arXiv subjects

Yong Lu

Publications and source records attributed to Yong Lu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Weak solutions and weak-strong uniqueness for a compressible power-law-Oldroyd--B fluid model

We consider a model of a viscoelastic compressible flow in $R^{3}$ which is additionally shear thickening (the stress tensor corresponds to the power law model, however, the divergence of the velocity is due to the model bounded). We prove existence of a weak solution to this model provided the growth in the power law model is larger or equal than $\frac 52$. We also prove that any sufficiently smooth solution of this model is unique in the class of weak solution, provided extra integrability of the initial value for the extra stress tensor is assumed.

math.AP↗

arXiv2025

Error estimates in the non-relativistic limit for the two-dimensional cubic Klein-Gordon equation

In this paper, we study the non-relativistic limit of the two-dimensional cubic nonlinear Klein-Gordon equation with a small parameter $0<\varepsilon \ll 1$ which is inversely proportional to the speed of light. We show the cubic nonlinear Klein-Gordon equation converges to the cubic nonlinear Schrödinger equation with a convergence rate of order $O(\varepsilon^2)$. In particular, for the defocusing case with high regularity initial data, we show error estimates of the form $C(1+t)^N \varepsilon^2$ at time $t$ up to a long time of order $\varepsilon^{-\frac{2}{N+1}}$, while for initial data with limited regularity, we also show error estimates of the form $C(1+t)^M\varepsilon$ at time $t$ up to a long time of order $\varepsilon^{-\frac{1}{M+1}}$. Here $N$ and $M$ are constants depending on initial data. The idea of proof is to reformulate nonrelativistic limit problems to stability problems in geometric optics, then employ the techniques in geometric optics to construct approximate solutions up to an arbitrary order, and finally, together with the decay estimates of the cubic Schrödinger equation, derive the error estimates.

math.AP↗

arXiv2025

Scattering number and $τ$-toughness in graphs involving $A_α$-spectral radius

The scattering number $s(G)$ of graph $G=(V,E)$ is defined as $s(G)$=max\big\{$c(G-S)-|S|$\big\}, where the maximum is taken over all proper subsets $S\subseteq V(G)$, and $c(G-S)$ denotes the number of components of $G-S$. In 1988, Enomoto introduced a variation of toughness $τ(G)$ of a graph $G$, which is defined by $τ(G)$=min\big\{$\frac{|S|}{c(G-S)-1}$, $S\subseteq V(G)$ and $c(G-S)>1$\big\}. Both the scattering number and toughness are used to characterize the invulnerability or stability of a graph, i.e., the ability of a graph to remain connected after vertices or edges are removed. The smaller the value of $s(G)$ (or the larger the value of $τ(G)$), the stronger the connectivity of a graph $G$. The $A_α$-spectral radius of $G$ is denoted by $ρ_α(G)$. Using typical $A_α$-spectral techniques and structural analysis, we present a sufficient condition such that $s(G)\leq 1$. This result generalizes the result of Chen, Li and Xu [Graphs Comb. 41 (2025)]. Furthermore, we establish a sufficient condition with respect to the $A_α$-spectral radius for a graph to be $τ$-tough. When $α=\frac{1}{2}$, our result reduces to that of Chen, Li and Xu [Graphs Comb. 41 (2025)].

math.CO↗

arXiv2025

Improved bounds on the $H$-rank of a mixed graph in terms of the matching number and fractional matching number

A mixed graph $\widetilde{G}$ is obtained by orienting some edges of a graph $G$, where $G$ is the underlying graph of $\widetilde{G}$. Let $r(\widetilde{G})$ be the $H$-rank of $\widetilde{G}$. Denote by $r(G)$, $κ(G)$, $m(G)$ and $m^{\ast}(G)$ the rank, the number of even cycles, the matching number and the fractional matching number of $G$, respectively. Zhou et al. [Discrete Appl. Math. 313 (2022)] proved that $2m(G)-2κ(G)\leq r(G)\leq 2m(G)+ρ(G)$, where $ρ(G)$ is the largest number of disjoint odd cycles in $G$. We extend their results to the setting of mixed graphs and prove that $2m(G)-2κ(G)\leq r(\widetilde{G}) \leq 2m^{\ast}(G)$ for a mixed graph $\widetilde{G}$. Furthermore, we characterize some classes of mixed graphs with rank $r(\widetilde{G})=2m(G)-2κ(G)$, $r(\widetilde{G})=2m(G)-2κ(G)+1$ and $r(\widetilde{G})=2m^{\ast}(G)$, respectively. Our results also improve those of Chen et al. [Linear Multiliear Algebra. 66 (2018)]. In addition, our results can be applied to signed graphs and oriented graphs in some situations.

