arXiv subjects

Yan Guo

Publications and source records attributed to Yan Guo.

At least 37 records · Page 2Linked to original sources

arXiv2025

Nonlinear stability of the Larson-Penston collapse

We prove nonlinear stability of the Larson-Penston family of self-similarly collapsing solutions to the isothermal Euler-Poisson system. Our result applies to radially symmetric perturbations and it is the first full nonlinear stability result for radially imploding compressible flows. At the heart of the proof is the ground state character of the Larson-Penston solution, which exhibits important global monotonicity properties used throughout the proof. One of the key challenges is the proof of mode-stability for the non self-adjoint spectral problem which arises when linearising the dynamics around the Larson-Penston collapsing solution. To exclude the presence of complex growing modes other than the trivial one associated with time translation symmetry, we use a high-order energy method in low and high frequency regimes, for which the monotonicity properties are crucially exploited, and use rigorous computer-assisted techniques in the intermediate regime. In addition, the maximal dissipativity of the linearised operator is proven on arbitrary large backward light cones emanating from the singular point using the global monotonicity of the Larson-Penston solutions. Such a flexibility in linear analysis also facilitates nonlinear analysis and allows us to identify the exact number of derivatives necessary for the nonlinear stability statement. The proof is based on a two-tier high-order weighted energy method which ties bounds derived from the Duhamel formula to quasilinear top order estimates. To prove global existence we further use the Brouwer fixed point theorem to identify the final collapse time, which suppresses the trivial instability caused by the time-translation symmetry of the system.

math.AP↗

arXiv2024

Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain

The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classical perfect conducting conditions at the wall, $$ \mathbf{E} \times n_x = 0, \quad \mathbf{B} \cdot n_x = 0, $$ plays an important role in fusion plasma dynamics studies. Since the early 1990s, it has been understood that the Lorentz force can penetrate into the domain at the boundary and create a singularity. Consequently, the uniqueness for any nonlinear kinetic plasma models in the presence of a perfectly conducting boundary remained open until our recent local well-posedness result. In this paper, we finally establish a global well-posedness theory for the relativistic Vlasov-Maxwell-Landau system in a general $3D$ domain with a specularly reflective, perfectly conducting boundary.

math.AP↗

arXiv2024

Diffusive Expansion of the Boltzmann equation for the flow past an obstacle

The exterior domain problem is essential in fluid and kinetic equations. In this paper, we establish the validity of the diffusive expansion for the Boltzmann equations to the Navier-Stokes-Fourier system up to the critical time in an exterior domain with non-zero passing flow. We apply the $L^3-L^6$ framework to the unbounded domain in this paper.

math.AP↗

arXiv2024

Small scales in inviscid limits of steady fluids

In this article, we study the 2D incompressible steady Navier-Stokes equation in a channel $(-L,0)\times(-1,1)$ with the no-slip boundary condition on $\{Y = \pm 1\}$, and consider the inviscid limit $\varepsilon \to 0$. In the special case of Euler shear flow $(u_e(Y),0)$, we construct a steady Navier-Stokes solution for $\varepsilon \ll1$, $$\left\{ \begin{aligned} &u^\varepsilon \sim u_e + u_p + O(\sqrt{\varepsilon}),\\ &v^\varepsilon \sim h(Y) \exp\{Xu_e(Y)/\varepsilon\} + O(\sqrt{\varepsilon}), \end{aligned}\right. $$ where $u_p$ represents the classical Prandtl layer profile, and $h(Y)$ is an arbitrary smooth, compactly-supported function with small magnitude. While the classical Prandtl boundary layer $u_p$ exhibits a small scale of order $\sqrt{\varepsilon}$ in $Y$ near $Y = \pm 1$, the profile we construct reveals an $\varepsilon$ small scale of $Xu_e(Y)$ in the vertical velocity component.

math.AP↗

arXiv2024

EdgeNAT: Transformer for Efficient Edge Detection

Transformers, renowned for their powerful feature extraction capabilities, have played an increasingly prominent role in various vision tasks. Especially, recent advancements present transformer with hierarchical structures such as Dilated Neighborhood Attention Transformer (DiNAT), demonstrating outstanding ability to efficiently capture both global and local features. However, transformers' application in edge detection has not been fully exploited. In this paper, we propose EdgeNAT, a one-stage transformer-based edge detector with DiNAT as the encoder, capable of extracting object boundaries and meaningful edges both accurately and efficiently. On the one hand, EdgeNAT captures global contextual information and detailed local cues with DiNAT, on the other hand, it enhances feature representation with a novel SCAF-MLA decoder by utilizing both inter-spatial and inter-channel relationships of feature maps. Extensive experiments on multiple datasets show that our method achieves state-of-the-art performance on both RGB and depth images. Notably, on the widely used BSDS500 dataset, our L model achieves impressive performances, with ODS F-measure and OIS F-measure of 86.0%, 87.6% for multi-scale input,and 84.9%, and 86.3% for single-scale input, surpassing the current state-of-the-art EDTER by 1.2%, 1.1%, 1.7%, and 1.6%, respectively. Moreover, as for throughput, our approach runs at 20.87 FPS on RTX 4090 GPU with single-scale input. The code for our method will be released soon.

