Radius Of Region Research Articles

Exploring the dark matter disk model in dwarf galaxies: Insights from the LITTLE THINGS sample

We conducted an analysis of the velocity field of dwarf galaxies in the sample collected by the Local Irregulars That Trace Luminosity Extremes and The H I Nearby Galaxy Survey (LITTLE THINGS) and focused on deriving 2D velocity maps that encompass the transverse and radial velocity fields. Within the range of radial distances in which velocity anisotropies are sufficiently small for the disk to be considered supported by rotation and where the warped geometry of the disk can be neglected, we reconstructed the rotation curve while taking the effect of the asymmetric drift into account. To fit the rotation curves, we employed the standard halo model and the dark matter disk (DMD) model, which assumes that dark matter is primarily confined to the galactic disks and can be traced by the distribution of H I. Interestingly, our analysis revealed that the fits from the DMD model are statistically comparable to those obtained using the standard halo model, but the inferred masses of the galaxies in the DMD model are approximately 10 to 100 times lower than the masses inferred in the standard halo model. In the DMD model, the inner slope of the rotation curve is directly related to a linear combination of the surface density profiles of the stellar and gas components, which generally exhibit a flat core. Consequently, the observation of a linear relation between the rotation curve and the radius in the central disk regions is consistent with the framework of the DMD model.

ОБЛАСТЬ ПРИМЕНИМОСТИ ДАННЫХ СПУТНИКОВОЙ АЛЬТИМЕТРИИ ДЛЯ ВАЛИДАЦИИ АЛГОРИТМОВ ОЦЕНКИ ВЫСОТЫ ВЕТРОВОГО ВОЛНЕНИЯ

Satellite altimetry stands as one of the paramount sources of information regarding significant wave height, primarily due to its global coverage and near real-time availability. This study evaluates the radius of the quasihomogenity region of the eind waves field is estimated based on in situ and altimetry measurements. In situ data were collected during five marine expeditions utilizing drifting wave buoys (Spotter) and the Sea Vision radar system. Ten altimetric missions (Level 3) provided by CMEMS, as well as ERA5 reanalysis of wind speed, were processed. The outcome of the study is an assessment of the maximum radius circle centered on the satellite measurement point, within which the wave field can be considered homogeneous, enabling the use of altimetry data as reference for comparison with other data sources, as well as a methodology for refining this estimate taking into account the heterogeneity of the wind field.

Emergence of the Galaxy Morphology–Star Formation Activity–Clustercentric Radius Relations in Galaxy Clusters

We investigate when and how the relations of galaxy morphology and star-forming activity with clustercentric radius become evident in galaxy clusters. We identify 162 galaxy clusters with total mass Mtotcl>5×1013M⊙ at z = 0.625 in the Horizon Run 5 cosmological hydrodynamical simulation and study how the properties of the galaxies with stellar mass M * > 5 × 109 M ⊙ near the cluster main progenitors have evolved in the past. Galaxies are classified into disk, spheroid, and irregular morphological types according to the asymmetry and Sérsic index of their stellar mass distribution. We also classify galaxies into active and passive ones depending on their specific star formation rate. We find that the morphology–clustercentric radius relation (MRR) emerges at z ≃ 1.8 as the fraction of spheroidal types exceeds 50% in the central region (d ≲ 0.1R 200). Galaxies outside the central region remain disk-dominated. Numerous encounters between galaxies in the central region seem to be responsible for the morphology transformation from disks to spheroids. We also find that the star formation activity–clustercentric radius relation emerges at an epoch different from that of MRR. At z ≃ 0.8, passive galaxies start to dominate the intermediate radius region (0.1 ≲ d/R 200 ≲ 0.3), and this “quenching region” grows inward and outward thereafter. The region dominated by early-type galaxies (spheroids and passive disks) first appears at the central region at z ≃ 1.8, expands rapidly to larger radii as the population of passive disks grows in the intermediate radii, and clusters are dominated by early types after z ≃ 0.8.

