arXiv subjects

Gang Zhao

Publications and source records attributed to Gang Zhao.

At least 73 records · Page 4Linked to original sources

arXiv2025

An Actinide-boost Star Discovered in the Gaia-Sausage-Enceladus

We report the discovery of an actinide-boost, very metal-poor ($\left[\mathrm{Fe/H} \right]=-2.38$), $r$-process-enhanced ($\left[\mathrm{Eu/Fe} \right]=0.80$) star, LAMOST J0804+5740, within the Gaia-Sausage-Enceladus (GSE). Based on the high-resolution ($R\sim36,000\; and \;60,000$) and high signal-to-noise ratio spectra obtained with the High Dispersion Spectrograph on the Subaru Telescope, the abundances of 48 species are determined. Its $\logε\rm(\mathrm{Th}/\mathrm{Eu}) = -0.22 $ establishes it as the first confirmed actinide-boost star within the GSE. Comparative analysis of its abundance pattern with theoretical $r$-process models reveals that the magnetorotationally driven jet supernova $r$-process model with $\hat{L}v$ = 0.2 provides the best fit and successfully reproduces the actinide-boost signature. Kinematic analysis of actinide-boost stars reveals that approximately two-thirds of them are classified as $\textit{ex-situ}$ stars, suggesting that actinide-boost stars are more likely to originate from accreted dwarf galaxies. As the first actinide-boost star identified within the GSE, J0804+5740 will provide valuable insights into $r$-process nucleosynthesis in accreted dwarf galaxies like the GSE, especially on the production of the heaviest elements.

astro-ph.SR↗

arXiv2025

The Impact of Neutrino Magnetic Moments on the Evolution of the Helium Flash and Lithium-Rich Red Clump Stars

The detection of the neutrino magnetic moment (NMM,$μ_v$) is one of the most significant challenges in physics. The additional energy loss due to NMM can significantly influence the He flash evolution in low-mass stars. Using the MESA code, we investigated the impact of NMM on the He flash evolution in low-mass stars. We found that NMM leads to an increase in both the critical He core mass required for the He flash and the luminosity of TRGB. For a typical $Z = 1 Z_{\odot}$ , $M$ = 1.0 $M_{\odot}$, and $μ_v = 3 \times 10^{-12} μ_{\mathrm{B}}$ model, the He core mass increases by $\sim 5\%$, and the TRGB luminosity increases by $\sim 35\%$ compared to the model without NMM. However, contrary to previous conclusions, our model indicates that the He flash occurs earlier, rather than delayed, with increasing NMM values. This is because the additional energy loss from NMM accelerates the contraction of the He core, releases more gravitational energy that heats the H shell and increases the hydrogen burning rate, thereby causing the He core to reach the critical mass faster and advancing the He flash. An increase in NMM results in a higher peak luminosity for the first He flash, a more off-center ignition position, and sub-flashes with higher luminosities, shorter intervals, and higher frequency. We found that the internal gravity wave (IGW) mixing generated by the He flash can induce sufficient mixing in the radiative zone, turning the overshoot region into a low-Dmix bottleneck within the stellar interior. The increase in NMM in the model narrows the overshoot bottleneck region, enabling Li to enter the surface convection zone more quickly, thereby enhancing the enrichment effect of IGW mixing on surface Li. For models incorporating both NMM and IGW mixing, the reduction in the overshoot bottleneck region allows them to effectively produce super Li-rich red clump star samples.

astro-ph.SR↗

arXiv2025

Mapping the Milky Way with Gaia Bp/Rp spectra I: Systematic flux corrections and atmospheric parameters for 68 million stars

