systems. With the incredible precision of these instruments, we can detect astrometric “wobbles” from companions down to a few tens of microarcseconds. This allows us to detect any previously unseen triple systems in our list of binaries. We present the orbits of 12 companions around early F- to B-type binaries, 9 of which are new detections and 3 of which are first astrometric detections of known radial velocity (RV) companions. The masses of these newly detected components range from 0.45 to 1.3 M ⊙. Our orbits constrain these systems to a high astrometric precision, with median residuals to the orbital fit of 20–50 μas in most cases. For seven of these systems we include newly obtained RV data, which help us to identify the system configuration and to solve for masses of individual components in some cases. Although additional RV measurements are needed to break degeneracy in the mutual inclination, we find that the majority of these inner triples are not well aligned with the wide binary orbit. This hints that higher-mass triples are more misaligned compared to solar and lower-mass triples, though a thorough study of survey biases is needed. We show that the ARMADA survey is extremely successful at uncovering previously unseen companions in binaries. This method will be used in upcoming papers to constrain companion demographics in intermediate-mass binary systems down to the planetary-mass regime.
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Fang, Qun, Zhen Zhang, Haodong Meng, Xiaolong Wang, and Xiuwei Zhang. "Maneuver Strategy for Active Spacecraft to Avoid Space Debris and Return to the Original Orbit." International Journal of Aerospace Engineering 2022 (April 13, 2022): 1–16. http://dx.doi.org/10.1155/2022/4650730.
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During normal operation of the on-orbit spacecraft, if some satellite in a nearby orbit suddenly breaks apart, its debris will threat the safe operation of the on-orbit spacecraft. Therefore, it is necessary to study the active spacecraft’s avoidance of the space debris group and returning to the original orbit. In this way, the safe operation of on-orbit spacecraft will be guaranteed. However, as the geometric structure of the space debris group is constantly changing, it is hard to accurately demonstrate the changing shape of the debris group, let alone determine the unreachable domain. Traditional obstacle avoidance problems involve low speed of the vehicle; so, the application of artificial potential field and particle swarm algorithms is suitable for such problems. However, these two methods are not applicable to the maneuver strategy of spacecraft with high initial velocity. Therefore, to help spacecraft avoid the space debris group, a new method is required. This paper has established a simplified model to simulate the unreachable domain of the space debris group. It has modified the artificial potential field (APF) method and particle swarm optimization algorithm, with an aim to help spacecraft avoid the space debris group and return to the original orbit. Based on the method, the paper has proposed a three-stage maneuver strategy for the spacecraft to avoid the debris. To show the effectiveness of the method, this paper has simulated an on-orbit spacecraft’s avoidance of the space debris group nearby and returning to its original orbit. Through simulation, the feasibility of the maneuver strategy for spacecraft in the geosynchronous orbit is evaluated. The simulation results show that the method proposed in this paper can effectively accomplish the task.
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Lloret-Climent, Miguel, Andrés Montoyo, Yoan Gutierrez, Rafael Muñoz Guillena, and Kristian Alonso. "A systemic and cybernetic perspective on causality, big data and social networks in tourism." Kybernetes 48, no. 2 (February 4, 2019): 287–97. http://dx.doi.org/10.1108/k-02-2018-0084.
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PurposeThe purpose of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on an algorithm and applying an interpretation of chaos theory developed in the context of General Systems Theory and Big Data.Design/methodology/approachTourism is one of the most digitalized sectors of the economy, and social networks are an important source of data for information gathering. However, the high levels of redundant information on the Web and the appearance of contradictory opinions and facts produce undesirable effects that must be cross-checked against real data. This paper sets out the causal relationships associated with tourist flows to enable the formulation of appropriate strategies.FindingsThe results can be applied to numerous cases, for example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups, as well as analysing tourist behaviour in terms of the most relevant variables.Originality/valueThe technique presented here breaks with the usual treatment of the tourism topics. Unlike statistical analyses that merely provide information on current data, the authors use orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.