An X-ray flaring event and a variable soft X-ray excess in the Seyfert LCRS B040659.9–385922 as detected with eROSITA

Context. Extreme continuum variability in extragalactic nuclear sources can indicate extreme changes in accretion flows onto supermassive black holes. Aims. We explore the multiwavelength nature of a continuum flare in the Seyfert LCRS B040659.9−385922. The all-sky X-ray surveys conducted by the Spectrum Roentgen Gamma (SRG)/extended ROentgen Survey with an Imaging Telescope Array (eROSITA) showed that its X-ray flux increased by a factor of roughly five over six months, and concurrent optical photometric monitoring with the Asteroid Terrestrial-impact Last Alert System (ATLAS) showed a simultaneous increase. Methods. We complemented the eROSITA and ATLAS data by triggering a multiwavelength follow-up monitoring program (X-ray Multi-Mirror Mission: XMM-Newton, Neutron star Interior Composition Explorer: NICER; optical spectroscopy) to study the evolution of the accretion disk, broad-line region, and X-ray corona. During the campaign, X-ray and optical continuum flux subsided over roughly six months. Our campaign includes two XMM-Newton observations, one taken near the peak of this flare and the other taken when the flare had subsided. Results. The soft X-ray excess in both XMM-Newton observations was power law-like (distinctly nonthermal). Using a simple power law, we observed that the photon index of the soft excess varies from a steep value of Γ ∼ 2.7 at the flare peak to a relatively flatter value of Γ ∼ 2.2 as the flare subsided. We successfully modeled the broadband optical/UV/X-ray spectral energy distribution at both the flare peak and post-flare times with the AGNSED model, incorporating thermal disk emission into the optical/UV and warm thermal Comptonization in the soft X-rays. The accretion rate falls by roughly 2.5, and the radius of the hot Comptonizing region increases from the flaring state to the post-flare state. Additionally, from the optical spectral observations, we find that the broad He IIλ4686 emission line fades significantly as the optical/UV/X-ray continuum fades, which could indicate a substantial flare of disk emission above 54 eV. We also observed a redshifted broad component in the Hβ emission line that is present during the high flux state of the source and disappears in subsequent observations. Conclusions. A sudden strong increase in the local accretion rate in this source manifested itself via an increase in accretion disk emission and in thermal Comptonized emission in the soft X-rays, which subsequently faded. The redshifted broad Balmer component could be associated with a transient kinematic component distinct from that comprising the rest of the broad-line region.

An Improved Non-Monotonic Adaptive Trust Region Algorithm for Unconstrained Optimization

The trust region method is an effective method for solving unconstrained optimization problems. Incorrectly updating the rules of the trust region radius will increase the number of iterations and affect the calculation efficiency. In order to obtain an effective radius for the trust region, an adaptive radius updating criterion is proposed based on the gradient of the current iteration point and the eigenvalue of the Hessian matrix which avoids calculating the inverse of the Hessian matrix during radius updating. This approach reduces the computation time and enhances the algorithm’s performance. On this basis, we apply adaptive radius and non-monotonic techniques to the trust region algorithm and propose an improved non-monotonic adaptive trust region algorithm. Under proper assumptions, the convergence of the algorithm is analyzed. Numerical experiments confirm that the suggested algorithm is effective.

Otolith Microchemistry Reveals the Diversity of Migration Patterns and Spawning Ground Distribution of Coilia nasus from the Yangtze River Estuary

Coilia nasus are an important fish resource in the Yangtze River, and the Yangtze River Estuary is a crucial migration pathway for them. In this study, we used otolith microchemistry to analyze the strontium/calcium (Sr/Ca) ratios and Sr contents in the sagitta otolith of C. nasus from the south branch (SB) and north branch (NB) of the Yangtze River Estuary and obtained the diversity of migration patterns and spawning ground distribution for C. nasus. The results indicate that C. nasus from both branches include two types of habitat history: freshwater (F)–brackish water (B) (Type I) and F-B seawater (S) (Type II), with Type I being dominant at 62.50% in both branches. The C. nasus from the SB comprise six migration patterns, while that from the NB has seven migration patterns. The C. nasus from both branches hatch in F habitats. At the time of capture, the C. nasus from the SB predominantly remain in F, accounting for 62.5%, while C. nasus from the NB primarily stay in B, accounting for 87.5%. Throughout the migration process, C. nasus from both branches switch between different habitats, with C. nasus from the NB exhibiting more frequent transitions between F and B, showing a greater reliance on the estuarine brackish habitat. The radius of the first blue region near the core (Lf) and freshwater coefficient (Fc) of the otolith for C. nasus from both branches are divided into three groups: long-distance freshwater dependence (LD), medium-distance freshwater dependence (MD), and short-distance freshwater dependence (SD), with the LD only appearing in the SB, while the NB is primarily represented by MD. There is a correlation between the differences in Lf among different groups of C. nasus and the differences in the distance from the spawning grounds of C. nasus in different sections of the Yangtze River to the estuary (DYRE), reflecting the distribution pattern of C. nasus spawning grounds in different sections of the Yangtze River. This study provides theoretical guidance for the protection of migration pathways and maintenance of spawning grounds for C. nasus, which have significant practical value in the precise management of C. nasus resources in the Yangtze River Estuary.