Gaia Bp/Rp spectra for over two hundred million stars have great potential for mapping metallicity across the Milky Way. We aim to construct an alternative catalog of atmospheric parameters from Gaia Bp/Rp spectra by fitting them with synthetic spectra based on model atmospheres, and provide corrections to the Bp/Rp fluxes according to stellar colors, magnitudes, and extinction. We use GaiaXPy to obtain calibrated spectra and apply FERRE to match the corrected Bp/Rp spectra with models and infer atmospheric parameters. We train a neural network using stars in APOGEE to predict flux corrections as a function of wavelength for each target. Based on the comparison with APOGEE parameters, we conclude that our estimated parameters have systematic errors and uncertainties in $T_{\mathrm{eff}}$, $\log g$, and [M/H] about $-38 \pm 167$ K, $0.05 \pm 0.40$ dex, and $-0.12 \pm 0.19$ dex, respectively, for stars in the range $4000 \le T_{\mathrm{eff}} \le 7000$ K. The corrected Bp/Rp spectra show better agreement with both models and Hubble Space Telescope CALSPEC data. Our correction increases the precision of the relative spectrophotometry of the Bp/Rp data from $3.2\% - 3.7\%$ to $1.2\% - 2.4\%$. Finally, we have built a catalog of atmospheric parameters for stars within $4000 \le T_{\mathrm{eff}} \le 7000$ K, comprising $68,394,431$ sources, along with a subset of $124,188$ stars with $\mathrm{[M/H]} \le -2.5$. Our results confirm that the Gaia Bp/Rp flux calibrated spectra show systematic patterns as a function of wavelength that are tightly related to colors, magnitudes, and extinction. Our optimization algorithm can give us accurate atmospheric parameters of stars with a clear and direct link to models of stellar atmospheres, and can be used to efficiently search for extremely metal-poor stars.

astro-ph.GA↗

arXiv2025

Formation of Ultra-short-period Planet in Hot Jupiter Systems: Application to WASP-47

The WASP-47 system is notable as the first known system hosting both inner and outer low-mass planetary companions around a hot Jupiter, with an ultra-short-period (USP) planet as the innermost planetary companion. The formation of such an unique configuration poses challenges to the lonely hot Jupiter formation model. Hot Jupiters in multiple planetary systems may have a similar formation process with warm Jupiter systems, which are more commonly found with companions. This implies that the WASP-47 system could bridge our understanding of both hot and warm Jupiter formation. In this work, we propose a possible formation scenario for the WASP-47 system based on its orbital configuration. The mean motion resonance trapping, giant planet perturbations, and tidal effects caused by the central star are key factors in the formation of USP planets in multiple planetary systems with hot Jupiters. Whether a planet can become an USP planet or a short period super-earth (SPSE) planet depends on the competition between eccentricity excitation by nearby giant planet perturbations and the eccentricity damping due to tidal effects. The $Q_p'$ value of the innermost planet is essential for the final planetary configuration. Our results suggest that a $Q_p'$ in the range of [1, 10] is favorable for the formation of the WASP-47 system. Based on the formation scenario, we estimate an occurrence rate of 8.4$\pm$2.4\% for USP planets in systems similar to WASP-47.

astro-ph.EP↗

arXiv2025

The Impact of $^{12}$C($α, γ$)$^{16}$O Reaction on the Presupernova Evolution and Supernova Explodability of Massive Stars

Among the uncertainties of stellar evolution theory, we investigate how the $^{12}$C($α, γ$)$^{16}$O reaction rate affects the evolution of massive stars for the initial masses of $M ({\rm ZAMS})=$ 13 - 40 M$_\odot$ and the solar metallicity. We show that the {\sl explodability} of these stars, i.e., which of a neutron star (NS) or a black hole (BH) is formed, is sensitive to the strength of convective shell burning of C and O, and thus the mass fractions of C ($X$(C)) and O in the shell. For the small $^{12}$C($α, γ$)$^{16}$O reaction rate that yields larger $X$(C), $X$(C) is further enhanced by mixing of C from the overlying layer and then C shell burning is strengthened. The extra heating by C shell burning tends to prevent the contraction of outer layers and decrease the {\sl compactness parameter} at $M_r$ = 2.5 M$_\odot$. This effect leads to the formation of smaller mass cores of Si and Fe and steeper density and pressure gradients at the O burning shell in the presupernova models. If the pressure gradient there is steeper, the model is more likely to explode to form a NS rather than a BH. We describe the pressure gradient against $M_r$ with $V/U$ and the density drop with $1/U$, where $U$ and $V$ are non-dimensional variables to describe the stellar structure. We estimate the critical values of $V/U$ and $1/U$ at the O-burning shell above which the model is more likely to explode. We conclude that the smaller $^{12}$C($α, γ$)$^{16}$O reaction rate makes the mass range of $M ({\rm ZAMS})$ that forms a NS larger.

astro-ph.SR↗

arXiv2025

Explainable LLM-driven Multi-dimensional Distillation for E-Commerce Relevance Learning

