arXiv subjects

Kun Xu

Publications and source records attributed to Kun Xu.

At least 163 records · Page 9Linked to original sources

arXiv2024

Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes II: unsteady flows

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time step for unsteady simulations. In order to improve the efficiency and keep the high-order accuracy, a two-stage third-order implicit time-accurate discretization is proposed. In each stage, an artificial steady solution is obtained for the implicit system with the pseudo-time iteration. In the iteration, the classical implicit methods are adopted to solve the nonlinear system, including the lower-upper symmetric Gauss-Seidel (LUSGS) and generalized minimum residual (GMRES) methods. To achieve the spatial accuracy, the HGKSs with both non-compact and compact reconstructions are constructed. For the non-compact scheme, the weighted essentially non-oscillatory (WENO) reconstruction is used. For the compact one, the Hermite WENO (HWENO) reconstruction is adopted due to the updates of both cell-averaged flow variables and their derivatives. The expected third-order temporal accuracy is achieved with the two-stage temporal discretization. For the smooth flow, only a single artificial iteration is needed. For uniform meshes, the efficiency of the current implicit method improves significantly in comparison with the explicit one. For the flow with discontinuities, compared with the well-known Crank-Nicholson method, the spurious oscillations in the current schemes are well suppressed. The increase of the artificial iteration steps introduces extra reconstructions associating with a reduction of the computational efficiency. Overall, the current implicit method leads to an improvement in efficiency over the explicit one in the cases with a large variation of mesh size.

math.NA↗

arXiv2024

On the Formation of Double Neutron Stars in the Milky Way: Influence of Key Parameters

The detection of gravitational wave events has stimulated theoretical modeling of the formation and evolution of double compact objects (DCOs). However, even for the most studied isolated binary evolution channel, there exist large uncertainties in the input parameters and treatments of the binary evolution process. So far, double neutron stars (DNSs) are the only DCOs for which direct observations are available through traditional electromagnetic astronomy. In this work, we adopt a population synthesis method to investigate the formation and evolution of Galactic DNSs. We construct 324 models for the formation of Galactic DNSs, taking into account various possible combinations of critical input parameters and processes such as mass transfer efficiency, supernova type, common envelope efficiency, neutron star kick velocity, and pulsar selection effect. We employ Bayesian analysis to evaluate the adopted models by comparing with observations. We also compare the expected DNS merger rate in the Galaxy with that inferred from the known Galactic population of Pulsar-NS systems. Based on these analyses we derive favorable range of the aforementioned key parameters.

astro-ph.HE↗

arXiv2024

A Compact Gas-Kinetic Scheme with Scalable Geometric Multigrid Acceleration for Steady-State Computation on 3D Unstructured Meshes

In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves cell-averaged flow variables and their gradients on the original mesh. Mesh coarsening employs a two-step parallel agglomeration algorithm using a random hash for cell interface selection and a geometric skewness metric for deletion confirmation, ensuring both efficiency and robustness. For the coarser meshes, first-order kinetic flux vector splitting (KFVS) schemes with explicit or implicit time-stepping are used. The proposed multigrid CGKS is tested across various flow regimes on hybrid unstructured meshes, demonstrating significant improvements. A three-layer V-cycle multigrid strategy, coupled with an explicit forward Euler method on coarser levels, results in a convergence rate up to ten times faster than standard CGKS. In contrast, the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence acceleration. Our findings indicate that the explicit multigrid CGKS is highly scalable and effective for large-scale computations, marking a substantial step forward in computational fluid dynamics.

physics.comp-ph↗

arXiv2024

A robustness-enhanced reconstruction based on discontinuity feedback factor for high-order finite volume scheme

In this paper, a robustness-enhanced reconstruction for the high-order finite volume scheme is constructed on the 2-D structured mesh, and both the high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are considered to verify the validity of this algorithm. The strategy of the successful WENO reconstruction is adopted to select the smooth sub-stencils. However, there are cases where strong discontinuities exist in all sub-stencils of the WENO reconstruction, which leads to a decrease in the robustness. To improve the robustness of the algorithm in discontinuous regions in two-dimensional space, the hybrid reconstruction based on a combination of discontinuity feedback factor(DF) \cite{ji2021gradient} and WENO reconstruction is developed to deal with the possible discontinuities. Numerical results from smooth to extreme cases have been presented and validate that the new finite volume scheme is effective for robustness enhancement and maintains high resolution compared to the WENO scheme.

