arXiv subjects

Hailiang Li

Publications and source records attributed to Hailiang Li.

At least 19 recordsLinked to original sources

arXiv2026

Spectrum analysis and optimal time decay rates of a kinetic-fluid-Poisson system

In this paper, we consider the Cauchy problem for the Vlasov-Poisson-Fokker-Planck/Navier-Stokes-Poisson (VPFP/NSP) system, which couples the VPFP system with the compressible NSP system through a friction force dependent on the relative velocity and a self-consistent Poisson equation. Motivated by the spectrum analysis for the Vlasov-Poisson-Boltzmann (VPB) system, we introduce a suitable norm to capture the effect of the forcing induced by the Poisson equation and give a detailed spectrum analysis of the linearized system around a global equilibrium. Our results show that the two coupling mechanisms lead to an essentially different spectrum structure of the coupled system from those of the individual VPFP and NSP systems. More precisely, the low-frequency spectrum contains a pair of acoustic branches with the propagation speed $\sqrt{\frac{\gamma+1}{2}}~(\gamma\ge1)$ and two diffusive branches, thereby restoring the usual acoustic wave propagation of classical compressible fluids. Moreover, we establish the global existence of the solution to the nonlinear system and obtain the optimal time decay rate $(1+t)^{-\frac34}$, with a faster rate $(1+t)^{-\frac54}$ for the electric field and relative velocity. The present analysis also provides a useful framework for studying related kinetic-fluid models coupled through friction and self-consistent fields.

math.AP↗

arXiv2026

Numerical estimation of the capture ability of Neptunian mean motion resonances

Resonant populations of trans-Neptunian objects serve as crucial dynamical archives for unraveling the early migratory history of the Solar System. A quantitative assessment of the capture efficiency into various mean motion resonances (MMRs) during migration is essential for understanding the origins of these populations, constraining migration parameters, and reconstructing of the primordial planetesimal disk. Using numerical simulations, this study systematically investigates the capture capability of exterior MMRs during Neptune's outward migration in a planar model. For a specific p:q MMR, the small bodies can be captured only when their eccentricities surpass a certain threshold, which increases with faster migration rates, greater distances of MMRs, and higher resonance orders. On the other hand, as long as a particle's eccentricity is suitable, its capture efficiency shows little dependence on the migration rate; instead, it mainly depends on the p value and heliocentric distance, decaying exponentially as either parameter increases. Based on our simulation results, we derive for the first time a simple empirical expression to calculate eccentricity threshold and the capture efficiency. This research provides a systematic quantitative framework for understanding capture into Neptunian MMRs during migration. Future integrations of more comprehensive observational data will facilitate a more precise reconstruction of the Solar System's early dynamical evolution.

astro-ph.EP↗

arXiv2026

Lunar ejecta as the missing piece to resolve the lunar cratering asymmetry

The leading-trailing asymmetry in lunar crater distribution provides a critical record of inner solar system dynamics, yet the long-standing discrepancy between the observed higher asymmetry and lower theoretical predictions indicates a gap in our understanding of the impactor population. This paper hypothesizes that lunar impact ejecta, which can enter Earth-like orbits and return, constitute a previously unaccounted-for component. Through numerical simulations, we find that ~25% of escaped ejecta will re-impact the Earth-Moon system within 3 Myr, with about 1.2% striking the Moon. Crucially, these lunar impacts exhibit an extreme leading-trailing asymmetry with a ratio of 5.9. Our results indicate that lunar ejecta, if comprising ~15% of total impactors, can fully explain the observed asymmetry, leading to their recognition as active agents shaping the lunar impact record. This work provides new constraints for understanding the impact environment of the Earth-Moon system, with direct relevance to the interpretation of lunar geology, the transport of lunar material to Earth, and ongoing space exploration missions.

