arXiv subjects

Fei Xu

Publications and source records attributed to Fei Xu.

At least 73 records · Page 4Linked to original sources

arXiv2022

Direct Immersogeometric Fluid Flow and Heat Transfer Analysis of Objects Represented by Point Clouds

Immersogeometric analysis (IMGA) is a geometrically flexible method that enables one to perform multiphysics analysis directly using complex computer-aided design (CAD) models. In this paper, we develop a novel IMGA approach for simulating incompressible and compressible flows around complex geometries represented by point clouds. The point cloud object's geometry is represented using a set of unstructured points in the Euclidean space with (possible) orientation information in the form of surface normals. Due to the absence of topological information in the point cloud model, there are no guarantees for the geometric representation to be watertight or 2-manifold or to have consistent normals. To perform IMGA directly using point cloud geometries, we first develop a method for estimating the inside-outside information and the surface normals directly from the point cloud. We also propose a method to compute the Jacobian determinant for the surface integration (over the point cloud) necessary for the weak enforcement of Dirichlet boundary conditions. We validate these geometric estimation methods by comparing the geometric quantities computed from the point cloud with those obtained from analytical geometry and tessellated CAD models. In this work, we also develop thermal IMGA to simulate heat transfer in the presence of flow over complex geometries. The proposed framework is tested for a wide range of Reynolds and Mach numbers on benchmark problems of geometries represented by point clouds, showing the robustness and accuracy of the method. Finally, we demonstrate the applicability of our approach by performing IMGA on large industrial-scale construction machinery represented using a point cloud of more than 12 million points.

physics.flu-dyn↗

arXiv2022

Advanced Characterization-Informed Framework and Quantitative Insight to Irradiated Annular U-10Zr Metallic Fuels

U-10Zr-based metallic nuclear fuel is a promising fuel candidate for next-generation sodium-cooled fast reactors.The research experience of the Idaho National Laboratory for this type of fuel dates back to the 1960s. Idaho National Laboratory researchers have accumulated a considerable amount of experience and knowledge regarding fuel performance at the engineering scale. The limitation of advanced characterization and lack of proper data analysis tools prevented a mechanistic understanding of fuel microstructure evolution and properties degradation during irradiation. This paper proposed a new workflow, coupled with domain knowledge obtained by advanced post-irradiation examination methods, to provide unprecedented and quantified insights into the fission gas bubbles and pores, and lanthanide distribution in an annular fuel irradiated in the Advanced Test Reactor. In the study, researchers identify and confirm that the Zr-bearing secondary phases exist and generate the quantitative ratios of seven microstructures along the thermal gradient. Moreover, the distributions of fission gas bubbles on two samples of U-10Zr advanced fuels were quantitatively compared. Conclusive findings were obtained and allowed for evaluation of the lanthanide transportation through connected bubbles based on approximately 67,000 fission gas bubbles of the two advanced samples.

cond-mat.mtrl-sci↗

arXiv2022

Modified gravitational wave propagation with higher modes and its degeneracies with lensing

Low-energy alternatives to General Relativity (GR) generically modify the phase of gravitational waves (GWs) during their propagation. As detector sensitivities increase, it becomes key to understand how these modifications affect the GW higher modes and to disentangle possible degeneracies with astrophysical phenomena. We apply a general formalism -- the WKB approach -- for solving analytically wave propagation in the spatial domain with a modified dispersion relation (MDR). We compare this WKB approach to applying a stationary phase approximation (SPA) in the temporal domain with time delays associated to the group or particle velocity. To this end, we extend the SPA to generic signals with higher modes, keeping careful track of reference phases and arrival times. We find that the WKB approach coincides with the SPA using the group velocity, in agreement with the principles of wave propagation. We then explore the degeneracies between a GW propagation with an MDR and a strongly-lensed GW in GR, since the latter can introduce a frequency-independent phase shift which is not degenerate with source parameters in the presence of higher modes. We find that for a particular MDR there is an exact degeneracy for wave propagation, unlike with the SPA for particle propagation. For the other cases, we search for the values of the MDR parameters that minimize the $χ^2$ and conclude that strongly-lensed GR GWs could be misinterpreted as GWs in modified gravity. Future MDR constraints with higher mode GWs should include the possibility of frequency-independent phase shifts, allowing for the identification of modified gravity and strong lensing distortions at the same time.

