Radius Constraints Research Articles

Iterative Robust Ellipsoid Fitting Based on M-Estimator With Geometry Radius Constraint

The ellipsoid fitting technique has been popularly used in many application scenarios, especially in triaxial sensor calibration in recent years. The conventional method to achieve ellipsoid fitting is the pseudo-inverse technique with algebraic constraints to obtain proper fitting results. This technique ensures the least mean square (LMS) error relative to all measured data and prevents trivial solutions. However, this approach lacks robustness against outliers resulting in nonideal fitting performance in real calibration situations. The M-estimator technique with several robust cost functions is adopted and applied in this research to attenuate the outlier’s effect to offer a more accurate fitting performance. In contrast, the constraint with geometric meaning is also applied and examined to prevent trivial solutions. These two methods are achieved by using the iterative constrained gradient descent (G.D.) method to approach the proper ellipsoid fitting. The performances are validated through synthesis and real measured data. Through calibrated experiments, the proposed methods are found to be able to increase robustness against outliers and prevent parameters of ellipsoid degeneration toward trivial solutions.

Study of nonstrange quark stars within a modified NJL model

In this work, a modified Nambu-Jona-Lasinio (NJL) model with proper-time regularization is employed to study the properties of hypothetical nonstrange quark stars. The coupling constant of the four-fermion interaction in the conventional NJL model is modified as $G={G}_{1}+{G}_{2}⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩$ to highlight the feedback of the quark propagator to the gluon propagator. To study the dependence of the equation of state (EOS) on this modification as well as the vacuum pressure, we choose nine representative EOSs for comparison. It is found that a smaller ${G}_{1}$ leads to a stiffer EOS, and a higher vacuum pressure (i.e., a smaller bag constant) yields a softer EOS at low energy density. It is further shown that the heaviest quark star under this modified NJL model satisfies not only the recent mass measurement of PSR $\mathrm{J}0740+6620$, but also the radius constraints from x-ray timing observations. The corresponding tidal deformability is also in agreement with the observations of GW170817.

The Relation between Gas-phase Metallicity and Stellar Mass Surface Density in Post-starburst E+A and E+A+ Galaxies within the Coma Cluster Observed by the SDSS-IV MaNGA Survey

We present an analysis of the Mass–Metallicity Relation (MZR) in 29 post-starburst galaxies in the Coma Cluster. Outward from the central dominant galaxy, NGC 4889, we conducted a conical survey of all galaxies observed by the Sloan Digital Sky Survey Data Release 17 (SDSS DR17) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey within a 5° radius and redshift constraints 0.013 < z < 0.033. We identified 21 E+A galaxies and 8 “E+A+ galaxies” whose spectra matched the criteria of an E+A galaxy, but contain Balmer emission lines, indicating star formation. We utilized the MaNGA data to calculate each galaxy’s star formation rate densities, gas-phase metallicity and stellar mass. We then compared the MZR between E+A galaxies and E+A+ galaxies to observe how varying star formation rates alter this relation.

Hybrid Ground-Space Target Visit Problem With a Coplanar Impulse

The hybrid ground–space target visit problem is solved by applying a single coplanar impulse. Considering the linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> perturbation, the ground target visit problem is transformed into the ground track adjustment problem, and it is expressed as a time constraint equation. The space target visit problem is viewed as the orbit interception (or flyby) problem, and it is expressed as time and radius constraint equations. Then, based on Gauss’s variational equations, the hybrid ground–space target visit problem is simplified into solving a single-variable equation only of maneuver position. Finally, the exact solution under the high-precision dynamic model is obtained by the differential correction method. Several numerical examples are presented to validate the efficiency of this approach, and the results show that there are a series of discrete solutions to this problem.

On Trajectory Homotopy to Explore and Penetrate Dynamically of Multi-UAV

This paper examines a trajectory homotopy optimization framework for multiple unmanned aerial vehicles (multi-UAV) to solve the problem of dynamic penetration mission planning (PMP) with hostile obstacles and perception constraints. Constrained problems are usually more challenging and difficult to solve with some practical constraints and requirements. To improve the efficiency of the solution for the penetration path, a novel variable-time mechanism has been constructed to adapt to the updated delay time of unknown target search (UTS) and dynamic trajectory planning (DTP) two stages. The occupancy grid maps are established by a Gaussian probability field (GPF) for predicting the positions of enemy UAVs. To fully consider the hostile obstacle constraint, a hybrid adaptive obstacle avoidance approach dynamic window PRM (DW-PRM) is designed to shorten the planned path. The penetration strategy algorithm (SG) is developed based on the proposed strategy set and decision tree. To improve the ability of dynamic obstacle avoidance, the multiple coupled penetration homotopy trajectory is addressed with a turning radius constraint. The simulation results indicated that the penetration homotopy framework for multi-constraints can solve the multi-UAV PMP problem.

