Behavior Of Orbits Research Articles

Dynamics of three-dimensional capture orbits from libration region analysis

Low-energy trajectories take advantage of the mutual action of multiple celestial bodies on the spacecraft, and can conclude with ballistic capture about the arrival body, thus allowing significant savings in terms of propellant consumption, if compared to more traditional transfers. Because of the chaotic nature of multibody environments, the design of low-energy trajectories with given constraints can be complex and it is often obtained after a long, iterative, and eventually computationally expensive process.This work is aimed at identifying a limited set of characteristic parameters related both to the time behavior of three-dimensional ballistic capture orbits and to some osculating orbit elements (i.e., inclination, semimajor axis, and eccentricity), relative either to the departure or to the arrival body. The analysis is performed using the linear expansion of the Hamiltonian equations of motion in the equilibrium region around the collinear libration point L1 (or L2), in the dynamical framework of the 3 dimensional circular restricted 3-body problem. A correlation among some Hamiltonian parameters in the equilibrium region and the trajectory osculating orbital elements at capture is established. This result is used to design missions with ballistic capture having required orbital parameters at the arrival planet and it provides a strategy to control the target orbital elements at capture by small thrust maneuvers at the equilibrium region. Because of the long flight time, the solar perturbation is considered in the analysis, and suitable launch dates for the ballistically captured missions are determined.

Planet formation and stability in polar circumbinary discs

Context. Dynamical studies suggest that most circumbinary discs (CBDs) should be coplanar (i.e. the rotation vectors of the binary and the disc should be aligned). However, some theoretical works show that under certain conditions a CBD can become polar, which means that its rotation vector is orthogonal with respect to the binary orbital plane. Interestingly, very recent observations show that polar CBDs exist in nature (e.g. HD 98800). Aims. We test the predictions of CBD alignment around eccentric binaries based on linear theory. In particular, we compare prograde and retrograde CBD configurations. Then, assuming planets form in these systems, we thoroughly characterise the orbital behaviour and stability of misaligned (P-type) particles. This is done for massless and massive particles. Methods. The evolution of the CBD alignment for various configurations was modelled through three-dimensional hydrodynamical simulations. For the orbital characterisation and the analysis stability, we relied on long-term N-body integrations and structure and chaos indicators, such as Δe and MEGNO. Results. We confirm previous analytical predictions on CBD alignment, but find an unexpected symmetry breaking between prograde and retrograde configurations. More specifically, we observe polar alignment for a retrograde misaligned CBD that was expected to become coplanar with respect to the binary disc plane. Therefore, the likelihood of becoming polar for a highly misaligned CBD is higher than previously thought. Regarding the stability of circumbinary P-type planets (also know as Tatooines), polar orbits are stable over a wide range of binary parameters. In particular, for binary eccentricities below 0.4 the orbits are stable for any value of the binary mass ratio. In the absence of gas, planets with masses below 10−5 M⊙ have negligible effects on the binary orbit. Finally, we suggest that mildly eccentric equal-mass binaries should be searched for polar Tatooines.

Orbital stability of ensembles of particles in regions of magnetic reconnection in Earth's magneto-tail

We investigate the collective behavior of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of temporary capture of particle orbits in configuration space as well as locations, where strong particle accelerations take place. With this study, we are able to provide a detailed map, i.e., the topology, of high and low acceleration centers close to the reconnection site. Quasiregular and chaotic kinds of motions of elementary particles can be determined as well. The orbital stability of particle orbits is obtained by a statistical analysis of the outcome of the system of variational equations of particle orbits within the framework of particle-in-cell simulations. Using the concept of Lyapunov characteristic numbers to ensembles of particle orbits, we introduce Lyapunov ensemble averages to describe the response of particle orbits to local perturbations induced by the electromagnetic field.

Orbital-flop Induced Magnetoresistance Anisotropy in Rare Earth Monopnictide CeSb

The charge and spin of the electrons in solids have been extensively exploited in electronic devices and in the development of spintronics. Another attribute of electrons—their orbital nature—is attracting growing interest for understanding exotic phenomena and in creating the next-generation of quantum devices such as orbital qubits. Here, we report on orbital-flop induced magnetoresistance anisotropy in CeSb. In the low temperature high magnetic-field driven ferromagnetic state, a series of additional minima appear in the angle-dependent magnetoresistance. These minima arise from the anisotropic magnetization originating from orbital-flops and from the enhanced electron scattering from magnetic multidomains formed around the first-order orbital-flop transition. The measured magnetization anisotropy can be accounted for with a phenomenological model involving orbital-flops and a spin-valve-like structure is used to demonstrate the viable utilization of orbital-flop phenomenon. Our results showcase a contribution of orbital behavior in the emergence of intriguing phenomena.