gr-qc↗

arXiv2022

Skew category algebras and modules on ringed finite sites

Let $\mathcal{C}$ be a small category. We investigate ringed sites $(\mathbf{C},\mathfrak{R})$ on $\mathcal{C}$ and the resulting module categories $\mathfrak{M}{\rm od}\text{-}\mathfrak{R}$. When $\mathcal{C}$ is finite, based on Grothendieck and Verdier's classification of finite topoi, we prove that each $\mathfrak{M}{\rm od}\text{-}\mathfrak{R}$ is equivalent to ${\rm Mod}\text{-}\mathfrak{R}|_{\mathcal{D}}[\mathcal{D}]$, where $\mathfrak{R}|_{\mathcal{D}}[\mathcal{D}]$ is the skew category algebra, canonically defined on $(\mathbf{C},\mathfrak{R})$, for a uniquely determined full subcategory $\mathcal{D}\subset\mathcal{C}$ and the restriction $\mathfrak{R}|_{\mathcal{D}}$ of $\mathfrak{R}$ to $\mathcal{D}$.

math.RT↗

arXiv2022

Backward bifurcation, basic reinfection number and robustness of a SEIRE epidemic model with reinfection

Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds $R_0$ (the basic reproduction number) and Rc (a threshold less than one). Our investigations show that when $R_0 > 1$, the system has an endemic equilibrium, which is globally asymptotically stable. When $R_c < R_0 < 1$, the epidemic system exhibits bistable dynamics. That is, the system has backward bifurcation and the disease cannot be eradicated. In order to eradicate the disease, we must ensure that the basic reproduction number $R_0$ is less than $R_c$. The basic reinfection number is obtained to measure the reinfection force, which turns out to be a new tipping point for disease dynamics. We also give definition of robustness, a new concept to measure the difficulty of completely eliminating the disease for a bistable epidemic system. Numerical simulations are carried out to verify the conclusions.

q-bio.PE↗

arXiv2022

On indefinite $k$-universal integral quadratic forms over number fields

An integral quadratic lattice is called indefinite $k$-universal if it represents all integral quadratic lattices of rank $k$ for a given positive integer $k$. For $k\geq 3$, we prove that the indefinite $k$-universal property satisfies the local-global principle over number fields. For $k=2$, we show that a number field $F$ admits an integral quadratic lattice which is locally $2$-universal but not indefinite 2-universal if and only if the class number of $F$ is even. Moreover, there are only finitely many classes of such lattices over $F$. For $k=1$, we prove that $F$ admits a classic integral lattice which is locally classic $1$-universal but not classic indefinite $1$-universal if and only if $F$ has a quadratic unramified extension where all dyadic primes of $F$ split completely. In this case, there are infinitely many classes of such lattices over $F$. All quadratic fields with this property are determined.

math.NT↗

arXiv2022

The symmetry for two class of steady stratified periodic water waves

In this paper, we mainly consider two class of travelling stratified periodic water waves, one with negative (or without) surface tension and the other with constant Bernoulli's function and stagnation points. We first establish the symmetry result for stratified water waves with negative (or without) surface tension, but without stagnation by using the modified maximum principle. Furthermore, the symmetry property of stratified water waves with constant Bernoulli's function and stagnation points is also obtained provided the monotonic property is known.

math.AP↗

arXiv2022

Stylized Knowledge-Grounded Dialogue Generation via Disentangled Template Rewriting

Current Knowledge-Grounded Dialogue Generation (KDG) models specialize in producing rational and factual responses. However, to establish long-term relationships with users, the KDG model needs the capability to generate responses in a desired style or attribute. Thus, we study a new problem: Stylized Knowledge-Grounded Dialogue Generation (SKDG). It presents two challenges: (1) How to train a SKDG model where no triples are available. (2) How to cohere with context and preserve the knowledge when generating a stylized response. In this paper, we propose a novel disentangled template rewriting (DTR) method which generates responses via combing disentangled style templates (from monolingual stylized corpus) and content templates (from KDG corpus). The entire framework is end-to-end differentiable and learned without supervision. Extensive experiments on two benchmarks indicate that DTR achieves a significant improvement on all evaluation metrics compared with previous state-of-the-art stylized dialogue generation methods. Besides, DTR achieves comparable performance with the state-of-the-art KDG methods in standard KDG evaluation setting.