Neutron star mass formula with nuclear saturation parameters for asymmetric nuclear matter

Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $\eta\equiv (K_0L^2)^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by $\eta_\tau\equiv (-K_\tau L^5)^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matter, $K_\tau$, and derive the empirical relations for the neutron star mass and gravitational redshift as a function of $\eta_\tau$ and the normalized central number density. With these empirical relations, one can evaluate the mass and gravitational redshift of the neutron star, whose central number density is less than threefold the saturation density, within $\sim 10\%$ accuracy, and the radius within a few \% accuracies. In addition, we discuss the neutron star mass and radius constraints from the terrestrial experiments, using the empirical relations, together with those from the astronomical observations. Furthermore, we find a tight correlation between $\eta_\tau$ and $\eta$. With this correlation, we derive the constraint on $K_\tau$ as $-348\le K_\tau\le -237$ MeV, assuming that $L=60\pm 20$ and $K_0=240\pm 20$ MeV.

An aeroelastic optimisation framework for manufacturable variable stiffness composite wings including critical gust loads

This work presents a new aeroelastic optimisation framework for the preliminary design of variable stiffness composite wing structures. The framework is constructed by sequentially and iteratively solving two sub-problems: aeroelastic tailoring and lay-up retrieval, using gradient-based algorithms with full-analytical sensitivities provided. During aeroelastic tailoring, the wing mass is minimised by optimising the lamination parameters and thickness of wing laminates together with wing jig twist distribution. The load cases cover not only static loads, but also the critical gust loads that are identified across the entire flight envelop at every iteration of optimisation. Further, a cruise shape constraint is included in addition to other aerostructural constraints, so that the optimal aircraft performance can be ensured. During lay-up retrieval, the manufacturable stacking sequence is retrieved according to the optimal lamination parameters with the consideration of minimal steering radius constraint. Moreover, to fix the possible constraint violations caused by lay-up retrieval, a correction strategy is incorporated to tighten the violated constraints for repeating aeroelastic tailoring. Finally, several case studies on the design of NASA common research model wing are carried out and investigated. The results indicate that the critical gust loads and cruise shape constraint have a large influence on the design of tow-steered composite wing structures, which therefore demonstrate the usefulness and benefits of the proposed optimisation framework.

A Neighborhood Model with Both Distance and Quantity Constraints for Multilabel Data.

In this paper, a novel distance-based multilabel classification algorithm is proposed. The proposed algorithm combines k-nearest neighbors (kNN) with neighborhood classifier (NC) to impose double constraints on the quantity and distance of the neighbors. In short, the radius constraint is introduced in the kNN model to improve the classification accuracy, and the quantity constraint k is added in the NC model to speed up computing. From the neighbors with the double constraints, the probabilities for each label are estimated by the Bayesian rule, and the classification judgment is made according to the probabilities. Experimental results show that the proposed algorithm has slight advantages over similar algorithms in calculation speed and classification accuracy.

Three-dimensional topology optimization of Ni-YSZ anode for solid oxide fuel cells via multiphase level-set method

In the present study, numerical model is developed to optimize the 3D multiphase electrode microstructure for SOFC, e.g. nickel-yttria-stabilized zirconia (Ni-YSZ) anode. During the optimization, Ni-YSZ microstructure is deformed in order to maximize the total reaction current. Multiphase level-set (MLS) model is applied to represent the Ni-YSZ anode microstructure, and adjoint method is applied for the sensitivity analysis. In addition, in order to improve the computational accuracy and to make the optimized microstructure manufacturable, a radius constraint is imposed to ensure that the local particle radii are kept larger than a target value (Rtarget), where the interface is updated only when the local radius value is larger than Rtarget. It is also confirmed that the optimized microstructure and performance of the Ni-YSZ anode are independent of the initial structures and the phase division schemes. According to the optimization results, the optimized electrochemical performances are improved, and the particle and pore radii of the microstructure successfully remained larger than the target values. The optimized Ni-YSZ microstructures are composed of Ni particles embedded into a YSZ scaffold which has a pillar-like shape along the anode thickness direction.

