Unique Orbit Research Articles

Sculpting of Exoplanetary Systems Driven by a Misaligned Disk and Stellar Oblateness: Origin of Perpendicular Orbits in HD 3167

A significant proportion of exoplanets have been detected with highly tilted or even polar orbits relative to their host stars’ equatorial planes. These unusual orbital configurations are often linked to postdisk secular interactions among multiple bodies. However, many aspects remain elusive. In this study, we investigate the role of disk-induced spin–orbit misalignments in shaping the architecture of multiplanet systems, taking into account the combined effect of the host star’s oblateness and the full-space disk potential. We demonstrate that large mutual planetary inclinations can arise from a saddle-center bifurcation occurring during the photoevaporation of the disk. This bifurcation triggers an instant, nonadiabatic transition in the planet’s libration. Following this process, the orbital evolution diverges into several distinct patterns. Notably, in scenarios involving a near-polar primordial misalignment, the orbit, consistently librating about a coplanar equilibrium axis, can be captured by an orthogonal equilibrium during the decay of the stellar oblateness. However, the orbit will be eventually recaptured by the coplanar equilibrium, aligned or antialigned with the orientation of the outer orbit, resulting in either a prograde or retrograde inner–outer orbit configuration. Additionally, general relativity contributes to maintaining eccentricity stability within these dynamic scenarios. Through the proposed mechanism, we can provide a plausible explanation for the unique, near-perpendicular, and likely retrograde orbit architecture observed in the HD 3167 system, enhancing our understanding of exoplanetary system dynamics.

Autonomous disentangling for spectroscopic surveys

ABSTRACT A suite of spectroscopic surveys is producing vast sets of stellar spectra with the goal of advancing stellar physics and Galactic evolution by determining their basic physical properties. A substantial fraction of these stars are in binary systems, but almost all large-survey modelling pipelines treat them as single stars. For sets of multi-epoch spectra, spectral disentangling is a powerful technique to recover or constrain the individual components’ spectra of a multiple system. So far, this approach has focused on small samples or individual objects, usually with high-resolution ($R \gtrsim 10.000$) spectra and many epochs ($\gtrsim 8$). Here, we present a disentangling implementation that accounts for several aspects of few-epoch spectra from large surveys: that vast sample sizes require automatic determination of starting guesses; that some of the most extensive spectroscopic surveys have a resolution of only $\approx 2000$; that few epochs preclude unique orbit fitting; that one needs effective regularization of the disentangled solution to ensure resulting spectra are smooth. We describe the implementation of this code and show with simulated spectra how well spectral recovery can work for hot and cool stars at $R \approx 2000$. Moreover, we verify the code on two established binary systems, the ‘Unicorn’ and ‘Giraffe’. This code can serve to explore new regimes in survey disentangling in search of massive stars with massive dark companions, for example, the $\gtrsim 200\,000$ hot stars of the SDSS-V survey.

Exploring the structure and hydrogen storage capacity of CeHn0/+ clusters.

The unique 4f orbitals and abundant electronic energy levels of rare earth elements enable effective doping and modification to enhance hydrogen storage performance, making it an increasingly prominent focus of research. The structures of neutral and cationic CeHn0/+ (n = 2-20) clusters have been determined using the Crystal Structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method in conjunction with density functional theory (DFT). Interestingly, the CeH13 and CeH14+ exhibit remarkable stability in the doublet state with Cs and C2v symmetry, respectively. The adsorption energy of CeHn0/+ (n = 2-20) suggests a preference for H atoms to chemically adsorb on Ce atoms. The analysis of molecular orbital composition reveals that the stability of both CeH13 and CeH14+ is attributed to the significant hybridization between the H 1s and Ce 4f orbitals. Both CeH13 and CeH14+ demonstrate significant hydrogen storage capacities, with values reaching 8.5 wt% and 9.1 wt%, respectively.