astro-ph.EP↗

arXiv2026

Positive YORP effect induced by lateral heat conduction in a crater

The YORP effect plays an important role in the spin evolution of asteroids. Although craters are ubiquitous surface features, their influence on YORP torque has received limited attention. In this paper, we investigate the YORP torque of a circular crater on a spherical asteroid, focusing specifically on how lateral thermal conduction breaks symmetry to produce a net torque. Using three-dimensional finite element simulations, we calculate the resulting spin and obliquity accelerations and examine their dependence on the crater's location, depth, and thermal parameters. Our results show that the crater-induced spin torque is consistently positive, and craters at different latitudes drive the spin axis toward obliquity equilibria at 0, 90 or 180 degree. We demonstrate that the spin torque arises primarily from the lateral heat conduction inside the asteroid that occurs only in 3D model, while the contributions from self-heating and shadowing effects are negligible. While the YORP effect induced by internal heat conduction may be overtaken by torque components arising from shadowing and crater orientation, particularly on large asteroids, our numerical results show that for small craters, this spin torque amounts to approximately 10 to 100 percent of the normal YORP torque. Its persistent positivity may help explain the observed prevalence of positive spin accelerations in asteroids.

astro-ph.EP↗

arXiv2025

Acceleration of planetary migration: Resonance crossing and planetesimal ring

Planetary migration is a crucial stage in the early solar system, explaining many observational phenomena and providing constraints on details related to the solar system's origins. This paper aims to investigate the acceleration during planetary migration in detail using numerical simulations, delving deeper into the early solar system's preserved information. We confirm that planetary migration is a positive feedback process: the faster the migration, the more efficient the consumption of planetesimals; once the migration slows down, Neptune clears the surrounding space, making further migration more difficult to sustain. Quantitatively, a tenfold increase in migration rate corresponds to an approximately 30% reduction in the mass of planetesimals consumed to increase per unit angular momentum of Neptune. We also find that Neptune's final position is correlated with the initial surface density of planetesimals at that location, suggesting that the disk density at 30au was approximately 0.009$M_{\oplus}/au^2$ in the early solar system. Two mechanisms that can accelerate planetary migration are identified: the first is MMR between Uranus and Neptune. Migration acceleration will be triggered whenever these two giant planets cross their major MMR. The second mechanism is the ring structure within the planetesimal disk, as the higher planetesimal density in this region can provide the material support necessary for migration acceleration. Our research indicates that Neptune in the current solar system occupies a relatively delicate position. In case Neptune crossed the 1:2 MMR with Uranus, it could have migrated to a much more distant location. Therefore, under the influence of the positive feedback mechanism, the evolution of the solar system to its current configuration might be a stochastic outcome rather than an inevitable consequence.

astro-ph.EP↗

arXiv2025

Prediction for close approaches with terrestrial planets of asteroids from the main belt

Potentially Hazardous Asteroids (PHAs), a special subset of Near-Earth Objects, are both dangerous and scientifically valuable. PHAs that truly undergo close approaches with the Earth (dubbed CAPHAs) are of particular interest and extensively studied. The concept and study of CAPHA can be extended to other Solar system planets, which have significant implications for future planet-based observations and explorations. In this work, we conduct numerical simulations that incorporate the Yarkovsky effect to study the transformation of main belt asteroids into CAPHAs of terrestrial planets, using precise nominal timesteps, especially to ensure the reliability of the results for Mercury and Venus. Our simulations predict a total of 1893 Mercury-CAPHAs, 3014 Venus-CAPHAs, 3791 Earth-CAPHAs and 18066 Mars-CAPHAs, with an occurrence frequency of about 1, 9, 15 and 66 per year, respectively. The values for Mars-CAPHAs are consistent with our previous work, which were based on simulations with a larger nominal timestep. The predicted occurrence frequency and velocity distribution of Earth-CAPHAs are in reasonable agreement with the observed population of Earth-CAPHAs. We also find that certain asteroids can be caught in close approach with different planets at different times, raising an interesting possibility of using them as transportation between terrestrial planets in the future.

astro-ph.EP↗

arXiv2024

MARTIANS (MARs2020, TIANwen and So on) would see more potentially hazardous asteroids than Earthlings