Effective query-item relevance modeling is pivotal for enhancing user experience and safeguarding user satisfaction in e-commerce search systems. Recently, benefiting from the vast inherent knowledge, Large Language Model (LLM) approach demonstrates strong performance and long-tail generalization ability compared with previous neural-based specialized relevance learning methods. Though promising, current LLM-based methods encounter the following inadequacies in practice: First, the massive parameters and computational demands make it difficult to be deployed online. Second, distilling LLM models to online models is a feasible direction, but the LLM relevance modeling is a black box, and its rich intrinsic knowledge is difficult to extract and apply online. To improve the interpretability of LLM and boost the performance of online relevance models via LLM, we propose an Explainable LLM-driven Multi-dimensional Distillation framework for e-commerce relevance learning, which comprises two core components: (1) An Explainable LLM for relevance modeling (ELLM-rele), which decomposes the relevance learning into intermediate steps and models relevance learning as a Chain-of-Thought (CoT) reasoning, thereby enhancing both interpretability and performance of LLM. (2) A Multi-dimensional Knowledge Distillation (MKD) architecture that transfers the knowledge of ELLM-rele to current deployable interaction-based and representation-based student models from both the relevance score distribution and CoT reasoning aspects. Through distilling the probabilistic and CoT reasoning knowledge, MKD improves both the semantic interaction and long-tail generalization abilities of student models. Extensive offline evaluations and online experiments on Taobao search ad scene demonstrate that our proposed framework significantly enhances e-commerce relevance learning performance and user experience.

cs.IR↗

arXiv2025

The Stellar Abundances and Galactic Evolution Survey (SAGES). II. Machine Learning-Based Stellar parameters for 21 million stars from the First Data Release

Stellar parameters for large samples of stars play a crucial role in constraining the nature of stars and stellar populations in the Galaxy. An increasing number of medium-band photometric surveys are presently used in estimating stellar parameters. In this study, we present a machine-learning approach to derive estimates of stellar parameters, including [Fe/H], logg, and Teff, based on a combination of medium-band and broad-band photometric observations. Our analysis employs data primarily sourced from the SAGE Survey , which aims to observe much of the Northern Hemisphere. We combine the $uv$-band data from SAGES DR1 with photometric and astrometric data from Gaia EDR3, and apply the random forest method to estimate stellar parameters for approximately 21 million stars. We are able to obtain precisions of 0.09 dex for [Fe/H], 0.12 dex for logg, and 70 K for Teff. Furthermore, by incorporating 2MASS and WISE infrared photometric and GALEX ultraviolet data, we are able to achieve even higher precision estimates for over 2.2 million stars. These results are applicable to both giant and dwarf stars. Building upon this mapping, we construct a foundational dataset for research on metal-poor stars, the structure of the Milky Way, and beyond. With the forthcoming release of additional bands from SAGE Survey such DDO51 and H-alpha, this versatile machine learning approach is poised to play an important role in upcoming surveys featuring expanded filter sets

astro-ph.SR↗

arXiv2024

The Terminator Region Atmosphere of the hot Jupiter WASP-77Ab with ESPRESSO/VLT observations

Atmospheric studies are essential for elucidating the formation history, evolutionary processes, and atmospheric dynamics of exoplanets. High-resolution transmission spectroscopy offers the advantage of detecting subtle variations in stellar spectral profiles, thereby enabling the identification of the sources of observed signals. In this study, we present the transmission spectra of the exoplanet WASP-77Ab, a hot Jupiter with a 1.36-day orbital period around a G8 host star with $V=11.29$ mag. These observations were conducted using the high-resolution spectrograph ESPRESSO at the Very Large Telescope over three transit events. We analyze the Rossiter-McLaughlin effect for WASP-77A and determine a projected spin-orbit angle of ${λ= 16.131^{\circ}}^{+2.106}_{-2.324}$, indicating that the planet's orbit is nearly aligned. Following the generation of transmission spectra for the three nights, we model and correct for center-to-limb variation and the Rossiter-McLaughlin effects. In the residual transmission spectra, we detect H$α$, H$β$ and CaII H with a significance exceeding 3.5$σ$. After applying 0.1-0.5 Å masks to the cores of these lines to mitigate stellar contamination, all them still shows visible absorptions although not significant, suggesting at least partial planet contribution to them. Therefore, we are yet unable to confirm or reject the planetary origin of these spectral signals based on the current data set. Further investigation of WASP-77Ab's atmosphere, particularly in areas beyond the terminator region, is essential to illuminate the planet's two-dimensional atmospheric structure.

astro-ph.EP↗

arXiv2024

Investigating the vertical distribution of the disk as a function of radial action: Results from simulations