math.NA↗

arXiv2024

Photonic RF Channelization Based on Microcombs

In recent decades, microwave photonic channelization techniques have developed significantly. Characterized by low loss, high versatility, large instantaneous bandwidth, and immunity to electromagnetic interference, microwave photonic channelization addresses the requirements of modern radar and electronic warfare for receivers. Microresonator-based optical frequency combs are promising devices for photonic channelized receivers, enabling full advantage of multicarriers, large bandwidths, and accelerating the integration process of microwave photonic channelized receivers. In this paper, we review the research progress and trends in microwave photonic channelization, focusing on schemes that utilize integrated microcombs. We discuss the potential of microcomb-based RF channelization, as well as their challenges and limitations, and provide perspectives for their future development in the context of on-chip silicon-based photonics.

physics.optics↗

arXiv2024

Mean-field reflected BSDEs driven by a marked point process

In this paper, we study a class of mean-field reflected backward stochastic differential equations (MFRBSDEs) driven by a marked point process. Based on a g-expectation representation lemma, we give the existence and uniqueness of MFRBSDEs driven by a marked point process under Lipschitz generator conditions. Besides, the well-posedness of this kind of BSDEs with exponential growth generator and unbounded terminal is also provided by $θ$-method.

math.PR↗

arXiv2024

High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing arbitrary mesh into tetrahedrons and integrating flux function in a local coordinate system at the cell interface to ensure geometric conservation law. The scheme incorporates a compact reconstruction with third-order accuracy for updating both cell-averaged conservative flow variables and their gradients. HWENO-type nonlinear reconstruction and gradient compression factors are adopted to improve the accuracy and robustness of the scheme. A multi-stage multi-derivative (MSMD) time-stepping method is also implemented to achieve high-order time accuracy with fewer middle stages. The scheme is used to study problems involving moving boundaries. The numerical experiments demonstrate the effectiveness of the scheme in capturing the accurate solutions of both low-speed smooth flow and highly compressible ones with strong shock waves.

physics.comp-ph↗

arXiv2024

Formation of PSR J1012+5307 with an extremely low-mass white dwarf: testing magnetic braking models

PSR J1012+5307 is a millisecond pulsar with an extremely low-mass (ELM) white dwarf (WD) companion in an orbit of 14.5 hours. Magnetic braking (MB) plays an important role in influencing the orbital evolution of binary systems with a low-mass ($\lt 1-2~M_{\odot}$) donor star. At present, there exist several different MB descriptions. In this paper, we investigate the formation of PSR J1012+5307 as a probe to test the plausible MB model. Employing a detailed stellar evolution model by the MESA code, we find that the Convection And Rotation Boosted MB and the 'Intermediate' MB models can reproduce the WD mass, WD radius, WD surface gravity, neutron-star mass, and orbital period observed in PSR J1012+5307. However, our simulated WD has higher effective temperature than the observation. Other three MB mechanisms including the standard MB model are too weak to account for the observed orbital period in a Hubble time. A long cooling timescale caused by H-shell flashes of the WD may alleviate the discrepancy between the simulated effective temperature and the observed value.

astro-ph.SR↗

arXiv2023

Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation

The multi-frequency radiation transport equation (RTE) system models the photon transport and the energy exchange process between the background material and different frequency photons. In this paper, the unified gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed to capture the multiscale non-equilibrium transport in different optical regimes. In the UGKWP, a multiscale evolution process is properly designed to obtain both non-equilibrium transport in the optically thin regime and thermal diffusion process in the optically thick regime automatically. At the same time, the coupled macroscopic energy equations for the photon and material are solved implicitly by the matrix-free source iteration method. With the wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity for different regime physics. In the optically thick regime, no particles will be sampled in the computational domain and the thermal diffusion solution for the photon transport will be recovered. While in the optically thin regime, stochastic particles will play a dominant role in the evolution and the non-equilibrium free transport of photon is automatically followed. In the frequency-dependent transport, the frequency carried by the simulating particle will be determined by a linear-frequency sampling strategy. In addition, to better resolve the sharp of opacity in the photon transport across a cell interface, the free streaming time of simulating particle in the UGKWP method will be reset when it passes through the interface. Moreover, the numerical relaxation time is properly defined to increase the particle proportion in the sharp opacity transition region in order to avoid numerical oscillation. Several typical test cases for the RTE system have been calculated to demonstrate the accuracy and reliability of the current frequency-dependent UGKWP method.