Enhanced support vector machine-based moving regression strategy for response prediction and reliability estimation of complex structure

For predicting response property and estimating reliability level of complex structure, enhanced support vector machine-based moving regression (MR-ESVM) strategy is proposed based on support vector machine (SVM), heuristic algorithm and moving least square (MLS) technique. Under this strategy, we develop four different SVM models including SVM-based moving regression (MR-SVM), SVM-based improved moving regression (IMR-SVM), improved SVM-based moving regression (MR-ISVM) and bi-optimized SVM-based moving regression (BiOMR-SVM) methods. In these developed MR-ESVM approaches, the MR-SVM method is explored by introducing the MLS technique into the SVM model; the IMR-SVM method is discussed by fusing the MR-SVM method and artificial rabbits optimization (ARO), and the ARO is used to search the optimal radius of compact region; the MR-ISVM method is raised by integrating the ARO into the MR-SVM, and the ARO is applied to find the optimal values in the SVM model; The BiOMR-SVM method is emerged by merging the IMR-SVM and MR-ISVM methods. To verify the effectiveness of these developed MR-ESVM strategies, a multivariate nonlinear function approximation is implemented to illustrate the advantages from the mathematics perspective, an aeroengine turbine blisk radial deformation reliability analysis and an aircraft hydraulic system low pressure reliability analysis are derived to demonstrate the applicability in engineering practice. The analytical results show that these four MR-ESVM approaches hold excellent merits in modeling features and simulation characteristics. The efforts of this work provide a novel idea for the response prediction of complex structure, and enrich the reliability estimation principle of surrogate models of complex structure.

A fast and reliable semi-analytical method for assessing energy replenishment from fracturing-flooding in low-permeability and tight oil reservoirs

The development of low-permeability and tight oil reservoirs is challenged by insufficient natural energy and rapid production decline. Fracturing-flooding is a technique that relies on high-pressure and large-volume fluid injection to replenish reservoir energy, making it a significant method for rapidly boosting formation energy. To evaluate the energy replenishment effect of fracturing-flooding technology in low-permeability and tight reservoirs, this study proposes a semi-analytical method for quick calculation. This approach employs dimensionless simplification, Pedrosa's substitution, Laplace transformation, and Stehfest inversion methods to derive pressure solutions for both the stimulation region and the external matrix region, each with varying flow capacities. The average formation pressure (AFP) of the reservoir is determined using the area-weighted average method, and numerical verification is performed using a commercial simulator. A case study from the Binnan area, along with a sensitivity analysis, demonstrates that after 30 days of fracturing-flooding, the AFP of the reservoir increases to 46.97 MPa, the corresponding reservoir pressure coefficient rises from 1.2 to 1.68, and reservoir energy increases by 40%. The factors influencing energy replenishment are ranked as follows: reservoir thickness, injection rate, stress sensitivity coefficient, matrix permeability, stimulation region radius, and mobility ratio. This study provides theoretical guidance for optimizing fracturing-flooding development schemes in low-permeability and tight oil reservoirs and offers valuable reference for the industry.