Potentially Hazardous Asteroids (PHAs) are a special subset of Near-Earth Objects (NEOs) that can come close to the Earth and are large enough to cause significant damage in the event of an impact. Observations and researches of Earth-PHAs have been underway for decades. Here, we extend the concept of PHAs to Mars and study the feasibility of detecting Mars-PHAs in the near future. We focus on PHAs that truly undergo close approaches with a planet (dubbed CAPHAs) and aim to compare the actual quantities of Earth-CAPHAs and Mars-CAPHAs by conducting numerical simulations incorporating the Yarkovsky effect, based on observed data of the main asteroid belt. The estimated number of Earth-CAPHAs and Mars-CAPHAs are 4675 and 16910, respectively. The occurrence frequency of Mars-CAPHAs is about 52 per year, which is 2.6 times that of Earth-CAPHAs, indicating significant potential for future Mars-based observations. Furthermore, a few Mars-CAPHAs are predicted to be observable even from Earth around the time of next Mars opposition in 2025.

astro-ph.EP↗

arXiv2024

Secular Structure of 1:2 and 1:3 Resonances with Neptune

The 1:N mean motion resonances with Neptune are of particular interest because they have two asymmetric resonance islands, where the distribution of trapped objects may bear important clues to the history of the Solar System. To explore the dynamics of these resonances and to investigate whether the imprints left by the early stage evolution can be preserved in the resonances, we conduct a comprehensive analyses on the 1:2 and 1:3 resonances. Adopt mainly the frequency analysis method, we calculate the proper frequencies of the motion of objects in the resonances, with which the secular mechanisms that influence the dynamics are determined. Use the spectral number as an indicator of orbital regularity, we construct dynamical maps on representative planes. By comparing the structures in the maps with the locations of the secular mechanisms, we find that the von-Zeipel-Lidov-Kozai mechanism and the $g=2s$ mechanism destabilize the influenced orbits and portray the overall structure of the 1:2 and 1:3 resonances. The secular resonance $2g-s=s_8$ opens a channel for objects to switch between the leading and trailing resonance islands, which can alter the population ratio between these two islands. The secondary resonances associated with the quasi 2:1 resonance between Uranus and Neptune are also detected, and they introduce more chaos to the motion. The fine dynamical structures of the 1:2 and 1:3 resonances revealed in this paper, combined with knowledge of resonant capture, provide a compelling explanation for the eccentricity distribution of observed Twotinos. And we anticipate a more complete understanding of the history of planetary migration in the Solar System can be achieved by comparing the results in this paper with the populations in the 1:N resonances in future when further observations bring us more objects.

astro-ph.EP↗

arXiv2024

A Lightweight Inception Boosted U-Net Neural Network for Routability Prediction

As the modern CPU, GPU, and NPU chip design complexity and transistor counts keep increasing, and with the relentless shrinking of semiconductor technology nodes to nearly 1 nanometer, the placement and routing have gradually become the two most pivotal processes in modern very-large-scale-integrated (VLSI) circuit back-end design. How to evaluate routability efficiently and accurately in advance (at the placement and global routing stages) has grown into a crucial research area in the field of artificial intelligence (AI) assisted electronic design automation (EDA). In this paper, we propose a novel U-Net variant model boosted by an Inception embedded module to predict Routing Congestion (RC) and Design Rule Checking (DRC) hotspots. Experimental results on the recently published CircuitNet dataset benchmark show that our proposed method achieves up to 5% (RC) and 20% (DRC) rate reduction in terms of Avg-NRMSE (Average Normalized Root Mean Square Error) compared to the classic architecture. Furthermore, our approach consistently outperforms the prior model on the SSIM (Structural Similarity Index Measure) metric.