physics.comp-ph↗

arXiv2023

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale non-equilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman-Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS method with rotation and vibration non-equilibrium is developed. The real gas effect in different flow regimes has been captured. To capture aerodynamic heating accurately, the heat flux modifications are also included. Unstructured discrete particle velocity space is adopted to further improve the computational performance. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for non-equilibrium flow simulations, especially for the flows at low and medium speed.

physics.flu-dyn↗

arXiv2023

Black Hole Ultracompact X-Ray Binaries as Galactic Low-frequency Gravitational Wave Sources: the He Star Channel

Black hole (BH) ultracompact X-ray binaries (UCXBs) are potential Galactic low-frequency gravitational wave (GW) sources. As an alternative channel, BH UCXBs can evolve from BH+He star binaries. In this work, we perform a detailed stellar evolution model for the formation and evolution of BH UCXBs evolving from the He star channel to diagnose their detectability as low-frequency GW sources. Our calculations found that some nascent BH+He star binaries after the common-envelope (CE) phase could evolve into UCXB-LISA sources with a maximum GW frequency of $\sim5~\rm mHz$, which can be detected in a distance of 10 kpc (or 100 kpc). Once BH+He star systems become UCXBs through mass transfer, they would emit X-ray luminosities of $\sim10^{38}~\rm erg\, s^{-1}$, making them ideal multimessenger objects. If the initial He-star masses are $\geq 0.7 M_{\odot}$, those systems are likely to experience two Roche lobe overflows, and the X-ray luminosity can reach a maximum of $3.5\times 10^{39}~\rm erg\, s^{-1}$ in the second mass-transfer stage. The initial He-star masses and initial orbital periods of progenitors of Galactic BH UCXB-LISA sources are in the range of 0.32-2.9 $M_{\odot}$ and 0.02-0.19 days, respectively. Nearly all BH+He star binaries in the above parameter space can evolve into GW sources whose chirp masses can be accurately measured. Employing a population synthesis simulation, we predict the birthrate and detection number of Galactic BH UCXB-LISA source evolving from the He star channel are $R=2.2\times10^{-6}~\rm yr^{-1}$ and 33 for an optimistic CE parameter, respectively.

astro-ph.HE↗

arXiv2023

A Step Closer to Comprehensive Answers: Constrained Multi-Stage Question Decomposition with Large Language Models

While large language models exhibit remarkable performance in the Question Answering task, they are susceptible to hallucinations. Challenges arise when these models grapple with understanding multi-hop relations in complex questions or lack the necessary knowledge for a comprehensive response. To address this issue, we introduce the "Decompose-and-Query" framework (D&Q). This framework guides the model to think and utilize external knowledge similar to ReAct, while also restricting its thinking to reliable information, effectively mitigating the risk of hallucinations. Experiments confirm the effectiveness of D&Q: On our ChitChatQA dataset, D&Q does not lose to ChatGPT in 67% of cases; on the HotPotQA question-only setting, D&Q achieved an F1 score of 59.6%. Our code is available at https://github.com/alkaidpku/DQ-ToolQA.

cs.CL↗

arXiv2023

The Splitting of Chiral and Deconfinement Phase Transitions induced by Rotation

The chiral and deconfinement phase transitions under rotation have been simultaneously investigated in the Polyakov-Nambu-Jona-Lasinio (PNJL) model. An interesting observation has been found that the chiral phase transition is catalyzed and the deconfinement phase transition is decelerated by rotation, therefore a chiral symmetric but confined phase is induced by rotation, which indicates that chiral dynamics and gluon dynamics can be split by rotation.