Acoustic emission accuracy from a tensile test of a ceramic matrix composite

AbstractCeramic matrix composites (CMCs) on one level are excellent materials for acoustic emission (AE) analysis. They are excellent waveguides for AE waveform transmission due to the high modulus to density ratio. CMC inelastic behavior is due to micro‐ and macrocrack formation from matrix crack interaction with the fibers via a relatively weak fiber/matrix interface which create ideal stress waves. Because of this, AE is an excellent detector of microcracks in general, and most importantly in the case of CMCs, the initial or lowest stress crack formation. This property can be related to long time stressed‐oxidation degradation of nonoxide composites, in particular. In addition, AE has been used to effectively determine the stress distribution for matrix cracks which cause the nonlinear stress–strain behavior. However, a key to quantitatively correlating AE with sources is first and foremost to locate where the AE originated. For a tensile test, most AE comes from the near‐grip region and the radius region outside the gage area of interest. Outside the gage region AE would not be considered useful data pertaining to stress/strain behavior and must be sorted out from the AE dataset. Location is determined by the difference in time of arrivals (TOAs) of waveforms received on each sensor from a given AE source. Automated TOA techniques such as threshold voltage crossing or Akaike information criteria (AIC) have limitations in overall accuracy of differences in TOA (Δt) of two different sensors required for location analysis. This study has incorporated several signal filter and enhancement techniques and an approach toward increasing the accuracy of the classic TOA techniques. First TOA was determined for the two sensors of the AE tests “manually” based on first extensional peak of the waveform, this served as the “exact” difference in TOA. Δt’s were then determined for the various filter/TOA techniques and compared to those from the manual determined Δt. The best filter/TOA techniques resulted in more than two times better accuracy (defined as percentage of events within 0.1 µs of the exact Δt) than the conventional threshold crossing or AIC technique.

Activation Energy of DC Hopping Conductivity of Lightly Doped Weakly Compensated Crystalline Semiconductors

A model is proposed for calculating the thermal activation energy of direct current hopping conductivity via nearest neighbors in lightly doped and weakly compensated crystalline semiconductors with hydrogen‐like impurities. The temperature region is considered in which hops of single holes occur only between acceptors randomly distributed over the crystal (or hops of single electrons only between donors). The model is based on the idea of the Coulomb blockade of charge carriers by the field of compensating impurities (trap impurities). The hopping length of a hole between acceptors (or an electron between donors) is assumed to be equal to the critical (percolation) radius of the spherical region per a majority (doping) impurity atom. At a critical radius, an infinite cluster connecting ohmic contacts is formed in the crystal, along which charge carriers move in a hopping manner via majority impurities. The value of is defined as average work on overcoming the electrostatic Coulomb blockade by a charge carrier and its hopping via the electrically conducting cluster to “infinity”. The results of calculating by the proposed model of the Coulomb blockade for the most well‐studied bulk germanium and silicon p‐ and n‐type crystals are consistent with known experimental data.

The Radio Galaxy Environment Reference Survey (RAGERS): a submillimetre study of the environments of massive radio-quiet galaxies at z = 1–3

ABSTRACT Measuring the environments of massive galaxies at high redshift is crucial to understanding galaxy evolution and the conditions that gave rise to the distribution of matter we see in the Universe today. While high-z radio galaxies (HzRGs) and quasars tend to reside in protocluster-like systems, the environments of their radio-quiet counterparts are relatively unexplored, particularly in the submillimetre, which traces dust-obscured star formation. In this study, we search for 850 μm-selected submillimetre galaxies (SMGs) in the environments of massive ($M_{\star }$$\gt 10^{11}$${\rm M}_{\odot }$), radio-quiet ($L_{500 {\rm MHz}}$$\lesssim 10^{25}$ WHz$^{-1}$) galaxies at $z \sim 1\!-\!3$ using data from the SCUBA-2 COSMOS (S2COSMOS) survey. By constructing number counts in circular regions of radius 1–6 arcmin and comparing with blank-field measurements, we find no significant overdensities of SMGs around massive radio-quiet galaxies at any of these scales, despite being sensitive down to overdensities of $\delta \sim 0.4$. To probe deeper than the catalogue we also examine the distribution of peaks in the SCUBA-2 signal-to-noise (SNR) map, which reveals only tentative signs of any difference in the SMG densities of the radio-quiet galaxy environments compared to the blank field, and only on smaller scales (1 arcmin radii, corresponding to $\sim 0.5$ Mpc) and higher SNR thresholds. We conclude that massive, radio-quiet galaxies at cosmic noon are typically in environments with $\delta \lesssim 0.4$, which are either consistent with the blank field or contain only weak overdensities spanning sub-Mpc scales. The contrast between our results and studies of HzRGs with similar stellar masses and redshifts implies an intrinsic link between the wide-field environment and the radio luminosity of the active galactic nucleus at high redshift.