Obstacle avoidance flocking motion in multi-agent systems with limited sensing radius and heterogeneous input constraints

This paper addresses the leaderless and leader-followers flocking motion problems of multi-agent systems in a workspace with obstacles. We consider inertial agents with equally limited communication radius and heterogeneous input constraints. Using the notion of proximity graphs, we provide distributed controllers to induce the desired flocking behaviour. Unlike previous results, our controller designs do not require predicted states or a target determination scheme and allow edge deletions. Also, by taking advantage of the group's heterogeneity, our controllers allow agents with less restrictive input constraints to compensate for the control effort that their less capable neighbours cannot provide. We illustrate the effectiveness of our proposals through numerical simulations.

Confirming the Existence of Twin Stars in a NICER Way

We demonstrate that future radius measurements of the NICER mission have the potential to reveal the existence of a strong phase transition in dense neutron star matter by confirming the existence of so-called twin stars, compact star configurations with the same mass but different radii. The latest radius constraints from NICER for the pulsars J0740+6620 as well as J0030+0451 are discussed using relativistic mean field equations of state with varying stiffness, connected with a first-order phase transition to quark matter. We show that twin star solutions are compatible with the new radius constraint but are located at radii below the present constraints from NICER, serving as a smoking gun for a strong phase transition in neutron star matter. This scenario is realized if a strong phase transition takes place in neutron stars of the first branch with masses above 2 M ⊙.

Shortest Dubins Paths to Intercept a Target Moving on a Circle

We present a path planning problem for a pursuing unmanned aerial vehicle (UAV) to intercept a target traveling on a circle. The target is cooperative, and its position, heading, and speed are precisely known. The pursuing UAV has nonholonomic motion constraints, and therefore the path traveled must satisfy the minimum turn radius constraints. We consider the class of Dubins paths as candidate solutions, and analyze the characteristics of the six modes of Dubins paths where the final position is restricted to lie on the target circle with heading in the tangential direction of the circle. For each Dubins mode, we derive the feasibility limits, discontinuities, and local extrema. Using this analysis the intercepting paths are found by a systematic bisection search in the feasible regions of each of the Dubins modes. We prove that the algorithm finds the optimal (shortest length) intercepting path if it is a Dubins path. If the shortest intercepting path is not a Dubins path for any given instance, the algorithm finds a tight lower bound and an upper bound to the optimal solution.

The disk of FU Orionis viewed with MATISSE/VLTI

Aims. We studied the accretion disk of the archetypal eruptive young star FU Orionis with the use of mid-infrared interferometry, which enabled us to resolve the innermost regions of the disk down to a spatial resolution of 3 milliarcseconds (mas) in the L band, that is, within 1 au of the protostar. Methods. We used the interferometric instrument MATISSE/VLTI to obtain observations of FU Ori’s disk in the L, M, and N bands with multiple baseline configurations. We also obtained contemporaneous photometry in the optical (UBVRIr′i′; SAAO and Konkoly Observatory) and near-infrared (JHKs; NOT). Our results were compared with radiative transfer simulations modeled by RADMC-3D. Results. The disk of FU Orionis is marginally resolved with MATISSE, suggesting that the region emitting in the thermal infrared is rather compact. An upper limit of ~1.3 ± 0.1 mas (in L) can be given for the diameter of the disk region probed in the L band, corresponding to 0.5 au at the adopted Gaia EDR3 distance. This represents the hot, gaseous region of the accretion disk. The N-band data indicate that the dusty passive disk is silicate-rich. Only the innermost region of said dusty disk is found to emit strongly in the N band, and it is resolved at an angular size of ~5 mas, which translates to a diameter of about 2 au. The observations therefore place stringent constraints for the outer radius of the inner accretion disk. Dust radiative transfer simulations with RADMC-3D provide adequate fits to the spectral energy distribution from the optical to the submillimeter and to the interferometric observables when opting for an accretion rate M ~ 2 × 10−5 M⊙ yr−1 and assuming M* = 0.6 M⊙, Most importantly, the hot inner accretion disk’s outer radius can be fixed at 0.3 au. The outer radius of the dusty disk is placed at 100 au, based on constraints from scattered-light images in the literature. The dust mass contained in the disk is 2.4 × 10−4 M⊙, and for a typical gas-to-dust ratio of 100, the total mass in the disk is approximately 0.02 M⊙. We did not find any evidence for a nearby companion in the current interferometric data, and we tentatively explored the case of disk misalignment. For the latter, our modeling results suggest that the disk orientation is similar to that found in previous imaging studies by ALMA. Should there be an asymmetry in the very compact, inner accretion disk, this might be resolved at even smaller spatial scales (≤1 mas).