cs.AR↗

arXiv2023

Asymmetric Capture into Neptunian 1:2 Resonance

The asymmetric resonance configuration characterized by the critical angle librating around centres other than 0 or 180 degree, is found in the 1:N mean motion resonance. The asymmetric 1:2 resonance with Neptune is of particular interest because the two asymmetric islands seem to host different populations, and this might be a direct clue to understanding the early evolution of the Solar system. The asymmetry has been investigated from both observational and theoretical perspectives, but conclusions among studies vary widely. In this paper using toy models, we carefully designed a series of tests to systematically study the capture of planetesimals into the leading and trailing resonance islands. Although these tests may not reproduce exactly the real processes the Solar system experienced, they reveal some typical dynamics in the resonance capture. Since the real Twotinos have small to moderate inclinations, as the first attempt, we adopted in this paper planar models to investigate the mechanisms that may lead to asymmetric capture by the leading and trailing islands, including their size variation during the outward migration of Neptune, the stickiness of the leading island, and the migration slowdown effect. Particularly, we find that the ratio between the populations of the leading and trailing islands can be easily tuned by introducing the slowdown effect in the migration model, thus may be not a good tracer of the migration history. However, the eccentricity of objects trapped in two asymmetric islands may conserve some valuable information of the early evolution of the Solar system.

astro-ph.EP↗

arXiv2019

An Augmented Transformer Architecture for Natural Language Generation Tasks

The Transformer based neural networks have been showing significant advantages on most evaluations of various natural language processing and other sequence-to-sequence tasks due to its inherent architecture based superiorities. Although the main architecture of the Transformer has been continuously being explored, little attention was paid to the positional encoding module. In this paper, we enhance the sinusoidal positional encoding algorithm by maximizing the variances between encoded consecutive positions to obtain additional promotion. Furthermore, we propose an augmented Transformer architecture encoded with additional linguistic knowledge, such as the Part-of-Speech (POS) tagging, to boost the performance on some natural language generation tasks, e.g., the automatic translation and summarization tasks. Experiments show that the proposed architecture attains constantly superior results compared to the vanilla Transformer.

cs.CL↗

arXiv2017

Image Super-resolution via Feature-augmented Random Forest

Recent random-forest (RF)-based image super-resolution approaches inherit some properties from dictionary-learning-based algorithms, but the effectiveness of the properties in RF is overlooked in the literature. In this paper, we present a novel feature-augmented random forest (FARF) for image super-resolution, where the conventional gradient-based features are augmented with gradient magnitudes and different feature recipes are formulated on different stages in an RF. The advantages of our method are that, firstly, the dictionary-learning-based features are enhanced by adding gradient magnitudes, based on the observation that the non-linear gradient magnitude are with highly discriminative property. Secondly, generalized locality-sensitive hashing (LSH) is used to replace principal component analysis (PCA) for feature dimensionality reduction and original high-dimensional features are employed, instead of the compressed ones, for the leaf-nodes' regressors, since regressors can benefit from higher dimensional features. This original-compressed coupled feature sets scheme unifies the unsupervised LSH evaluation on both image super-resolution and content-based image retrieval (CBIR). Finally, we present a generalized weighted ridge regression (GWRR) model for the leaf-nodes' regressors. Experiment results on several public benchmark datasets show that our FARF method can achieve an average gain of about 0.3 dB, compared to traditional RF-based methods. Furthermore, a fine-tuned FARF model can compare to or (in many cases) outperform some recent stateof-the-art deep-learning-based algorithms.

cs.CV↗

arXiv2017

Stability of the Superposition of a Viscous Contact Wave with two Rarefaction Waves to the bipolar Vlasov-Poisson-Boltzmann System

We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for one-dimensional bipolar Vlasov-Poisson-Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under the additional electrostatic potential force. Based on a new micro-macro type decomposition around the local Maxwellian related to the bipolar VPB system in our previous work [26], we prove that the superposition of a viscous contact wave and two rarefaction waves is time-asymptotically stable to 1D bipolar VPB system under some smallness conditions on the initial perturbations and wave strength, which implies that this typical composite wave pattern is nonlinearly stable under the combined effects of the binary collisions, the electrostatic potential force, and the mutual interactions of different charged particles. Note that this is the first result about the nonlinear stability of the combination of two different wave patterns for the Vlasov-Poisson-Boltzmann system.