math.CO↗

arXiv2025

Sufficient conditions for $t$-tough graphs to be Hamiltonian and pancyclic or bipartite

The toughness of graph $G$, denoted by $τ(G)$, is $τ(G)=\min\{\frac{|S|}{c(G-S)}:S\subseteq V(G),c(G-S)\geq2\}$ for every vertex cut $S$ of $V(G)$ and the number of components of $G$ is denoted by $c(G)$. Bondy in 1973, suggested the ``metaconjecture" that almost any nontrivial condition on a graph which implies that the graph is Hamiltonian also implies that the graph is pancyclic. Recently, Benediktovich [Discrete Applied Mathematics. 365 (2025) 130--137] confirmed the Bondy's metaconjecture for $t$-tough graphs in the case when $t\in\{1;2;3\}$ in terms of the size, the spectral radius and the signless Laplacian spectral radius of the graph. In this paper, we will confirm the Bondy's metaconjecture for $t$-tough graphs in the case when $t\geq4$ in terms of the size, the spectral radius, the signless Laplacian spectral radius, the distance spectral radius and the distance signless Laplacian spectral radius of graphs.

math.CO↗

arXiv2025

Distance signless Laplacian spectral radius and tough graphs involving minimun degree

Let $G=(V(G),E(G))$ be a simple graph, where $V(G)$ and $E(G)$ are the vertex set and the edge set of $G$, respectively. The number of components of $G$ is denoted by $c(G)$. Let $t$ be a positive real number, and a connected graph $G$ is $t$-tough if $t c(G-S)\leq|S|$ for every vertex cut $S$ of $V(G)$. The toughness of graph $G$, denoted by $τ(G)$, is the largest value of $t$ for which $G$ is $t$-tough. Recently, Fan, Lin and Lu [European J. Combin. 110(2023), 103701] presented sufficient conditions based on the spectral radius for graphs to be 1-tough with minimum degree $δ(G)$ and graphs to be $t$-tough with $t\geq 1$ being an integer, respectively. In this paper, we establish sufficient conditions in terms of the distance signless Laplacian spectral radius for graphs to be 1-tough with minimum degree $δ(G)$ and graphs to be $t$-tough, where $\frac{1}{t}$ is a positive integer. Moreover, we consider the relationship between the distance signless Laplacian spectral radius and $t$-tough graphs in terms of the order $n$.

math.CO↗

arXiv2025

The row left rank of quaternion unit gain graphs in terms of pendant vertices

Let $\widetilde{G}=(G,U(\mathbb{Q}),φ)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph), where $G$ is the underlying graph of $\widetilde{G}$, $U(\mathbb{Q})=\{q\in \mathbb{Q}: |q|=1\}$ and $φ:\overrightarrow{E}\rightarrow U(\mathbb{Q})$ is the gain function such that $φ(e_{ij})=φ(e_{ji})^{-1}=\overline{φ(e_{ji})}$ for any adjacent vertices $v_{i}$ and $v_{j}$. Let $A(\widetilde{G})$ be the adjacency matrix of $\widetilde{G}$ and let $r(\widetilde{G})$ be the row left rank of $\widetilde{G}$. In this paper, we prove some lower bounds on the row left rank of $U(\mathbb{Q})$-gain graphs in terms of pendant vertices. All corresponding extremal graphs are characterized.

math.CO↗

arXiv2025

The row left rank of a quaternion unit gain graph in terms of maximum degree

Let $Φ=(G,U(\mathbb{Q}),φ)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph) of order $n$, $A(Φ)$ be the adjacency matrix of $Φ$ and $r(Φ)$ be the row left rank of $Φ$. Let $Δ$ be the maximum degree of $Φ$. In this paper, we prove that $r(Φ)\geq\frac{n}Δ$. Moreover, if $Φ$ is connected, we obtain that $r(Φ)\geq\frac{n-2}{Δ-1}$. All the corresponding extremal graphs are characterized.

math.CO↗

arXiv2025

Phonon vibrational and transport properties of SnSe/SnS superlattice at finite temperatures