Valence electronic engineering of superhydrophilic Dy-evoked Ni-MOF outperforming RuO2 for highly efficient electrocatalytic oxygen evolution

Tackling the problem of poor conductivity and catalytic stability of pristine metal-organic frameworks (MOFs) is crucial to improve their oxygen evolution reaction (OER) performance. Herein, we introduce a novel strategy of dysprosium (Dy) doping, using the unique 4f orbitals of this rare earth element to enhance electrocatalytic activity of MOFs. Our method involves constructing Dy-doped Ni-MOF (Dy@Ni-MOF) nanoneedles on carbon cloth via a Dy-induced valence electronic perturbation approach. Experiments and density functional theory (DFT) calculations reveal that Dy doping can effectively modify the electronic structure of the Ni active centers and foster a strong electronic interaction between Ni and Dy. The resulting benefits include a reduced work function and a closer proximity of the d-band center to the Fermi level, which is conducive to improving electrical conductivity and promoting the adsorption of oxygen-containing intermediates. Furthermore, the Dy@Ni-MOF achieves superhydrophilicity, ensuring effective electrolyte contact and thus accelerating reaction kinetics. Ex-situ and in-situ analysis results manifest Dy2O3/NiOOH as the actual active species. Therefore, Dy@Ni-MOF shows impressive OER performance, significantly surpassing Ni-MOF. Besides, the overall water splitting device with Dy@Ni-MOF as an anode delivers a low cell voltage of 1.51 V at 10 mA cm−2 and demonstrates long-term stability for 100 h, positioning it as a promising substitute for precious metal catalysts.

1,3-Butadiynamides the Ethynylogous Ynamides: Synthesis, Properties and Applications in Heterocyclic Chemistry.

1,3-butadiynamides-the ethynylogous variants of ynamides-receive considerable attention as precursors of complex molecular scaffolds for organic and heterocyclic chemistry. The synthetic potential of these C4-building blocks reveals itself in sophisticated transition-metal catalyzed annulation reactions and in metal-free or silver-mediated HDDA (Hexa-dehydro-Diels-Alder) cycloadditions. 1,3-Butadiynamides also gain significance as optoelectronic materials and in less explored views on their unique helical twisted frontier molecular orbitals (Hel-FMOs). The present account summarizes different methodologies for the synthesis of 1,3-butadiynamides followed by the description of their molecular structure and electronic properties. Finally, the surprisingly rich chemistry of 1,3-butadiynamides as versatile C4-building blocks in heterocyclic chemistry is reviewed by compiling their exciting reactivity, specificity and opportunities for organic synthesis. Besides chemical transformations and use in synthesis, a focus is set on the mechanistic understanding of the chemistry of 1,3-butadiynamides-suggesting that 1,3-butadiynamides are not just simple alkynes. These ethynylogous variants of ynamides have their own molecular character and chemical reactivity and reflect a new class of remarkably useful compounds.

Aerosol Detection from the Cloud–Aerosol Transport System on the International Space Station: Algorithm Overview and Implications for Diurnal Sampling

Concentrations of particulate aerosols and their vertical placement in the atmosphere determine their interaction with the Earth system and their impact on air quality. Space-based lidar, such as the Cloud–Aerosol Transport System (CATS) technology demonstration instrument, is well-suited for determining the vertical structure of these aerosols and their diurnal cycle. Through the implementation of aerosol-typing algorithms, vertical layers of aerosols are assigned a type, such as marine, dust, and smoke, and a corresponding extinction-to-backscatter (lidar) ratio. With updates to the previous aerosol-typing algorithms, we find that CATS, even as a technology demonstration, observed the documented seasonal cycle of aerosols, comparing favorably with the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) space-based lidar and the NASA Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2) model reanalysis. By leveraging the unique orbit of the International Space Station, we find that CATS can additionally resolve the diurnal cycle of aerosol altitude as observed by ground-based instruments over the Maritime Continent of Southeast Asia.

Enhanced performance of p-type SnO x thin film transistors through defect compensation

Due to the unique outermost orbitals of Sn, hole carriers in tin monoxide (SnO) possess small effective mass and high mobility among oxide semiconductors, making it a promising p-channel material for thin film field-effect transistors (TFTs). However, the Sn vacancy induced field-effect mobility deterioration and threshold voltage (V th) shift in experiments greatly limit its application in complementary metal-oxide-semiconductor (CMOS) transistors. In this study, the internal mechanism of vacancy defect compensation by aluminum (Al) doping in SnO x film is studied combining experiments with the density functional theory (DFT). The doping is achieved by an argon (Ar) plasma treatment of Al2O3 deposited onto the SnO x film, in which the Al2O3 provides both the surface passivation and Al doping source. Experimental results show a wide V th modulation range (6.08 to −19.77 V) and notable mobility enhancement (11.56 cm2V−1s−1) in the SnO x TFTs after the Al doping by Ar plasma. DFT results reveal that the most possible positions of Al in SnO and SnO2 segments are the compensation to Sn vacancy and interstitial. The compensation will create an n-type doping effect and improve the hole carrier transport by reducing the hole effective mass (m h*), which is responsible for the device performance variation, while the interstitial in the SnO2 segment can hardly affect the valence transport of the film. The defect compensation is suitable for the electronic property modulation of SnO towards the high-performance CMOS application.