Previous research has established a relationship between radial action and scale height in Galactic disks, unveiling a correlation between radial and vertical heating. This finding poses a challenge to our existing comprehension of heating theories and consequently encodes crucial insights into the formation and heating history of Galactic disks. In this study, we perform N-body simulations with the aim of verifying the existence of this correlation between radial action and scale height, thereby enhancing our comprehension of the heating history of Galactic disks. We find that the relationship between radial action and scale height in our simulations can be described by the same functional form observed in previous work. Furthermore, the relationships derived from our simulations align well with those of the Galactic thin disk. However, they do not coincide with the inner thick disk but exhibit a rough correspondence with the outer thick disk, suggesting the possibility that additional heating mechanisms may be required to explain the inner thick disk. We also find that the mean radial action and scale height undergo rapid increases during the initial stages of the simulation, yet remain relatively unchanged as the disk evolves further. By tracing example particles, we uncover a correlation between radial and vertical heating in our simulation: as a particle in the disk gains or loses radial action, its vertical motion tends to oscillate on a more or less extended orbit, accompanied by a tendency to migrate outward or inward, respectively. The massive, long-lasting particles in our simulation contribute to disk heating by solely enhancing the rate of increase in scale height with radial action, while maintaining the functional form that describes the relationship between these two variables.

astro-ph.GA↗

arXiv2024

Chemical abundances of 20 barium stars from the OHP spectra

Based on the high resolution and high signal-to-noise spectra, we derived the chemical abundances of 20 elements for 20 barium (Ba-) stars. For the first time, the detailed abundances of four sample stars, namely HD 92482, HD 150430, HD 151101 and HD 177304 have been analyzed. Additionally, Ba element abundance has been measured using high resolution spectra for the first time in six of the other 16 sample stars. Based on the [s/Fe] ratios, the Ba-unknown star HD 115927 can be classified as a strong Ba-star, while the Ba-likely star HD 160538 can be categorized into a mild Ba-star. Consequently, our sample comprises three strong and 17 mild Ba-stars. The light odd-Z metal elements and Fe-peak elements exhibit near-solar abundances. The [α/Fe] ratios demonstrate decreasing trends with increasing metallicity. Moreover, the abundances of n-capture elements show significant enhancements in different degrees. Using a threshold of the signed distances to the solar r-process abundance pattern ds = 0.6, we find that all of our sample stars are normal Ba-stars, indicating that the enhancements of s-process elements should be attributed to material transfer from their companions. We compare the observed n-capture patterns of sample stars with the FRUITY models, and estimate the mass of the Thermally-Pulsing Asymptotic Giant Branch stars that previously contaminated the Ba-stars. The models with low masses can successfully explain the observations. From a kinematic point of view, we note that most of our sample stars are linked with the thin disk, while HD 130255 may be associated with the thick disk.

astro-ph.SR↗

arXiv2024

The Stellar Abundances and Galactic Evolution Survey (SAGES) III -- The g/r/i-band Data Release

The Stellar Abundances and Galactic Evolution Survey (SAGES) is a multi-band survey that covers the northern sky area of ~12000 deg2. Nanshan One-meter Wide-field Telescope (NOWT) of Xinjiang Astronomical Observatory (XAO) carried out observations on g/r/i bands. We present here the survey strategy, data processing, catalog construction, and database schema. The observations of NOWT started in 2016 August and was completed in 2018 January, total 17827 frames were obtained and ~4600 deg2 sky areas were covered. In this paper, we released the catalog of the data in the g/r/i bands observed with NOWT. In total, there are 109,197,578 items of the source records. The catalog is the supplement for the SDSS for the bright end, and the combination of our catalog and these catalogs could be helpful for source selections for other surveys and the Milky Way sciences, e.g., white dwarf candidates and stellar flares.

astro-ph.GA↗

arXiv2024

A Modified Initial Mass Function of the First Stars with Explodability Theory under Different Enrichment Scenarios

The most metal-poor stars record the earliest metal enrichment triggered by Population III stars. By comparing observed abundance patterns with theoretical yields of metal-free stars, physical properties of their first star progenitors can be inferred, including zero-age main-sequence mass and explosion energy. In this work, the initial mass distribution (IMF) of first stars is obtained from the largest analysis to date of 406 very metal-poor stars with the newest LAMOST/Subaru high-resolution spectroscopic observations. However, the mass distribution fails to be consistent with the Salpeter IMF, which is also reported by previous studies. Here we modify the standard power-law function with explodability theory. The mass distribution of Population III stars could be well explained by ensuring the initial metal enrichment to originate from successful supernova explosions. Based on the modified power-law function, we suggest an extremely top-heavy or nearly flat initial mass function with a large explosion energy exponent. This indicates that supernova explodability should be considered in the earliest metal enrichment process in the Universe.