cs.CV↗

arXiv2024

The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition

We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $Ω$ with the specular reflection condition. Our result covers the case when $Ω$ is a non-convex domain, e.g., solid torus. To the best of our knowledge, this is the first local well-posedness result for a nonlinear kinetic model with a self-consistent magnetic effect in a three-dimensional $\textbf{bounded}$ domain.

math.AP↗

arXiv2024

DrugLLM: Open Large Language Model for Few-shot Molecule Generation

Large Language Models (LLMs) have made great strides in areas such as language processing and computer vision. Despite the emergence of diverse techniques to improve few-shot learning capacity, current LLMs fall short in handling the languages in biology and chemistry. For example, they are struggling to capture the relationship between molecule structure and pharmacochemical properties. Consequently, the few-shot learning capacity of small-molecule drug modification remains impeded. In this work, we introduced DrugLLM, a LLM tailored for drug design. During the training process, we employed Group-based Molecular Representation (GMR) to represent molecules, arranging them in sequences that reflect modifications aimed at enhancing specific molecular properties. DrugLLM learns how to modify molecules in drug discovery by predicting the next molecule based on past modifications. Extensive computational experiments demonstrate that DrugLLM can generate new molecules with expected properties based on limited examples, presenting a powerful few-shot molecule generation capacity.

q-bio.BM↗

arXiv2024

Catalogue of nearby blue and near-solar gas metallicity SDSS dwarf galaxies

A less explored aspect of dwarf galaxies is their metallicity evolution. Generally, dwarfs have lower metallicities than Hubble sequence late type galaxies but in reality, dwarfs span a wide range of metallicities with several open questions regarding the formation and evolution of the lowest and the highest metallicity dwarfs. We present a catalogue of 3459 blue, nearby, star forming dwarf galaxies extracted from SDSS DR16 including calculation of their metallicities using the mean of several calibrators. To compile our catalogue we applied redshift, absolute magnitude, stellar mass, optical diameter, and line flux signal to noise criteria. This produced a catalogue from the upper end of the dwarf galaxy stellar mass range. Our catalogued dwarfs have blue g - i colours and Hbeta equivalent widths, indicative of having undergone a recent episode of star formation, although their star formation rates (SFR) suggest only a moderate to low enhancement in star formation, similar to the SFRs in low surface brightness and evolved tidal dwarfs. While the catalogued dwarfs cover a range of metallicities, their mean metallicity is about 0.2 dex below solar metallicity, indicating relatively chemically evolved galaxies. The vast majority of the catalogue, with clean photometry, are relatively isolated dwarfs with only modest star formation rates and a narrow range of g - i colour, consistent with internally driven episodic mild bursts of star formation. The presented catalogue's robust metallicity estimates for nearby SDSS dwarf galaxies will help target future studies to understand the physical processes driving the metallicity evolution of dwarfs.

astro-ph.GA↗

arXiv2023

HI in high gas-phase metallicity dwarf galaxy WISEA J230615.06+143927.9

We present resolved GMRT HI observations of the high gas-phase metallicity dwarf galaxy WISEA J230615.06+143927.9 (z = 0.005) (hereafter J2306) and investigate whether it could be a Tidal Dwarf Galaxy (TDG) candidate. TDGs are observed to have higher metallicities than normal dwarfs. J2306 has an unusual combination of a blue g -- r colour of 0.23 mag, irregular optical morphology and high-metallicity (12 + log(O/H) = 8.68$\pm$0.14), making it an interesting galaxy to study in more detail. We find J2306 to be an HI rich galaxy with a large extended, unperturbed rotating HI disk. Using our HI data we estimated its dynamical mass and found the galaxy to be dark matter (DM) dominated within its HI radius. The quantity of DM, inferred from its dynamical mass, appears to rule out J2306 as an evolved TDG. A wide area environment search reveals J2306 to be isolated from any larger galaxies which could have been the source of its high gas metallicity. Additionally, the HI morphology and kinematics of the galaxy show no indication of a recent merger to explain the high-metallicity. Further detailed optical spectroscopic observations of J2306 might provide an answer to how a seemingly ordinary irregular dwarf galaxy achieved such a high level of metal enrichment.