Neutron star properties with careful parametrization in the vector and axial-vector meson extended linear sigma model

The existence of quark matter inside the cores of heavy neutron stars is a possibility which can be probed with modern astrophysical observations. We use a vector and axial-vector meson extended quark-meson model to describe quark matter in the core of neutron stars. We discover that an additional parameter constraint is necessary in the quark model to ensure chiral restoration at high densities. By investigating hybrid star sequences with various parameter sets, we show that low sigma meson masses are needed to fulfill the upper radius constraints and that the maximum mass of stable hybrid stars is only slightly dependent on the parameters of the crossover-type phase transition. Using this observation and results from recent astrophysical measurements, a constraint of $2.5&lt;{g}_{V}&lt;4.3$ is set for the constituent quark--vector meson coupling. The effect of a nonzero bag constant is also investigated, and we observe that its effect is small for values adopted in previous works.

Four new deeply eclipsing white dwarfs in Zwicky Transient Facility

ABSTRACT We present the results of a search for deeply eclipsing white dwarfs in the Zwicky Transient Facility (ZTF) Data Release 4 (DR4). We identify nine deeply eclipsing white dwarf candidates, four of which we followed up with high-cadence photometry and spectroscopy. Three of these systems show total eclipses in the ZTF data and our follow-up Apache Point Observatory 3.5 m telescope observations. Even though the eclipse duration is consistent with sub-stellar companions, our analysis shows that all four systems contain a white dwarf with low-mass stellar companions of ∼0.1 M⊙. We provide mass and radius constraints for both stars in each system based on our photometric and spectroscopic fitting. Finally, we present a list of 41 additional eclipsing WD+M candidates identified in a preliminary search of ZTF DR7, including 12 previously studied systems. We identify two new candidate short-period, eclipsing, white dwarf–brown dwarf binaries within our sample of 41 WD+M candidates based on Pan-STARRS colours.

The Donor of the Black Hole X-Ray Binary MAXI J1820+070

We estimate the parameters of the donor of the accreting black hole binary MAXI J1820+070. The measured values of the binary period, rotational and radial velocities, and constraints on the orbital inclination imply the donor is a subgiant with the mass of and the radius of . We reanalyze the previously obtained optical spectrum from the Gran Telescopio Canarias and found it yields a strict lower limit on the effective temperature of T > 4200 K. We compile optical and infrared fluxes observed during the quiescence of this system. From the minima r- and i-band fluxes found in Pan-STARSS1 Data Release 2 prediscovery imaging and for a distance of D ≈ 3 kpc, reddening of E(B – V) = 0.23, and R 2 ≈ 1.11R ⊙, we find T ≲ 4230 K, very close to the above lower limit. For a larger distance, the temperature can be higher, up to about 4500 K (corresponding to a K5 spectral type, preferred by previous studies) at D = 3.5 kpc, allowed by the Gaia parallax. We perform evolutionary calculations for the binary system and compare them to the observational constraints. Our model fitting the above temperature and radius constraints at D ≈ 3 kpc has a mass of 0.4M ⊙, T ≈ 4200 K, and solar metallicity. Two alternative models require D ≳ 3.3–3.4 kpc at 0.4M ⊙, T ≈ 4500 K and half-solar metallicity, and 0.5M ⊙, T ≈ 4300 K, and solar metallicity. These models yield mass-transfer rates of ∼10−10 M ⊙ yr−1, compatible with those based on the estimated accreted mass of ≈2 × 1025 g and the time between the 2018 discovery and the 1934 historical outburst.