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

Abstract For investigating efficiently the stagnation kinetic-process of Z-pinch, we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used. In our algorithm, the electric field in z-direction is solved by a parallel electrode-plate model, the azimuthal magnetic field is obtained by Ampere’s law, and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field. In simulation results of 2 MA deuterium plasma shell Z-pinch, the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation, and the plasma current also closely aligns with the external current. The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained. The main kinetic characteristic of electron motion is thermal equilibrium and oscillation, which should be oscillated around the ions, while that of ion motion is implosion inwards. In the region of stagnation radius, the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing, while of electrons is basically the equilibrium state. When the initial ion density and current peak are not high enough, the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

A Catalog of Broad Hα and Hβ Active Galactic Nuclei in MaNGA

Broad Hα and Hβ emission lines (FWHM > 1000 km s−1) are incredibly efficient tracers of the high-velocity clouds encircling active galactic nuclei (AGNs). As a result, we search for these broad-line AGN in the Sloan Digital Sky Survey’s Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) catalog. We identify 301 broad-line Hα galaxies and 801 broad-line Hβ galaxies in the catalog. In total, we detect 1042 unique broad-line galaxies with luminosities between 1037 and 1043 erg s−1; 60 feature both broad Hα and broad Hβ emission. We also determine that the broad-line region radius ranges between 0.01 and 46 lt-days, with a median radius of 0.1 lt-days (0.02 pc) for our broad Hβ sample. In addition, we find that both samples feature a higher fraction of galaxy mergers (44% for the broad Hα sample and 43% for the broad Hβ sample), compared to the full MaNGA galaxy sample (26%), which suggests that merger-driven fueling is strongly active in our sample.

The MOSDEF-KCWI Survey: Spectral Properties of Lyα Halos around z ∼ 2 Star-forming Galaxies

We present Keck Cosmic Web Imager integral field observations of extended Lyα emission in the circumgalactic medium of 27 typical star-forming galaxies at z ∼ 2, drawn from the Multi-Object Spectrometer for Infra-Red Exploration (MOSFIRE) Deep Evolution Field (MOSDEF) survey. Using composite spectra in two bins of star formation rate (SFR), star formation rate surface density (ΣSFR), and other galactic properties, we measure spatial variations in the Lyα profile across three regions in the Lyα halo. We find single-peaked, redshifted profiles are ubiquitous within a central 7 kpc radius region. Further out in the halo (7–14 and 14–21 kpc), the Lyα profile of the resonantly scattered emission exhibits more diversity, either transitioning to a double-peaked profile or remaining single peaked across the halo. We find a shorter scale length of the Lyα halo surface brightness profile for composite halos with faster winds. The composites have a similar average inclination, suggesting those with faster winds clear channels in the interstellar medium (ISM), reducing the fraction of Lyα photons resonantly scattered to large radii. A uniform expanding shell radiative transfer model reproduces the shape but not the normalization of the observed double-peaked Lyα profiles. Models that adopt a more realistic, clumpy ISM are likely needed to reproduce both the shape and normalization of the Lyα profiles.

Thin-wall monopoles in a false vacuum

We study numerically the existence in a false vacuum of magnetic monopoles that are “thin walled,” i.e., which correspond to a spherical region of radius R that is essentially trivial surrounded by a wall of thickness Δ≪R, hence the name thin wall, and finally an exterior region that essentially corresponds to a pure Abelian magnetic monopole. Such monopoles were dubbed false monopoles and can occur in non-Abelian gauge theories where the symmetry-broken vacuum is actually the false vacuum. This idea was first proposed in Kumar []; however, the proof of the existence of thin-wall, false monopoles given there was incorrect. Here, we fill this lacuna and demonstrate numerically, for an appropriately modified potential, the existence of thin-wall false monopoles. The decay via quantum tunneling of the false monopoles could be of importance to cosmological scenarios that entertain epochs in which the Universe is trapped in a symmetry-broken false vacuum. Published by the American Physical Society 2024

Modeling the Propagation of Slow Magnetoacoustic Waves in a Multistranded Coronal Loop