Asymptotic behavior of orbits of holomorphic semigroups

Let (ϕt) be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let Ω be the starlike at infinity domain image of the Koenigs function of (ϕt). In this paper we characterize the type of convergence of the orbits of (ϕt) to the Denjoy-Wolff point in terms of the shape of Ω. In particular we prove that the convergence is non-tangential if and only if the domain Ω is “quasi-symmetric with respect to vertical axis”. We also prove that such conditions are equivalent to the curve [0,∞)∋t↦ϕt(z) being a quasi-geodesic in the sense of Gromov. Also, we characterize the tangential convergence in terms of the shape of Ω.

Correlation effect on the electronic properties of pair-checkerboard AFM monolayer FeSe: a first-principles study

We presented a study of the influence of on-site Coulomb correlation U and Hund coupling J on the electronic properties of monolayer FeSe in a pair-checkerboard antiferromagnetic (PAFM) state based on Hubbard-corrected density functional theory (DFT + U). The results demonstrated the Hubbard-U have a strong influence on the electronic bands and lattice structure of monolayer FeSe in PAFM state. The in-plane lattice constant changes under U > 1.85 eV has been identified under full structure optimization. Furthermore, the Hund coupling J has significant influence on the electronic bands and exhibits a remarkable orbital selective behavior at U = 0. Additionally, our results also demonstrated the Hund coupling J has a weaker effect on electronic properties of FeSe when U gets larger. These results are useful for elucidating the possible role of correlation strength on the electronics band and magnetic ground state of monolayer FeSe.

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

Probing the relationship between the null geodesics and thermodynamic phase transition for rotating Kerr-AdS black holes

In this paper, we aim to examine the relationship between the unstable circular photon orbit and the thermodynamic phase transition for a rotating Kerr-AdS black hole. On one side, we give a brief review of the phase transition for the Kerr-AdS black hole. The coexistence curve and the metastable curve corresponding to the phase transition are clearly shown. On the other side, we calculate the radius and the angular momentum of the unstable circular orbits for a photon by analyzing the effective potential. Then combining these two sides, we find the following results. i) The radius and the angular momentum of the unstable circular photon orbits demonstrate the non-monotonic behaviors when the thermodynamic phase transition takes place. So from the behavior of the circular orbit, one can determine whether there exists a thermodynamic phase transition. ii) The difference of the radius or the angular momentum for the coexistence small and large black holes can be treated as an order parameter to describe the phase transition. And near the critical point, it has a critical exponent of $\frac{1}{2}$. iii) The temperature and pressure corresponding to the extremal points of the radius or the angular momentum of the unstable circular photon orbit completely agree with that of the metastable curves from the thermodynamic side. Thus, these results confirm the relationship between the geodesics and thermodynamic phase transition for the Kerr-AdS black hole. Therefore, on one hand, we are allowed to probe the thermodynamic phase transition from the gravity side. On the other hand, the signature of the strong gravitational effect can also be revealed from the black hole thermodynamics.

Orbital-order driven ferroelectricity and dipolar relaxation dynamics in multiferroic GaMo4S8

We present the results of broadband dielectric spectroscopy of $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$, a lacunar spinel system that recently was shown to exhibit non canonical, orbitally driven ferroelectricity. Our study reveals complex relaxation dynamics of this multiferroic material, both above and below its Jahn-Teller transition at ${T}_{\mathrm{JT}}=47\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Above ${T}_{\mathrm{JT}}$, two types of coupled dipolar-orbital dynamics seem to compete: relaxations within cluster-like regions with short-range polar order as in relaxor ferroelectrics and critical fluctuations of only weakly interacting dipoles, the latter resembling the typical dynamics of order-disorder type ferroelectrics. Below the Jahn-Teller transition, the onset of orbital order drives the system into long-range ferroelectric order and dipolar dynamics within the ferroelectric domains is observed. The coupled dipolar and orbital relaxation behavior of $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$ above the Jahn-Teller transition markedly differs from that of the skyrmion host $\mathrm{Ga}{\mathrm{V}}_{4}{\mathrm{S}}_{8}$, which seems to be linked to differences in the structural distortions of the two systems on the unit-cell level.

