An Improved Equivalent Squint Range Model and Imaging Approach for Sliding Spotlight SAR Based on Highly Elliptical Orbit

As an emerging orbital system with flexibility and brand application prospects, the highly elliptical orbit synthetic aperture radar (HEO SAR) can achieve both a low orbit detailed survey and continuous earth surface observation in high orbit, which could be applied to marine reconnaissance and surveillance. However, due to its large eccentricity, two challenges have been faced in the signal processing of HEO SAR at present. The first challenge is that the traditional equivalent squint range model (ESRM) fails to accurately describe the entire range for the whole orbit period including the perigee, the apogee, and the squint subduction section. The second one is to exploit an efficient HEO SAR imaging algorithm in the squinted case which solves the problem that traditional imaging algorithm fails to achieve the focused imaging processing of HEO SAR during the entire orbit period. In this paper, a novel imaging algorithm for HEO SAR is presented. Firstly, the signal model based on the geometric configuration of the large elliptical orbit is established and the Doppler parameter characteristics of SAR are analyzed. Secondly, due to the particularity of Doppler parameters variation in the whole period of HEO, the equivalent velocity and equivalent squint angle used in MESRM can no longer be applied, a refined fourth-order equivalent squint range model(R4-ESRM) that is suitable for HEO SAR is developed by introducing fourth-order Doppler parameter into Modified ESRM (MESRM), which accurately reconstructs the range history of HEO SAR. Finally, a novel imaging algorithm combining azimuth resampling and time-frequency domain hybrid correlation based on R4-ESRM is derived. Simulation is performed to demonstrate the feasibility and validity of the presented algorithm and range model, showing that it achieves the precise phase compensation and well focusing.

Effect of Hollow Shape on the Behavior of Reinforced Self-Compacting Concrete Slender Column Under Eccentric Loading

Results of testing reinforced self-compacted concrete slender columns having longitudinal holes concealing PVC pipe in their cross sections under axial compression load and uniaxial bending are presented in this paper. The effect of hollow shape on the performance of slender columns having 200x200mm quadratic cross section and 1300mm long under concentric and eccentric loads was investigated. Three different shapes of central hole: circular, square, and lozenge pattern in addition to the different load eccentricity values were considered to investigate the axial loading resistance and cracking load, lateral and longitudinal deflections of the columns. Test results have showed that altering the hollow shape inside the area of column cross section does not show a great influence on the column behavior unless the hollow ratio changed. The effect of hole shape or the hollow ratio on loading capacity is insignificant but the existence of a hole embedded longitudinally in the column significantly decreases its ultimate capacity. The effect of hollow shape or hollow ratio on a slender columns behavior subjected to eccentric loading with small ratio of load eccentricity to total column thickness (e/h=.33) was more than that of large eccentricity (e/h=1.0). Accordingly, the decrease in loading column capacity of columns was (5.0%, 2.5%, and 6.6%) compared to (3.2%, 2.2%, and 4.7%) for the same hole shapes respectively.

Eight new millisecond pulsars from the first MeerKAT globular cluster census

ABSTRACT We have used the central 44 antennas of the new 64-dish MeerKAT radio telescope array to conduct a deep search for new pulsars in the core of nine globular clusters (GCs). This has led to the discovery of eight new millisecond pulsars in six different clusters. Two new binaries, 47 Tuc ac and 47 Tuc ad, are eclipsing ‘spiders’, featuring compact orbits (≲0.32 d), very low mass companions, and regular occultations of their pulsed emission. The other three new binary pulsars (NGC 6624G, M62G, and Ter 5 an) are in wider (>0.7 d) orbits, with companions that are likely to be white dwarfs or neutron stars. NGC 6624G has a large eccentricity of e ≃ 0.38, which enabled us to detect the rate of advance of periastron. This suggests that the system is massive, with a total mass of Mtot = 2.65 ± 0.07 M⊙. Likewise, for Ter 5 an, with e ≃ 0.0066, we obtain Mtot = 2.97 ± 0.52 M⊙. The other three new discoveries (NGC 6522D, NGC 6624H, and NGC 6752F) are faint isolated pulsars. Finally, we have used the whole MeerKAT array and synthesized 288 beams, covering an area of ∼2 arcmin in radius around the centre of NGC 6624. This has allowed us to localize many of the pulsars in the cluster, demonstrating the beamforming capabilities of the TRAPUM software backend and paving the way for the upcoming MeerKAT GC pulsar survey.