astro-ph.GA↗

arXiv2024

High-performance magnesium/sodium hybrid ion battery based on sodium vanadate oxide for reversible storage of Na+ and Mg2+

Magnesium ion batteries (MIBs) are a potential field for the energy storage of the future but are restricted by insufficient rate capability and rapid capacity degradation. Magnesium-sodium hybrid ion batteries (MSHBs) are an effective way to address these problems. Here, we report a new type of MSHBs that use layered sodium vanadate ((Na, Mn)V8O20 5H2O, Mn-NVO) cathodes coupled with an organic 3,4,9,10-perylenetetracarboxylic diimide (PTCDI) anode in Mg2+/Na+ hybrid electrolytes. During electrochemical cycling, Mg2+ and Na+ co-participate in the cathode reactions, and the introduction of Na+ promotes the structural stability of the Mn-NVO cathode, as cleared by several ex-situ characterizations. Consequently, the Mn-NVO cathode presents great specific capacity (249.9 mAh g-1 at 300 mA g-1) and cycling (1500 cycles at 1500 mA g-1) in the Mg2+/Na+ hybrid electrolytes. Besides, full battery displays long lifespan with 10,000 cycles at 1000 mA g-1. The rate performance and cycling stability of MSHBs have been improved by an economical and scalable method, and the mechanism for these improvements was discussed.

cond-mat.mtrl-sci↗

arXiv2024

Study of a red clump giant, KIC~11087027, with high rotation and strong infrared excess -- Evidence of tidal interaction for high lithium abundance

This paper presents results from Kepler photometric light curves and high-resolution spectroscopic study of a super Li-rich giant KIC11087027. Using the light curve analysis, we measured the star's rotational period P$_{\rm rot}$=30.4$\pm$0.1~days, which translates to rotational velocity V$_{\rm rot}$=19.5 $\pm$ 1.7~km s$^{-1}$. Star's location in the HR-diagram, derived values of $^{12}C/^{13}C$ = 7$\pm$1 and $[C/N]=-0.95\pm 0.2$, and the inferred asteroseismic parameters from secondary calibration based on spectra suggest star is a low-mass red clump giant in the He-core burning phase. Using Gaia data, we found evidence of variation in radial velocity and proper motion, indicative of presence of an unresolved binary. The large V$_{\rm rot}$ is probably a result of tidal synchronization combined with the after-effects of He-flash, in which the size of the star is reduced significantly. The simultaneous presence of features like high rotation, very high Li abundance, strong dust shell, and strong flares in a single star is relatively uncommon, suggesting that the star experiencing tidal synchronization has recently undergone He-flash. The results pose a question whether the binary interaction, hence the high rotation, is a prerequisite for dredging-up of the high amounts of Li from the interior to the photosphere during or immediately after the He-flash event.

astro-ph.SR↗

arXiv2024

Dance of the ADS: Orchestrating Failures through Historically-Informed Scenario Fuzzing

As autonomous driving systems (ADS) advance towards higher levels of autonomy, orchestrating their safety verification becomes increasingly intricate. This paper unveils ScenarioFuzz, a pioneering scenario-based fuzz testing methodology. Designed like a choreographer who understands the past performances, it uncovers vulnerabilities in ADS without the crutch of predefined scenarios. Leveraging map road networks, such as OPENDRIVE, we extract essential data to form a foundational scenario seed corpus. This corpus, enriched with pertinent information, provides the necessary boundaries for fuzz testing in the absence of starting scenarios. Our approach integrates specialized mutators and mutation techniques, combined with a graph neural network model, to predict and filter out high-risk scenario seeds, optimizing the fuzzing process using historical test data. Compared to other methods, our approach reduces the time cost by an average of 60.3%, while the number of error scenarios discovered per unit of time increases by 103%. Furthermore, we propose a self-supervised collision trajectory clustering method, which aids in identifying and summarizing 54 high-risk scenario categories prone to inducing ADS faults. Our experiments have successfully uncovered 58 bugs across six tested systems, emphasizing the critical safety concerns of ADS.

cs.AI↗

arXiv2024

Candidate Members of the VMP/EMP Disk System of the Galaxy from the SkyMapper and SAGES Surveys