math.AP↗

arXiv2017

Stability of nonlinear wave patterns to the bipolar Vlasov-Poisson-Boltzmann system

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction wave for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in [21, 23], we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as the applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction wave, are proved for the 1D bipolar Vlasov-Poisson-Boltzmann system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of rarefaction wave fan to compressible Euler equations is proved to 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in [18] sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

math.AP↗

arXiv2017

Joint Maximum Purity Forest with Application to Image Super-Resolution

In this paper, we propose a novel random-forest scheme, namely Joint Maximum Purity Forest (JMPF), for classification, clustering, and regression tasks. In the JMPF scheme, the original feature space is transformed into a compactly pre-clustered feature space, via a trained rotation matrix. The rotation matrix is obtained through an iterative quantization process, where the input data belonging to different classes are clustered to the respective vertices of the new feature space with maximum purity. In the new feature space, orthogonal hyperplanes, which are employed at the split-nodes of decision trees in random forests, can tackle the clustering problems effectively. We evaluated our proposed method on public benchmark datasets for regression and classification tasks, and experiments showed that JMPF remarkably outperforms other state-of-the-art random-forest-based approaches. Furthermore, we applied JMPF to image super-resolution, because the transformed, compact features are more discriminative to the clustering-regression scheme. Experiment results on several public benchmark datasets also showed that the JMPF-based image super-resolution scheme is consistently superior to recent state-of-the-art image super-resolution algorithms.

cs.CV↗

arXiv2017

Non-Existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier-Stokes Equations

In this paper, we investigate the well-posedess of classical solutions to the Cauchy problem of Navier-Stokes equations,and prove that the classical solution with finite energy does not exist even in the inhomogeneous Sobolev space for any short time under some natural assumptions on initial data near the vacuum. This implies in particular that the homogeneous Sobolev space is crucial as studying the well-posedness for the Cauchy problem of compressible Navier-Stokes equations in the presence of vacuum at far fields even locally in time.

math.AP↗

arXiv2017

Cascaded Face Alignment via Intimacy Definition Feature

In this paper, we present a random-forest based fast cascaded regression model for face alignment, via a novel local feature. Our proposed local lightweight feature, namely intimacy definition feature (IDF), is more discriminative than landmark pose-indexed feature, more efficient than histogram of oriented gradients (HOG) feature and scale-invariant feature transform (SIFT) feature, and more compact than the local binary feature (LBF). Experimental results show that our approach achieves state-of-the-art performance when tested on the most challenging datasets. Compared with an LBF-based algorithm, our method can achieve about two times the speed-up and more than 20% improvement, in terms of alignment accuracy measurement, and save an order of magnitude of memory requirement.

cs.CV↗

arXiv2016

Efficient Likelihood Bayesian Constrained Local Model

The constrained local model (CLM) proposes a paradigm that the locations of a set of local landmark detectors are constrained to lie in a subspace, spanned by a shape point distribution model (PDM). Fitting the model to an object involves two steps. A response map, which represents the likelihood of the location of a landmark, is first computed for each landmark using local-texture detectors. Then, an optimal PDM is determined by jointly maximizing all the response maps simultaneously, with a global shape constraint. This global optimization can be considered as a Bayesian inference problem, where the posterior distribution of the shape parameters, as well as the pose parameters, can be inferred using maximum a posteriori (MAP). In this paper, we present a cascaded face-alignment approach, which employs random-forest regressors to estimate the positions of each landmark, as a likelihood term, efficiently in the CLM model. Interpretation from CLM framework, this algorithm is named as an efficient likelihood Bayesian constrained local model (elBCLM). Furthermore, in each stage of the regressors, the PDM non-rigid parameters of previous stage can work as shape clues for training each stage regressors. Experimental results on benchmarks show our approach achieve about 3 to 5 times speed-up compared with CLM models and improve around 10% on fitting quality compare with the same setting regression models.

cs.CV↗