Bulk and surface electronic structure of MnPSe3 revealed by photoemission and x-ray absorption spectroscopy

Bulk and surface electronic states of ${\mathrm{MnPSe}}_{3}$ have been investigated by means of x-ray photoemission spectroscopy (XPS), x-ray absorption spectroscopy (XAS), and theoretical calculations. In Mn $2p$ XPS, the main peak is accompanied by a charge-transfer satellite which is commonly observed in various Mn chalcogenides. The intensity of the charge-transfer satellite is considerably reduced by oxidization of the surface. The multiplet structure of Mn $2p$ XAS indicates the high spin ${\mathrm{Mn}}^{2+}$ configuration. The cluster model analyses of the XPS and XAS spectra indicate that the Se $4p$-to-Mn $3d$ charge-transfer energy $\mathrm{\ensuremath{\Delta}}$ is negative providing the strong $p\ensuremath{-}d$ hybridization. The magnetic interaction between the third nearest neighboring Mn spins is enhanced by the smallness of $\mathrm{\ensuremath{\Delta}}$ and the unique molecular orbitals of the ${\mathrm{P}}_{2}{\mathrm{Se}}_{6}$ cluster.

Coxeter Pop-Tsack Torsing

Given a finite irreducible Coxeter group W with a fixed Coxeter element c, we define the Coxeter pop-tsack torsing operator Pop T :W→W by Pop T (w)=w·π T (w) -1 , where π T (w) is the join in the noncrossing partition lattice NC(w,c) of the set of reflections lying weakly below w in the absolute order. This definition serves as a “Bessis dual” version of the first author’s notion of a Coxeter pop-stack sorting operator, which, in turn, generalizes the pop-stack sorting map on symmetric groups. We show that if W is coincidental or of type D, then the identity element of W is the unique periodic point of Pop T and the maximum size of a forward orbit of Pop T is the Coxeter number h of W. In each of these types, we obtain a natural lift from W to the dual braid monoid of W. We also prove that W is coincidental if and only if it has a unique forward orbit of size h. For arbitrary W, we show that the forward orbit of c -1 under Pop T has size h and is isolated in the sense that none of the non-identity elements of the orbit have preimages lying outside of the orbit.

Mitigating the Jahn-Teller distortion driven by the spin-orbit coupling of lithium manganate cathode

Spinel LiMn2O4 is recognized as one of the most competitive cathode candidates for lithium-ion batteries ascribed to environmentally benign and rich sources. However, the wholesale application of LiMn2O4 is predominately plagued by its severe capacity degradation, mainly associated with the innate Jahn-Teller effect. Herein, single-crystalline LiMn2O4 with Eu3+ doping is rationally designed to mitigate the detrimental Jahn-Teller distortion by tuning the chemical environment of MnO6 octahedra and accommodating localized electron, based on the unique aspheric flexible 4f electron orbit of rare-earth metal ions. Notably, the stretching of MnO6 octahedron stemmed from the Jahn-Teller effect in Eu-doped LiMn2O4 is effectively suppressed, confirmed by theoretical calculation. Meanwhile, the structural stability of the material has been significantly enhanced due to the robust Mn–O band coherency and weakened phase transition, proved by synchrotron radiation absorption spectrum and operando X-ray diffraction. The corresponding active cathode manifests superior long-cycle stability after 300 loops at 2C and displays only a 0.011% capacity drop per cycle even at 5C. Given this, this modification tactic sheds new light on achieving superior long-cycle performances by suppressing distortion in various cathode materials.