The structural stability and phonon properties of SnSe/SnS superlattices at finite temperatures have been studied using machine learning force field molecular dynamics and the anharmonic phonon approach. The vertical SnSe/SnS superlattice undergoes a phase transition from the Pnma phase to a novel P4/nmm phase at finite temperatures, which is different from the high-temperature Cmcm phase of the SnSe and SnS systems. The stability of P4/nmm phase is determined by molecular dynamics trajectories and anharmonic phonon dispersion relations. The imaginary modes of TO modes at the q=M(1/2,1/2,0) point of the P4/nmm phase in harmonic approximation become rigid at elevated temperatures. An analysis of phonon power spectra upon temperature also confirms the dynamic stabilization. The P4/nmm phase has higher symmetry than the Pnma phase, and the phase transition between them is accompanied by competition between the Jahn-Teller effect and phonon anharmonicity. Unlike the anisotropic distribution of Sn-Se/S bonds in the Pnma phase, the P4/nmm phase forms chemical bonds with similar bond lengths both in-plane and interlayer, and their resonance effect can significantly enhance phonon scattering. The calculated phonon density of states and lifetime is strongly temperature dependent, demonstrating the heavy anharmonicity in the SnSe/SnS system. The P4/nmm phase has an extremely low lattice thermal conductivity, close to the experimental values of SnSe and SnS. Moreover, with the reduction of band gap and the enhancement of band degeneracy near the Fermi level, the P4/nmm phase exhibits superior electronic transport properties and significantly enhanced response to infrared and visible light. This makes it show great potential in thermoelectric and photovoltaic applications.

cond-mat.mtrl-sci↗

arXiv2025

Homogenization of Inhomogeneous Incompressible Navier-Stokes Equations in Domains with Very Tiny Holes

In this paper, we study the homogenization problems of $3D$ inhomogeneous incompressible Navier-Stokes system perforated with very tiny holes whose diameters are much smaller than their mutual distances. The key is to establish the equations in the homogeneous domain without holes for the zero extensions of the weak solutions. This allows us to derive time derivative estimates and show the strong convergence of the density and the momentum by Aubin-Lions type argument. For the case of small holes, we finally show the limit equations remain unchanged in the homogenization limit.

math.AP↗

arXiv2025

Swin-X2S: Reconstructing 3D Shape from 2D Biplanar X-ray with Swin Transformers

The conversion from 2D X-ray to 3D shape holds significant potential for improving diagnostic efficiency and safety. However, existing reconstruction methods often rely on hand-crafted features, manual intervention, and prior knowledge, resulting in unstable shape errors and additional processing costs. In this paper, we introduce Swin-X2S, an end-to-end deep learning method for directly reconstructing 3D segmentation and labeling from 2D biplanar orthogonal X-ray images. Swin-X2S employs an encoder-decoder architecture: the encoder leverages 2D Swin Transformer for X-ray information extraction, while the decoder employs 3D convolution with cross-attention to integrate structural features from orthogonal views. A dimension-expanding module is introduced to bridge the encoder and decoder, ensuring a smooth conversion from 2D pixels to 3D voxels. We evaluate proposed method through extensive qualitative and quantitative experiments across nine publicly available datasets covering four anatomies (femur, hip, spine, and rib), with a total of 54 categories. Significant improvements over previous methods have been observed not only in the segmentation and labeling metrics but also in the clinically relevant parameters that are of primary concern in practical applications, which demonstrates the promise of Swin-X2S to provide an effective option for anatomical shape reconstruction in clinical scenarios. Code implementation is available at: \url{https://github.com/liukuan5625/Swin-X2S}.

cs.CV↗

arXiv2024

The left row rank of quaternion unit gain graphs in terms of girth

Let $Φ=(G,U(\mathbb{Q}),φ)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph). The adjacency matrix of $Φ$ is denoted by $A(Φ)$ and the left row rank of $Φ$ is denoted by $r(Φ)$. If $Φ$ has at least one cycle, then the length of the shortest cycle in $Φ$ is the girth of $Φ$, denoted by $g$. In this paper, we prove that $r(Φ)\geq g-2$ for $Φ$. Moreover, we characterize $U(\mathbb{Q})$-gain graphs satisfy $r(Φ)=g-i$ ($i=0,1,2$) and all quaternion unit gain graphs with rank 2. The results will generalize the corresponding results of simple graphs (Zhou et al. Linear Algebra Appl. (2021), Duan et al. Linear Algebra Appl. (2024) and Duan, Discrete Math. (2024)), signed graphs (Wu et al. Linear Algebra Appl. (2022)), and complex unit gain graphs (Khan, Linear Algebra Appl. (2024)).

math.CO↗

arXiv2024

Unified quantitative analysis of the Stokes equations in dilute perforated domains via layer potentials