hep-ph↗

arXiv2023

The DESI One-Percent Survey: A concise model for galactic conformity of ELGs

Galactic conformity is the phenomenon in which a galaxy of a certain physical property is correlated with its neighbors of the same property, implying a possible causal relationship. The observed auto correlations of emission line galaxies (ELGs) from the highly complete DESI One-Percent survey exhibit a strong clustering signal on small scales, providing clear evidence for the conformity effect of ELGs. Building upon the original subhalo abundance matching (SHAM) method developed by Gao et al. (2022, 2023), we propose a concise conformity model to improve the ELG-halo connection. In this model, the number of satellite ELGs is boosted by a factor of $\sim 5$ in the halos whose central galaxies are ELGs. We show that the mean ELG satellite number in such central halos is still smaller than 1, and the model does not significantly increase the overall satellite fraction. With this model, we can well recover the ELG auto correlations to the smallest scales explored with the current data (i.e. $r_{\mathrm{p}} > 0.03$ $\mathrm{Mpc}\,h^{-1}$ in real space and at $s > 0.3$ $\mathrm{Mpc}\,h^{-1}$ in redshift space), while the cross correlations between luminous red galaxies (LRGs) and ELGs are nearly unchanged. Although our SHAM model has only 8 parameters, we further verify that it can accurately describe the ELG clustering in the entire redshift range from $z = 0.8$ to $1.6$. We therefore expect that this method can be used to generate high-quality ELG lightcone mocks for DESI.

astro-ph.GA↗

arXiv2023

Toward a Physical Understanding of Galaxy-Halo Alignment

We investigate the alignment of galaxy and halo orientations using the TNG300-1 hydrodynamical simulation. Our analysis reveals that the distribution of the 2D misalignment angle $θ_{\rm{2D}}$ can be well described by a truncated shifted exponential (TSE) distribution with only {\textit{one}} free parameter across different redshifts and galaxy/halo properties. We demonstrate that the galaxy-ellipticity (GI) correlations of galaxies can be reproduced by perturbing halo orientations with the obtained $θ_{\rm{2D}}$ distribution, with only a small bias ($<3^{\circ}$) possibly arising from unaccounted couplings between $θ_{\rm{2D}}$ and other factors. We find that both the 2D and 3D misalignment angles $θ_{\rm{2D}}$ and $θ_{\rm{3D}}$ decrease with ex situ stellar mass fraction $F_{\rm{acc}}$, halo mass $M_{\rm{vir}}$ and stellar mass $M_{*}$, while increasing with disk-to-total stellar mass fraction $F_{\rm{disk}}$ and redshift. These dependences are in good agreement with our recent observational study based on the BOSS galaxy samples. Our results suggest that $F_{\rm{acc}}$ is a key factor in determining the galaxy-halo alignment. Grouping galaxies by $F_{\rm{acc}}$ nearly eliminates the dependence of $θ_{\rm{3D}}$ on $M_{\rm{vir}}$ for all three principle axes, and also reduces the redshift dependence. For $θ_{\rm{2D}}$, we find a more significant redshift dependence than for $θ_{\rm{3D}}$ even after controlling $F_{\rm{acc}}$, which may be attributed to the evolution of galaxy and halo shapes. Our findings present a valuable model for observational studies and enhance our understanding of galaxy-halo alignment.

astro-ph.GA↗

arXiv2023

Reflected BSDE driven by a marked point process with a convex/concave generator

In this paper, a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator is studied. Based on fixed point argument, $θ$-method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.

math.PR↗

arXiv2023

Mean reflected BSDE driven by a marked point process and application in insurance risk management

This paper aims to solve a super-hedging problem along with insurance re-payment under running risk management constraints. The initial endowment for the super-heding problem is characterized by a class of mean reflected backward stochastic differential equation driven by a marked point process (MPP) and a Brownian motion. By Lipschitz assumptions on the generators and proper integrability on the terminal value, we give the well-posedness of this kind of BSDEs by combining a representation theorem with the fixed point argument.

math.PR↗

arXiv2023

Exploring the Usage of Chinese Pinyin in Pretraining

Unlike alphabetic languages, Chinese spelling and pronunciation are different. Both characters and pinyin take an important role in Chinese language understanding. In Chinese NLP tasks, we almost adopt characters or words as model input, and few works study how to use pinyin. However, pinyin is essential in many scenarios, such as error correction and fault tolerance for ASR-introduced errors. Most of these errors are caused by the same or similar pronunciation words, and we refer to this type of error as SSP(the same or similar pronunciation) errors for short. In this work, we explore various ways of using pinyin in pretraining models and propose a new pretraining method called PmBERT. Our method uses characters and pinyin in parallel for pretraining. Through delicate pretraining tasks, the characters and pinyin representation are fused, which can enhance the error tolerance for SSP errors. We do comprehensive experiments and ablation tests to explore what makes a robust phonetic enhanced Chinese language model. The experimental results on both the constructed noise-added dataset and the public error-correction dataset demonstrate that our model is more robust compared to SOTA models.

cs.CL↗