Ordering graphs with large eccentricity-based topological indices

For a connected graph, the first Zagreb eccentricity index $\xi _{1}$ ξ 1 is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index $\xi _{2}$ ξ 2 is defined as the sum of the products of the eccentricities of pairs of adjacent vertices. In this paper, we mainly present a different and universal approach to determine the upper bounds respectively on the Zagreb eccentricity indices of trees, unicyclic graphs and bicyclic graphs, and characterize these corresponding extremal graphs, which extend the ordering results of trees, unicyclic graphs and bicyclic graphs in (Du et al. in Croat. Chem. Acta 85:359–362, 2012; Qi et al. in Discrete Appl. Math. 233:166–174, 2017; Li and Zhang in Appl. Math. Comput. 352:180–187, 2019). Specifically, we determine the n-vertex trees with the i-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2+1 \rfloor $ ⌊ n / 2 + 1 ⌋ compared with the first three largest results of $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 in (Du et al. in Croat. Chem. Acta 85:359–362, 2012), the n-vertex unicyclic graphs with respectively the i-th and the j-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2-1 \rfloor $ ⌊ n / 2 − 1 ⌋ and j up to $\lfloor 2n/5+1 \rfloor $ ⌊ 2 n / 5 + 1 ⌋ compared with respectively the first two and the first three largest results of $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 in (Qi et al. in Discrete Appl. Math. 233:166–174, 2017), and the n-vertex bicyclic graphs with respectively the i-th and the j-th largest indices $\xi _{1}$ ξ 1 and $\xi _{2}$ ξ 2 for i up to $\lfloor n/2-2\rfloor $ ⌊ n / 2 − 2 ⌋ and j up to $\lfloor 2n/15+1\rfloor $ ⌊ 2 n / 15 + 1 ⌋ compared with the first two largest results of $\xi _{2}$ ξ 2 in (Li and Zhang in Appl. Math. Comput. 352:180–187, 2019), where $n\ge 6$ n ≥ 6 . More importantly, we propose two kinds of index functions for the eccentricity-based topological indices, which can yield more general extremal results simultaneously for some classes of indices. As applications, we obtain and extend some ordering results about the average eccentricity of bicyclic graphs, and the eccentric connectivity index of trees, unicyclic graphs and bicyclic graphs.

Study on the Performance of Liquid Metal Lubricated V-Groove Bearing Considering Turbulence

To study the application of liquid metal (LM) in the field of practical lubrication, the viscosity of gallium based liquid metal (GBLM) was measured initially, and the relationship between viscosity and temperature was fitted to obtain the viscosity under high temperature. Under the simulated high temperature and vacuum working environment of computed tomography tube (CTT) machines, considering the influence of turbulence, the changes, with eccentricity, of bearing capacity, discharge, friction power consumption, temperature rise, stiffness, and critical mass of the GBLM lubricated V-groove bearing (V-g B) were analyzed. Due to the special structure of V-g B, the coordinate transformation was carried out and the turbulent Reynolds equation was solved by using the finite difference method and the local integral method. The bearing film thickness and pressure distribution under the two coordinate systems were analyzed and compared and the pressure distribution of V-g B under small eccentricity and large eccentricity was studied, respectively. The performance of GBLM lubricated V-g B was studied, which provides theoretical guidance and an analytical method for LM bearing of high-performance CT equipment.

Measuring the eccentricity of binary black holes in GWTC-1 by using the inspiral-only waveform

ABSTRACT In this article, we estimate the eccentricity of 10 binary black holes (BBHs) in the Gravitational-Wave Transient Catalog GWTC-1 by using the inspiral-only BBH waveform template EccentricFD. First, we test our method with simulated eccentric BBHs. Afterwards we apply the method to real BBH gravitational-wave data. We find that the BBHs in GWTC-1, with the exception of GW151226, GW170608 and GW170729, show very small eccentricity. Their upper limits on eccentricity range from 0.033–0.084 with 90 per cent credible interval at a reference frequency of 10 Hz. For GW151226, GW170608 and GW170729, the upper limits are higher than 0.1. The relatively large eccentricity of GW151226 and GW170729 is probably due to ignoring χeff and the low signal-to-noise ratio, and GW170608 is worthy of follow-up research. We also point out the limitations of the inspiral-only non-spinning waveform template in eccentricity measurement. Measurement of BBH eccentricity helps us to understand its formation mechanism. With an increase in the number of BBH gravitational-wave events and a more complete eccentric BBH waveform template, this will become a viable method in the near future.

Numerical Investigation of the Behavior of Strip Footings under Large Eccentric Loads

In this paper, numerical computations using the FLAC code are carried out to investigate of the behavior the bearing capacity of strip footings embedded in sandy soil and under large eccentric vertical load conditions. The study focuses on an evaluation of the non-dimensional reduction factor (RF), which is the ratio between the average bearing capacity of an eccentric footing and its bearing capacity when subjected to a central load. The results indicate a significant decrease in RF when the eccentricity increases and the curve of the decrease is parabolic, even in large eccentricity cases. Based on the numerical results obtained, a new formula of the RF is proposed, and the reasons for the discrepancy between the RF proposed by several authors are identified. The values provided by the proposed formula are in close agreement with some experimental results available in the literature.

A HERO for General Relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

Spectroscopic orbits of nearby stars

Aims. We observed stars with variable radial velocities to determine their spectroscopic orbits. Methods. Velocities are presented of 132 targets taken over a time span reaching 30 years. These were measured with the correlation radial velocity spectrometers (1917 velocities) and the new VUES echelle spectrograph (627 velocities), with a typical accuracy of 0.5 and 0.2 km s−1, respectively. Results. We derived spectroscopic orbits of 57 stars (including 53 first-time orbits), mostly nearby dwarfs of spectral types K and M, with some being HIPPARCOS astrometric binaries. Their periods range from 2.2 days to 14 years. Comments on individual objects are provided. Many stars belong to hierarchical systems containing three or more components, including 20 new hierarchies resulting from this project. The preliminary orbit of the young star HIP 47110B has a large eccentricity e = 0.47 despite having a short period of 4.4 d; it could still be circularizing. Conclusions. Our results enrich the data on nearby stars and contribute to a better definition of the multiplicity statistics.