We develop a unified method to obtain the quantitative homogenization of Stokes systems in periodically perforated domains with no-slip boundary conditions on the perforating holes. The main novelty of our paper is a quantitative analysis of the asymptotic behavior of the two-scale cell correctors via periodic Stokes layer potentials. The two-scale cell correctors were introduced and analyzed qualitatively by Allaire in the early 90's. Thanks to our layer potential approach, we also provide a novel explanation of the conductivity matrix in Darcy's model, of the Brinkman term in Brinkman's model, and explain the special behavior for $d=2$. Finally, we also prove quantitative homogenization error estimates in various regimes of ratios between the size of the perforating holes and the typical distance between holes. In particular we handle a subtle issue in the dilute Darcy regime related to the non-vanishing of the Darcy velocity on the boundary.

math.AP↗

arXiv2024

Convergence rates in the nonrelativistic limit of the cubic Klein-Gordon equation

In this paper, we study the nonrelativistic limit of the cubic nonlinear Klein-Gordon equation in $\mathbb{R}^{3}$ with a small parameter $0<\varepsilon \ll 1$, which is inversely proportional to the speed of light. We show that the cubic nonlinear Klein-Gordon equation converges to the cubic nonlinear Schrödinger equation with a convergence rate of order $\varepsilon^{2}$. In particular, for the defocusing case and smooth initial data, we prove error estimates of the form $(1+t)\varepsilon^{2}$ at time $t$ which is valid up to long time of order $\varepsilon^{-1}$; while for nonsmooth initial data, we prove error estimates of the form $(1+t)\varepsilon$ at time $t$ which is valid up to long time of order $\varepsilon^{-\frac{1}{2}}$. These specific forms of error estimates coincide with the numerical results obtained in \cite{BZ19,SZ20}.

math.AP↗

arXiv2024

Spectral Properties of Dual Unit Gain Graphs

In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if and only if the dual gain graph is balanced. By using the dual cosine functions, we establish the closed form of eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too.

math.CO↗

arXiv2024

Lattice thermal conductivity of ZrSe2 based on the anharmonic phonon approach and on-the-fly machine learning force fields

The lattice thermal conductivity (LTC) of ZrSe$_2$, a typical layered transition metal disulfide, has been calculated using a hybrid approach that combines force field molecular dynamics (MD) simulation and Boltzmann transport equation (BTE). In this approach, the phonon quasiparticle picture of each normal mode can be obtained directly by the velocity autocorrelation function and its power spectrum projected in $q$-space. By employing the retarded one phonon Green's function method, the phonon quasiparticle frequency and lifetime of each independent normal mode are effectively determined. On-the-fly machine learning force fields combine the precision of quantum mechanics and the scale of classical MD to analyze sizable supercells with long-wavelength phonons. This yields accurate LTC by using sufficient $q$-samples in the Brillouin zone, which cannot be achieved at the \emph{ab initio} molecular dynamics scale. The convergent LTC tensor of bulk and monolayer ZrSe$_2$ decays faster with increasing temperature than the well-known $\frac{1}{T}$ scale, which is typically observed when considering only three-phonon scattering. The phonon lifetime and mean free path exhibit significant dependence on temperature. MD simulations encompass all orders of anharmonic effects, thereby enabling an accurate description of anharmonic interactions between phonons at finite temperatures. Moreover, this approach respects the contribution of each normal mode to the LTC based on the BTE, which facilitates the quantitative analysis of phonon anharmonic properties and the role of specific normal modes.

cond-mat.mtrl-sci↗

arXiv2024

Spin-Lattice Coupling Induced Rich Magnetic States in CrF$_3$ monolayer

We systematically studied the spin-lattice couplings in the CrF$_3$ monolayer. Our study reveals that the spin exchange constants between the nearest neighbors are notably affected by these couplings. Specifically, the couplings arise predominantly from three distinct phonon modes, namely the covariant, rotation, and stretch of the Cr-F-Cr-F rhombus. By integrating out the phonon degrees of freedom, we derived an effective spin Hamiltonian featuring four-spin product terms, which yields a remarkably intricate magnetic phase diagram. Significantly, numerous plateau states characterized by fractional magnetizations, including 1/2, 1/3, 2/3, 1/4, 1/5, 5/8, 1/9, and 2/9, emerge in the vicinity of the phase transition boundary separating ferromagnetic and antiferromagnetic states. These findings show the profound influence of spin-lattice couplings on magnetic properties near the magnetic phase boundaries, and the predicted plateau states are expected to be observable in future experiments.

cond-mat.mtrl-sci↗

arXiv2024

Unconditional stability of equilibria in thermally driven compressible fluids

We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\' enard convection problem.

math.AP↗