Discovery of Tidal RR Lyrae Stars in the Bulge Globular Cluster M62∗

Abstract The RR Lyrae (RRL) rich globular cluster M62 (NGC 6266) is one of the most massive globular clusters in the Milky Way, located in the dense region of the Galactic bulge, where dynamical processes that affect the survival of globular clusters are maximized. Using Gaia second data release data we have found clear evidence for an excess of RRLs beyond the cluster tidal radius of M62, associated partly with stars stripped into the Galaxy field. This is confirmed with new Visible and Infrared Survey Telescope for Astronomy Variables in the Via Lactea Extended survey observations, which discard any differential reddening effect as the possible cause of the observed RRL density excess. We also determined the orbit of M62 using accurate new measurements of its distance, radial velocity, and proper motions, finding that its orbit is prograde with respect to the direction of the Galactic rotation. Orbits are integrated in the non-axisymmetric galactic model GravPot16, which includes the perturbations due to the central Galactic bar. M62 shows a particular orbital behavior, having a dynamical signature of the bar-bulge region. The small extra-tidal RRLs extensions that are observed are roughly aligned toward the galactic center, and the direction is almost perpendicular to the galactic plane, not with its motion along its orbit. This may be a clear sign of bulge-crossing shocks during the last passage close of the cluster toward its perigalacticon. M62 would be the first clear observed case of bulge shocking in the inner Galaxy acting on a globular cluster.

\u03b418O and SST signal decomposition and dynamic of the Pliocene-Pleistocene climate system: new insights on orbital nonlinear behavior vs. long-term trend

The global LR04 δ18O, the tropical ODP Site 846 sea surface temperature (SST), and the global ΔSST stack records were investigated using the advanced method for time-series decomposition singular spectrum analysis to outline the quantitative role of orbital forcings and to investigate the nonlinear dynamics of the Pliocene and Pleistocene climate system. For the first time, a detailed quantitative evaluation is provided of the δ18O and SST variance paced by long-period orbital modulation, short eccentricity, obliquity, precession, and half-precession cycles. New insights into the nonlinear dynamic of the orbital components suggest considering astronomical signals as composite feedback lagged responses paced by orbitals and damped (Early Pliocene) or amplified (Mid-Late Pleistocene) in a range of − 100 to + 400% the forcing. The Early Pliocene asymptotic decay of the δ18O and SST response sensitivity up to − 100% observed for the first time in all orbital responses is interpreted as damping effect of a wide global forest cover along with a possible high ocean primary productivity, through the CO2-related negative feedbacks during time of global greenhouse. An anomalous post-Mid-Pleistocene Transition (MPT) sharply declines to near-zero in obliquity response sensitivity observed in both global δ18O and tropical SST, suggesting an attenuation mechanism of the obliquity driving force and a reduction of the related feedback amplification processes. It is hypothesized the post-MPT obliquity damping has contributed to the strengthening of the short eccentricity response by mitigating the obliquity “ice killing”, favoring a long-life ice sheet sensitive to a synergistic ~ 100-kyr amplification of positive feedback processes during the time of a global icy state. The global δ18O, the tropical SST, and the global ΔSST trend components, all explaining ~ 76% of the Plio-Pleistocene variance and significantly modifying the mean climate state, appear to be related to the long-term pCO2 proxies, supposedly controlled by plate tectonics through the global carbon cycle (CO2 outgassing, explosive volcanism, orography and erosion, paleogeography, oceanic paleocirculation, and ocean fertilization). Finally, singular spectrum analysis provides a valuable tool in cyclostratigraphy with the remarkable advantage of separating full-resolution time series by variance strength.

Kelakuan Orbital Molekul Nanomangkin FeN4 /C untuk Tindak Balas Penurunan Oksigen (ORR) di Katod Sel Fuel Metanol Langsung (DMFC)

Approaching commercialization phase of Direct methanol fuel cell (DMFC) technology, developing high kinetic rate active area with inexpensive non-precious metal catalyst (NPMC) for ORR catalyst materials to replace currently used Pt-based catalysts is a compulsory and crucial requirement in order to reduce the catalyst and overall system cost. Thus, the objective of this study is to describe the molecule orbital behavior of NPMC FeN4/C and discuss of recent works in the area of non-precious metal electrocatalys for ORR. Several important kinds of free energy study for carbon supported non-precious metal electrocatalys for ORR by using density functional theory (DFT) in CASTEP module analysis. The properties of FeN4/C nanocatalyst were studied, and their energy properties, band structure and density of state were evaluated accordingly. Besides, electronic properties of the nanostructure of FeN4/C also calculated. The results indicated that optimized geometry shows the oxygen in 3.699 Ao from the catalyst opposite with the Fe atom. Moreover, HOMO occurs in the orbitals 173 and LUMO occur in orbitals 174 and the band gap -0.82 proved that FeN4/C nanostructure catalyst is conductive and suitable to use as catalyst in fuel cell.