astro-ph.GA↗

arXiv2023

Neural Implicit Field Editing Considering Object-environment Interaction

The 3D scene editing method based on neural implicit field has gained wide attention. It has achieved excellent results in 3D editing tasks. However, existing methods often blend the interaction between objects and scene environment. The change of scene appearance like shadows is failed to be displayed in the rendering view. In this paper, we propose an Object and Scene environment Interaction aware (OSI-aware) system, which is a novel two-stream neural rendering system considering object and scene environment interaction. To obtain illuminating conditions from the mixture soup, the system successfully separates the interaction between objects and scene environment by intrinsic decomposition method. To study the corresponding changes to the scene appearance from object-level editing tasks, we introduce a depth map guided scene inpainting method and shadow rendering method by point matching strategy. Extensive experiments demonstrate that our novel pipeline produce reasonable appearance changes in scene editing tasks. It also achieve competitive performance for the rendering quality in novel-view synthesis tasks.

cs.CV↗

arXiv2023

Comparison of multi-mode Hong-Ou-Mandel interference and multi-slit interference

Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by $\sin(Nx)/ \sin(x)$ ($[\sin(Nv)/\sin(v)]^2$) for MM-HOMI (MSI), where $N$ is the mode (slit) number and $x (v)$ is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.

quant-ph↗

arXiv2023

Ghost Effect from Boltzmann Theory

Taking place naturally in a gas subject to a given wall temperature distribution [Maxwell1879], the ``ghost effect'' exhibits a rare kinetic effect beyond the prediction of classical fluid theory and Fourier law in such a classical problem in physics. As the Knudsen number $\varepsilon$ goes to zero, the finite variation of temperature in the bulk is determined by an $\varepsilon$ infinitesimal, ghost-like velocity field, created by a given finite variation of the tangential wall temperature as predicted by Maxwell's slip boundary condition. Mathematically, such a finite variation leads to the presence of a severe $\varepsilon^{-1}$ singularity and a Knudsen layer approximation in the fundamental energy estimate. Neither difficulty is within the reach of any existing PDE theory on the steady Boltzmann equation in a general 3D bounded domain. Consequently, in spite of the discovery of such a ghost effect from temperature variation in as early as 1960's, its mathematical validity has been a challenging and intriguing open question, causing confusion and suspicion. We settle this open question in affirmative if the temperature variation is small but finite, by developing a new $L^2-L^6-L^{\infty}$ framework with four major innovations: 1) a key $\mathscr{A}$-Hodge decomposition and its corresponding local $\mathscr{A}$-conservation law eliminate the severe $\varepsilon^{-1}$ bulk singularity, leading to a reduced energy estimate; 2) A surprising $\varepsilon^{\frac{1}{2}}$ gain in $L^2$ via momentum conservation and a dual Stokes solution; 3) the $\mathscr{A}$-conservation, energy conservation and a coupled dual Stokes-Poisson solution reduces to an $\varepsilon^{-\frac{1}{2}}$ boundary singularity; 4) a crucial construction of $\varepsilon$-cutoff boundary layer eliminates such boundary singularity via new Hardy and BV estimates.

math.AP↗

arXiv2023

Ghost Effect from Boltzmann Theory: Expansion with Remainder

Consider the limit $\varepsilon\rightarrow0$ of the steady Boltzmann problem \begin{align} v\cdot\nabla_x\mathfrak{F}=\varepsilon^{-1}Q[\mathfrak{F},\mathfrak{F}],\quad \mathfrak{F}\big|_{v\cdot n<0}=M_w\displaystyle\int_{v'\cdot n>0} \mathfrak{F}(v')|v'\cdot n|\mathrm{d}{v'}, \end{align} where $\displaystyle M_w(x_0,v):=\frac{1}{2π\big(T_w(x_0)\big)^2} \exp\bigg(-\frac{|v|^2}{2T_w(x_0)}\bigg)$ for $x_0\in\partialΩ$ is the wall Maxwellian in the diffuse-reflection boundary condition. In the natural case of $|\nabla T_w|=O(1)$, for any constant $P>0$, the Hilbert expansion leads to \begin{align}\label{expansion} \mathfrak{F}\approx μ+\varepsilon\bigg\{μ\bigg(ρ_1+u_1\cdot v+T_1\frac{|v|^2-3T}{2}\bigg)-μ^{\frac{1}{2}}\left(\mathscr{A}\cdot\frac{\nabla_xT}{2T^2}\right)\bigg\} \end{align} where $\displaystyleμ(x,v):=\frac{ρ(x)}{\big(2πT(x)\big)^{\frac{3}{2}}} \exp\bigg(-\frac{|v|^2}{2T(x)}\bigg)$, and $(ρ,u_1,T)$ is determined by a Navier-Stokes-Fourier system with "ghost" effect. The goal of this paper is to construct $\mathfrak{F}$ in the form of \begin{align}\label{aa 08} \mathfrak{F}(x,v)=&μ+μ^{\frac{1}{2}}\Big(\varepsilon f_1+\varepsilon^2f_2\Big)+μ_w^{\frac{1}{2}}\Big(\varepsilon f^B_1\Big)+\varepsilon^αμ^{\frac{1}{2}}R, \end{align} for interior solutions $f_1$, $f_2$ and boundary layer $f^B_1$, where $μ_w$ is $μ$ computed for $T=T_w$, and derive equation for the remainder $R$ with some constant $α\geq1$. To prove the validity of the expansion suitable bounds on $R$ are needed, which are provided in the companion paper [Esposito-Guo-Rossana-Wu2023].