Dihedral Multi-Reference Alignment

We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from a generic distribution, the orbit of a generic signal is uniquely determined from the second moment of the observations. This implies that the optimal estimation rate in the high noise regime is proportional to the square of the variance of the noise. This is the first result of this type for multi-reference alignment over a non-abelian group with a non-uniform distribution of group elements. Based on tools from invariant theory and algebraic geometry, we also delineate conditions for unique orbit recovery for multi-reference alignment models over finite groups (namely, when the dihedral group is replaced by a general finite group) when the group elements are drawn from a generic distribution. Finally, we design and study numerically three computational frameworks for estimating the signal based on group synchronization, expectation-maximization, and the method of moments.

Analysis of Angles-Only Hybrid Space-Based/Ground-Based Approach for Geosynchronous Orbit Catalog Maintenance

Geosynchronous Equatorial Orbit (GEO) is critical to Earth communications, weather monitoring, and national defense. Orbit estimation of GEO objects is difficult due to physical constraints placed on ground-based tracking devices such as weather, object range, lighting conditions and tracking frequency restrictions. These constraints are commonly mitigated through the use of two-way signaling devices for cooperative GEO satellites. However, determining the position and velocity of uncooperative GEO satellites and/or objects is more challenging. The objective of this paper is to develop an efficient tool to quantify the increased orbit determination accuracy of objects in the GEO catalog when the Air Force Space Command Space Surveillance Network (AFSPC SSN) is augmented with space-based angles-only measurements from a sensor in a unique near-GEO orbit. To accomplish this, a linear covariance tool is developed and validated by Monte Carlo analysis over a range of problem parameters. It is shown that linear covariance analysis is an efficient approach in determining the covariance of the position and velocity estimation errors of an uncooperative GEO object. Additionally, the linear covariance tool is used to perform error budget analysis.

Energy regulation of torque–driven robot manipulators in joint space

The energy regulation of fully actuated torque–driven robot manipulators in joint space is addressed in this paper. The proposed controller is designed via an energy shaping plus damping injection approach. The contribution is the proposal of an energy regulator with partial damping injection capable of inducing oscillations in the undamped joints of robot manipulators, with an user specified desired frequency and amplitude, by adding only damping in the rest of the joints, which may require less control effort than a trajectory tracking controller with full damping injection. Although viscous friction is considered in all joints of robot manipulator, it has been compensated via the proposed energy regulator. Moreover, the controlled periodic motion oscillates around a desired joint position as reference, and this provides a nice feature in the robot, mainly when there is not interest in the undamped joint to follow an specified time-varying sinusoidal function, but generating an oscillatory motion of constant amplitude and frequency. Instrumental in stability analysis is the Lyapunov’s theory and LaSalle’s theorem, which allows concluding that the closed-loop trajectories approach an invariant set that could include a unique equilibrium or periodic orbits. Numerical simulations on a manipulator arm model of two degrees of freedom illustrate the main results.

Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

We consider the residues at the poles in the half plane \(Re(s)\ge 0\) of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

Helium and Hamiltonian delay equations

In this paper we study two electrons on a line on the same side of the nucleus which interact with each other by their mean value. We prove that there exists a unique periodic orbit and examine for which charges the two orbits of the electrons intersect.

A transitivity result for ad-nilpotent ideals in type [formula omitted

The paper considers subspaces of the strictly upper triangular matrices, which are stable under Lie bracket with any upper triangular matrix. These subspaces are called ad-nilpotent ideals and there are Catalan number of such subspaces. Each ad-nilpotent ideal I meets a unique largest nilpotent orbit OI in the Lie algebra of all matrices. The main result of the paper is that under an equivalence relation on ad-nilpotent ideals studied by Mizuno and others, the equivalence classes are the ad-nilpotent ideals I such that OI=O for a fixed nilpotent orbit O. We include two applications of the result, one to the higher vanishing of cohomology groups of vector bundles on the flag variety and another to the Kazhdan–Lusztig cells in the affine Weyl group of the symmetric group. Finally, some combinatorial results are discussed.