Properties of hybrid stars with hadron–quark crossover

The properties of hybrid stars are studied via the hybrid EOSs that are compatible with astrophysical observables. These hybrid EOSs are constructed by interpolating between hadronic EOS at lower densities and the quark EOS at higher densities. The BSR6 EOS derived from the RMF model is adopted as the hadronic EOS, while the quark EOS is calculated via a quasiparticle model. The maximum masses obtained from the hybrid EOSs are larger than [Formula: see text], and the tidal deformabilities for [Formula: see text] hybrid stars are smaller than 800. The combined tidal deformability [Formula: see text] is a monotonically increasing function of mass ratio [Formula: see text] for both hybrid EOSs and hadronic EOS, and it depends weakly on [Formula: see text]. The results of all hybrid EOSs can strictly satisfy the constraint of [Formula: see text] and the mass and radius constraints from the newest joint analysis of NICER, XMM-Newton and GW170817 data.

Decentralized route-planning for multi-vehicle teams to satisfy a subclass of linear temporal logic specifications

Linear temporal logic (LTL) formulae are widely used to provide high level behavioral specifications on mobile robots. We propose a decentralized route-planning method for a networked team of mobile robots to satisfy a common (global) LTL specification. The global specification is assumed to be a conjunction of multiple formulae, each of which is treated as a task to be assigned to one or more vehicles. The vehicle kinematic model consists of two modes: a hover mode and a constant-speed forward motion mode with bounded steering rate. The proposed method leverages the consensus-based bundle algorithm for decentralized task assignment, thereby decomposing the global specification into local specifications for each vehicle. We develop a new algorithm to assign collaborative tasks: those simultaneously assigned to multiple vehicles. Rewards in the proposed task assignment algorithm are computed using the so-called lifted graph, which ensures the satisfaction of minimum turn radius constraints on vehicular motion. This algorithm synchronizes the vehicles’ routes with minimum waiting durations. The proposed method is compared against a multi-vehicle task assignment algorithm from the literature, which we extend to apply for satisfying LTL specifications. The proposed route-planning method is demonstrated via numerical simulation examples and a hardware implementation on networked single-board computers.

Optimization analysis of NURBS curved variable stiffness laminates with a hole

Based on cubic NURBS curve, the optimization design of the variable stiffness laminates with a hole are carried out. Firstly, the reference trajectory of the fiber prepared by variable angle placement is defined by cubic NURBS curve, and the parameterized expression of variable-angle fiber placement is derived. Secondly, the linear buckling analyses of all constant stiffness laminates with a hole are carried out to obtain the constant stiffness laminates with the maximum first-order buckling load, the ± 45° placement of the constant stiffness laminates with a hole is replaced by the variable-angle fiber placements. The linear buckling analysis of the variable stiffness laminates with a hole is carried out. Then, the radial basis function is used to build an optimization model to optimize the variable stiffness laminates with a hole. Finally, under the constraints of curvature radius, MATLAB is used to conduct the optimization of variable stiffness laminates with a hole, and the optimal results under different curvature constraints are obtained. The results show that the buckling load coefficient of [±<10(0.1)(0.6)(0.6)53 > ]2sH laminates is 32.93% higher than that of [45/−45]2sH laminates. Using cubic NURBS curve to design laminates with a hole can avoid stress concentration and improve the buckling property of laminates with a hole.

Radius Constraints from Reflection Modeling of Cygnus X-2 with NuSTAR and NICER

Abstract We present a spectral analysis of NuSTAR and NICER observations of the luminous, persistently accreting neutron star (NS) low-mass X-ray binary Cygnus X-2. The data were divided into different branches that the source traces out on the Z-track of the X-ray color–color diagram; namely, the horizontal branch, the normal branch, and the vertex between the two. The X-ray continuum spectrum was modeled in two different ways that produced comparable quality fits. The spectra showed clear evidence of a reflection component in the form of a broadened Fe K line, as well as a lower-energy emission feature near 1 keV likely due to an ionized plasma located far from the innermost accretion disk. We account for the reflection spectrum with two independent models (relxillns and rdblur*rfxconv). The inferred inclination is in agreement with earlier estimates from optical observations of ellipsoidal lightcurve modeling (relxillns: i = 67° ± 4°; rdblur*rfxconv: i = 60° ± 10°). The inner disk radius remains close to the NS (R in ≤ 1.15 R ISCO) regardless of the source position along the Z-track or how the 1 keV feature is modeled. Given the optically determined NS mass of 1.71 ± 0.21 M ⊙, this corresponds to a conservative upper limit of R in ≤ 19.5 km for M = 1.92 M ⊙ or R in ≤ 15.3 km for M = 1.5 M ⊙. We compare these radius constraints to those obtained from NS gravitational wave merger events and recent NICER pulsar lightcurve modeling measurements.