math.AP↗

arXiv2023

Adjusting inverse regression for predictors with clustered distribution

A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|β^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|β^\mathsf{T}X)$ for the desired reduced predictor $β^\mathsf{T}X$. In this paper, we adjust the first and second-order inverse regression methods by modeling $E(X|β^\mathsf{T}X)$ and $\mathrm{var}(X|β^\mathsf{T}X)$ under the mixture model assumption on $X$, which allows these terms to convey more complex patterns and is most suitable when $X$ has a clustered sample distribution. The proposed SDR methods build a natural path between inverse regression and the localized SDR methods, and in particular inherit the advantages of both; that is, they are $\sqrt{n}$-consistent, efficiently implementable, directly adjustable under the high-dimensional settings, and fully recovering the desired reduced predictor. These findings are illustrated by simulation studies and a real data example at the end, which also suggest the effectiveness of the proposed methods for nonclustered data.

stat.ME↗

arXiv2023

$L^2$ Diffusive Expansion For Neutron Transport Equation

Grazing set singularity leads to a surprising counter-example and breakdown of the classical mathematical theory for $L^{\infty}$ diffusive expansion of neutron transport equation with in-flow boundary condition in term of the Knudsen number $\varepsilon$, one of the most classical problems in the kinetic theory. Even though a satisfactory new theory has been established by constructing new boundary layers with favorable $\varepsilon$-geometric correction for convex domains, the severe grazing singularity from non-convex domains has prevented any positive mathematical progress. We develop a novel and optimal $L^2$ expansion theory for general domain (including non-convex domain) by discovering a surprising $\varepsilon^{\frac{1}{2}}$ gain for the average of remainder.

math.AP↗

arXiv2023

A Survey on Automated Driving System Testing: Landscapes and Trends

Automated Driving Systems (ADS) have made great achievements in recent years thanks to the efforts from both academia and industry. A typical ADS is composed of multiple modules, including sensing, perception, planning, and control, which brings together the latest advances in different domains. Despite these achievements, safety assurance of ADS is of great significance, since unsafe behavior of ADS can bring catastrophic consequences. Testing has been recognized as an important system validation approach that aims to expose unsafe system behavior; however, in the context of ADS, it is extremely challenging to devise effective testing techniques, due to the high complexity and multidisciplinarity of the systems. There has been great much literature that focuses on the testing of ADS, and a number of surveys have also emerged to summarize the technical advances. Most of the surveys focus on the system-level testing performed within software simulators, and they thereby ignore the distinct features of different modules. In this paper, we provide a comprehensive survey on the existing ADS testing literature, which takes into account both module-level and system-level testing. Specifically, we make the following contributions: (1) we survey the module-level testing techniques for ADS and highlight the technical differences affected by the features of different modules; (2) we also survey the system-level testing techniques, with focuses on the empirical studies that summarize the issues occurring in system development or deployment, the problems due to the collaborations between different modules, and the gap between ADS testing in simulators and the real world; (3) we identify the challenges and opportunities in ADS testing, which pave the path to the future research in this field.

cs.SE↗

arXiv2023

Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system

Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and \cite{Deng-Ionescu-Pausader-ARMA-2017}, we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler-Maxwell system as the mean free path goes to zero. Our method is based on the $L^2-L^{\infty}$ framework and the Glassey-Strauss Representation of the electromagnetic field, with auxiliary $H^1$ estimate and $W^{1,\infty}$ estimates to control the characteristic curves and corresponding $L^{\infty}$ norm.

math.AP↗

arXiv2023

The Massless Electron limit of the Vlasov-Poisson-Landau system

Due to ion-electron collisions, it is impossible to derive any two-fluid model for plasma as a direct hydrodynamic limit of the Vlasov-Poisson-Landau system for ions and electrons. At the same time, electrons are much lighter than their ion counterparts. In this work, we derive the massless electron limit of the Vlasov-Poisson-Landau system. This is done via a re-scaling of the electron velocity, leading to multiple velocity scales. Importantly, we demonstrate that ion-electron collisions vanish in this limit, due to special structure of the Landau collisions. We also show that this is invalid for the classical Boltzmann kernel with hard sphere interaction. This mechanism serves as the first step for the derivation of the two-fluid model for ions from a two-species kinetic equation.

math.AP↗