Development of biometric systems for passenger identification based on noise-resistant coding means

The paper deals with the issues of using the biometric technologies to establish identity of a passenger. The purpose of the article is to analyze the techniques of enhancing reliability of various biometric identification facilities by means of using error correction codes. The basic elements and the principle of the classical biometric system functioning are presented. On the basis of the International Civil Aviation Organization (ICAO) recommendations, the procedure features of pattern recognition are presented. The versions to adopt the biometric passenger authentication procedures are under consideration. The conclusion is drawn that with the centralized biometric databases the issues of confidentiality and information security exist. The problems are characterized by the possibility of biometric images compromise, which can potentially lead to the loss of their confidentiality and the impossibility of their further usage for personal identification. The passenger authentication procedure involving the simultaneous use of biometric parameters and contact-free SMART cards seems more reliable. SMART cards are used for distributed storage of biometric and other additional data, thus neutralizing the disadvantages of access to the centralized databases. It is shown that the subsequent step in the development of this domain is the application of biometric cryptography proposing "linking" encryption keys and passwords with the biometric parameters of the subject. Consideration is given to the principle of "fuzzy extractor" operation as one of the variants for the "biometrics-code" converter. Feasibility and necessity of upgrading the means of noise-resistant coding in the systems being studied are shown. The use of permutation decoding data algorithms capable of adequately corresponding to the particular problems of biometric identification is proposed. On the basis of the results of optical communication channels statistical modeling, the necessary and sufficient conditions for application of the permutation decoding tools for binary codes are determined. The problem to minimize memory amount for the permutation decoder cognitive map due to the permutation orbits allocation and usage of the generated loops combinations as pointers of reference plane is solved. The resulting algorithm for finding a unique orbit number and its corresponding reference plane by means of receiver formation of arbitrary parameters permutation from the set of permissible permutations is proposed.

Solution of transport safety problems based on biometric systems with error-correcting coding procedures

The paper considers models and methods for solving processing biometric data at the physical and channel levels. A classification of the parameters of such systems is given and those characteristics that play a decisive role in achieving the objective function in limited time intervals are distinguished from them. The work aims to analyze the possibilities of increasing the reliability of biometric devices at the channel level by using error correction codes. The practicability and necessity of error-correcting coding mean using the permutation data decoding algorithms capable of matching biometric identification adequately. Based on the results of statistical modelling of optical communication channels, the necessary and sufficient conditions for the application of permutation decoding tools for binary codes are determined. The problem of minimizing the memory size of the cognitive map of a permutation decoder is solved by allocating the permutation orbits and using the generating combinations of loops as indexes of the reference matrices. An efficient algorithm is proposed for finding a unique orbit number and the corresponding reference matrix when the receiver generates an arbitrary permutation of characters from the set of permissible permutations.

Multiplicity of stable orbits for deformable prolate capsules in shear flow.

This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded simple shear flow at zero Reynolds number using direct simulations. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by the nondimensional capillary number Ca, which represents the ratio of viscous stresses to elastic restoring stresses on the capsule. For a capsule with small bending stiffness, at a given Ca, the orientation converges over time towards a unique stable orbit independent of the initial orientation. With increasing Ca, four dynamical modes are found for the stable orbit, namely, rolling, wobbling, oscillating-swinging, and swinging. On the other hand, for a capsule with large bending stiffness, multiplicity in the orbit dynamics is observed. When the viscosity ratio λ ≲ 1, the long-axis of the capsule always tends towards a stable orbit in the flow-gradient plane, either tumbling or swinging, depending on Ca. When λ ≳ 1, the stable orbit of the capsule is a tumbling motion at low Ca, irrespective of the initial orientation. Upon increasing Ca, there is a symmetry-breaking bifurcation away from the tumbling orbit, and the capsule is observed to adopt multiple stable orbital modes including nonsymmetric precessing and rolling, depending on the initial orientation. As Ca further increases, the nonsymmetric stable orbit loses existence at a saddle-node bifurcation, and rolling becomes the only attractor at high Ca, whereas the rolling state coexists with the nonsymmetric state at intermediate values of Ca. A symmetry-breaking bifurcation away from the rolling orbit is also found upon decreasing Ca. The regime with multiple attractors becomes broader as the aspect ratio of the capsule increases, while narrowing as viscosity ratio increases. We also report the particle contribution to the stress, which also displays multiplicity.

Principal Curvatures of Homogeneous Hypersurfaces in a Grassmann Manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action

We compute the principal curvatures of homogeneous hypersurfaces in a Grassmann manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action. As applications, we show that there is a unique orbit which is an austere submanifold, and that there are just two orbits which are proper biharmonic homogeneous hypersurfaces. We also show that the austere orbit is a weakly reflective submanifold.