We study the propagation properties of slow magnetoacoustic waves in a multithermal coronal loop using a 3D MHD model, for the first time. A bundle of 33 vertical cylinders, each of 100 km radius, randomly distributed over a circular region of radius 1 Mm, is considered to represent the coronal loop. The slow waves are driven by perturbing the vertical velocity (v z ) at the base of the loop. We apply forward modeling to the simulation results to generate synthetic images in the coronal channels of the Solar Dynamics Observatory/Atmospheric Imaging Assembly. Furthermore, we add appropriate data noise to enable direct comparison with the real observations. It is found that the synthetic images at the instrument resolution show noncospatial features in different temperature channels in agreement with previous observations. Time–distance maps are constructed from the synthetic data to study the propagation properties. The results indicate that the oscillations are only visible in specific channels, depending on the temperature range of the plasma existing within the loop. Additionally, the propagation speed of slow waves is also found to be sensitive to the available temperature range. Overall, we propose that the cross-field thermal properties of coronal structures can be inferred using a combination of numerical simulations and observations of slow magnetoacoustic waves.

Performance enhancement of nanotube junctionless FETs with low doping concentration rings

To reduce the static power consumption of the NT JLFET and the effect of SCEs on the NT JLFET, A nanotube junctionless field effect transistor with cyclic low doping concentration regions (C NT JLFET) is proposed. Based on Sentaurus TCAD numerical simulations, the electrical properties of the C NT JLFET and the NT JLFET were comparatively investigated, and the effects of the length (L CD) and radius (R CD) of cyclic low doping concentration regions on the electrical properties of the C NT JLFETs were studied. The C NT JLFET reduces the gate-induced drain leakage (GIDL) due to lateral band-to-band-tunneling (L-BTBT) as compared to the NT JLFET. As the L CD or R CD increases, the off-state current decreases. In addition, the C NT JLFET suffers from fewer short channel effects (SCEs), such as threshold voltage roll-off, drain-induced barrier lowering and subthreshold swing deterioration, compared to the NT JLFET. The inhibition of L-BTBT and attenuation of SCEs by cyclic low doping concentration regions remains when the channel length of the C NT JLFET is shortened to 10 nm. The C NT JLFET are suitable for low power applications as they exhibit reduced L-BTBT and suffer from fewer SCEs.

A nonmonotone adaptive trust region technique with a forgetting factor

Nonmonotonicity has been considered to be essentially influential on the efficiency of the iterative procedures of nonlinear optimization. A review of the literature shows that the objective function values available from recent iterations provide worthier information in the nonmonotone schemes. So, with the aim of enhancing probability of applying more recent available function values, a nonmonotone trust region ratio is suggested using a forgetting factor. Meanwhile, modification of a recent adaptive formula for the trust region radius is devised by a nonmonotone reflection as well. Then, based on the two mentioned modifications, an adaptive nonmonotone trust region algorithm is given. In addition, convergence of the method is analysed under classic assumptions. To provide support for our theoretical arguments, computational merits of the given algorithm on a set of CUTEr test functions are depicted.

Quark star matter in the color-flavor-locked state with a density-dependent quark mass model

The properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter are investigated in quark stars (QSs) at zero temperature case within confined-isospin-density-dependent-mass (CIDDM) model. The mass–radius relation of QSs are also studied by considering newly proposed mass–radius constraints in CFL phase. Our results indicate that we can obtain more stable and stiffer equation of state (EOS) by considering CFL phase within CIDDM model at zero temperature. While the GW190814's secondary component with a mass around 2.6 M ⊙ cannot be QSs within CIDDM model in SQM case, it can be well described as QSs by considering CFL phase within CIDDM model in this work. In particular, we further construct a density-dependent pairing energy gap to connect the EOS of SQM and CFL quark matter with constant pairing energy gap Δ, and the results indicate that by extending the paring energy gap to include density dependence, the mass–radius lines within CIDDM model can satisfy most of the mass–radius region constraints in recent pulsar observations.

Sub‐sampled adaptive trust region method on Riemannian manifolds

AbstractWe consider the problem of large‐scale finite‐sum minimization on Riemannian manifold. We develop a sub‐sampled adaptive trust region method on Riemannian manifolds. Based on inexact information, we adopt adaptive techniques to flexibly adjust the trust region radius in our method. We present the iteration complexity is when the algorithm attains an ‐second‐order stationary point, which matches the result on trust region method. Numerical results for PCA on Grassmann manifold and low‐rank matrix completion are reported to demonstrate the effectiveness of the proposed Riemannian method.