Photometric stellar surveys now cover a large fraction of the sky, probe to fainter magnitudes than large-scale spectroscopic surveys, and are relatively free from the target-selection biases often associated with such studies. Photometric-metallicity estimates that include narrow/medium-band filters can achieve comparable accuracy and precision to existing low-resolution spectroscopic surveys such as SDSS/SEGUE and LAMOST. Here we report on an effort to identify likely members of the Galactic disk system among the very metal-poor (VMP; [Fe/H] $\leq$ --2) and extremely metal-poor (EMP; [Fe/H] $\leq$ --3) stars. Our analysis is based on an initial sample of $\sim11.5$ million stars with full space motions selected from the SkyMapper Southern Survey (SMSS) and Stellar Abundance and Galactic Evolution Survey (SAGES). After applying a number of quality cuts to obtain the best available metallicity and dynamical estimates, we analyze a total of $\sim$5.86 million stars in the combined SMSS/SAGES sample. We employ two techniques that, depending on the method, identify between 876 and 1,476 VMP stars (6.9%-11.7% of all VMP stars) and between 40 and 59 EMP stars (12.4%-18.3% of all EMP stars) that appear to be members of the Galactic disk system on highly prograde orbits (v$_ϕ > 150$ km/s). The total number of candidate VMP/EMP disk-like stars is 1,496, the majority of which have low orbital eccentricities, ecc $\le 0.4$; many have ecc $\le 0.2$. The large fractions of VMP/EMP stars associated with the Milky Way disk system strongly suggest the presence of an early forming ``primordial" disk.

astro-ph.GA↗

arXiv2024

Four-hundred Very Metal-poor Stars Studied with LAMOST and Subaru. III. Dynamically Tagged Groups and Chemodynamical Properties

Very metal-poor (VMP) stars record the signatures of early accreted galaxies, making them essential tools for unraveling the early stages of Galaxy formation. Understanding the origin of VMP stars requires comprehensive studies of their chemical compositions and kinematics, which are currently lacking. Hence, we conduct a chemodynamical analysis of 352 VMP stars selected from one of the largest uniform high-resolution VMP star samples, jointly obtained from LAMOST and Subaru. We apply a friends-of-friends clustering algorithm to the master catalog of this high-resolution sample, which consists of 5778 VMP stars. It results in 131 dynamically tagged groups with 89 associated with known substructures in the Milky Way, including Gaia-Sausage-Enceladus (GSE), Thamnos, Helmi streams, Sequoia, Wukong, Pontus, and the very metal-poor disk (VMPD). Our findings are: (i) the VMPD shows lower Zn abundances than the rest, which indicates that it could be a relic of small stellar systems; (ii) Sequoia shows moderately high r-process abundances; (iii) Helmi streams show deficiencies in carbon and light neutron-capture elements; (iv) the fraction of carbon-enhanced metal-poor stars with no enhancement in heavy elements (CEMP-no stars) seems low in the VMPD and the Helmi streams; and (v) a subgroup in GSE exhibits a very high fraction of r-process enhanced stars, with four out of five showing [Eu/Fe]> +1.0. The abundance patterns of other elements in VMP substructures largely match the whole VMP sample. We also study large-scale correlations between abundance ratios and kinematics without classifying stars into substructures, but it does not yield significant correlations once the overall chemical evolution is considered for most elements.

astro-ph.GA↗

arXiv2024

A Nonnested Augmented Subspace Method for Kohn-Sham Equation

In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent field iterative algorithm which requires to solve the Kohn-Sham equation directly in each adaptive finite element space, our algorithm transforms the Kohn-Sham equation into some linear boundary value problems of the same scale in each adaptive finite element space, and then the wavefunctions derived from the linear boundary value problems are corrected by solving a small-scale Kohn-Sham equation defined in a low-dimensional augmented subspace. Since the new algorithm avoids solving large-scale Kohn-Sham equation directly, a significant improvement for the solving efficiency can be obtained. In addition, the adaptive moving mesh technique is used to generate the nonnested adaptive mesh for the nonnested augmented subspace method according to the singularity of the approximate wavefunctions. The modified Hessian matrix of the approximate wavefunctions is used as the metric matrix to redistribute the mesh. Through the moving mesh adaptive technique, the redistributed mesh is almost optimal. A number of numerical experiments are carried out to verify the efficiency and the accuracy of the proposed algorithm.

math.NA↗