The Period Analysis of the Hierarchical System DI Peg

The existence of an additional body around a binary system can be detected by the help of the light-travel time effect. Due to the motions of binary and the companion stars around the common mass center of the ternary system, the light-time effect produces an irregularity on the eclipse timings. Monitoring the variations in these timings, sub-stellar or planet companions orbiting around the binary system can be identified. In this paper, additional bodies orbiting the Algol type binary DI Peg are examined by using the archival eclipse timings including our CCD data observed at the Ankara University Kreiken Observatory. More than five hundred minimum times equivalent to around nine decades are employed to identify the orbital behavior of the binary system. The best fit to the timings shows that the orbital period of DI Peg has variation due to an integration of two sinusoids with the periods of $P_3 = 49.50\pm0.36$ yr and $P_4 = 27.40\pm0.24$ yr. The orbital change is thought to be most likely due to the existence of two M-type red dwarf companions with the masses of $M_3 =0.213 \pm 0.021$ M$_\odot$ and $M_4 = 0.151 \pm 0.008$ M$_\odot$, assuming that the orbits of additional bodies are co-planar with the orbit of the binary system. Also, the residuals of two sinusoidal fits still seem to show another modulation with the period of roughly $P = 19.5$ yr. The origin of this modulation is not clear and more observational data are required to reveal if the periodicity is caused by another object gravitationally bounded to the system.

P-Flurophenyldicyanovinyl as electron-withdrawing group for highly soluble and thermally stable donor–acceptor small molecules

Solution-processed small molecule-based solar cells have demonstrated high power conversion efficiencies in recent years. However, several challenges have yet to be overcome, including achieving of low cost and excellent long-term stability of donor small molecules. Therefore, development of stable blocks to design organic semiconductors with optimal properties remains an actual problem. We report an alkyl-free star-shaped donor–acceptor (D–A) molecule, N(Ph-2T-DCV-PhF)3, containing p-fluorophenyldicyanovinyl (FPh-DCV) electron-withdrawing groups, triphenylamine as the donor core, and 2,2′-bithiophenes as the π-bridges between them. The study of thermal, optical, and electrochemical properties of the molecule in comparison to the direct analog with phenyldicyanovinyl groups, N(Ph-2T-DCV-Ph)3, made it possible to demonstrate the effect of the fluorine substituent on such key parameters as solubility, bandgap, lowest unoccupied molecular orbital energy level, phase behavior, thermal stability, and wettability. This work suggests that usage of the FPh-DCV block is an effective and simple tool to tune physical and physicochemical properties of stable D–A small molecules.

Periodic orbit analysis for the deterministic path-preference traffic flow cellular automaton

The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we propose an exact analysis for the simplest version of this model. We find that the density of particles is dominant to the dynamics of this cellular automaton and observed that there are not only expected phase shift but also several gaps as the density increases. By considering the behavior of periodic orbits, we also determine the point where such gaps in the flow appear and the exact value of the flow.

Experimental Observation of Multiple Attractor Bifurcation in an Electronic Circuit

Multiple attractor bifurcations occurring in piecewise smooth dynamical systems may lead to potentially damaging situations. The striking feature of these bifurcations is that, in the presence of arbitrarily small noise, they lead to fundamentally unpredictable behavior of orbits as a system parameter is varied through its bifurcation value. In earlier works, the conditions of occurrence of multiple attractor bifurcation were reported in the context of a piecewise linear 2-D map. In this brief, we report the first experimental observation of this phenomenon in an electronic switching system.

Statistical properties of quadratic polynomials with a neutral fixed point

We describe the statistical properties of the dynamics of the quadratic polynomials P_\alpha(z)=e^{2\pi \alpha \mathbf{i}} z+ z^2 on the complex plane, with \alpha of high type. In particular, we show that these maps are uniquely ergodic on their measure-theoretic attractors, and the unique invariant probability is a physical measure describing the statistical behaviour of typical orbits in the Julia set. This confirms a conjecture of Pérez–Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.

Homoclinic orbits in the Euler problem of two fixed centers

We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers.

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.

Periodic motion around libration points in the Elliptic Restricted Three-Body Problem

Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.