cs.CL↗

arXiv2022

Multimodal Dialogue Response Generation

Responsing with image has been recognized as an important capability for an intelligent conversational agent. Yet existing works only focus on exploring the multimodal dialogue models which depend on retrieval-based methods, but neglecting generation methods. To fill in the gaps, we first present a multimodal dialogue generation model, which takes the dialogue history as input, then generates a textual sequence or an image as response. Learning such a model often requires multimodal dialogues containing both texts and images which are difficult to obtain. Motivated by the challenge in practice, we consider multimodal dialogue generation under a natural assumption that only limited training examples are available. In such a low-resource setting, we devise a novel conversational agent, Divter, in order to isolate parameters that depend on multimodal dialogues from the entire generation model. By this means, the major part of the model can be learned from a large number of text-only dialogues and text-image pairs respectively, then the whole parameters can be well fitted using the limited training examples. Extensive experiments demonstrate our method achieves state-of-the-art results in both automatic and human evaluation, and can generate informative text and high-resolution image responses.

cs.CL↗

arXiv2022

On sheaves in finite group representations

Given a general finite group $G$, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categories and their quotients, equipped with atomic topology, we explicitly compute their sheaf categories via sheafification. This enables us to identify $G$-representations with various fixed-point sheaves. As a consequence, it provides an intrinsic new proof to the equivalence of M. Artin between the category of sheaves on the orbit category and that of group representations.

math.RT↗

arXiv2022

An Efficient Adaptive Finite Element Method for Eigenvalue Problems

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on each adaptive partitions and very low dimensional eigenvalue problems on some special meshes which are controlled by the proposed algorithm. Since we Hence the efficiency of solving eigenvalue problems can be improved to be similar to the adaptive finite element method for the associated boundary value problems. The convergence and optimal complexity is theoretically verified and numerically demonstrated.

math.NA↗

arXiv2022

The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line

This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data by using the combinatorial analysis method developed in earlier papers by Christ, Damanik-Goldstein, and the present authors. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem for the gBBM equation with quasi-periodic initial data.

math.AP↗

arXiv2021

Backward bifurcation and saddle-node bifurcation in virus-immune dynamics

Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our investigation demonstrates the existence of post-bifurcation phenomenon in the system when the immune strength was selected as the bifurcation parameter. The bifurcation of saddle knot is then analyzed. The values of backward bifurcation point and saddle node bifurcation point are the elite control threshold and post-treatment control threshold respectively. The time interval between the two thresholds is the bi-stable interval.

q-bio.PE↗

arXiv2021

The Contribution From TeV Halos to the Isotropic Gamma-Ray Background

Recent observations have shown that pulsars are surrounded by extended regions which emit TeV-scale gamma rays through the inverse Compton scattering of very high energy electrons and positrons. Such TeV halos are responsible for a large fraction of the Milky Way's TeV-scale gamma-ray emission. In this paper, we calculate the gamma-ray spectrum from the population of TeV halos located within the Andromeda Galaxy, predicting a signal that is expected to be detectable by the Cherenkov Telescope Array (CTA). We also calculate the contribution from TeV halos to the isotropic gamma-ray background (IGRB), finding that these sources should contribute significantly to this flux at the highest measured energies, constituting up to $\sim 20\%$ of the signal observed above $\sim 0.1 \, {\rm TeV}$.

astro-ph.HE↗

arXiv2021

On indefinite and potentially universal quadratic forms over number fields

A number field $k$ admits a binary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is bigger than one. In this case, there are only finitely many classes of such binary integral quadratic forms over $k$. A number field $k$ admits a ternary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is even. In this case, there are infinitely many classes of such ternary integral quadratic forms over $k$. An integral quadratic form over a number field $k$ with more than one variables represents all integers of $k$ over the ring of integers of a finite extension of $k$ if and only if this quadratic form represents $1$ over the ring of integers of a finite extension of $k$.

math.NT↗

arXiv2021

Stacked polarimeters with twisted black phosphorus

The real-time, in-line analysis of light polarization is critical in optical communication networks, which suffers from the complex systems with numerous bulky opto-electro-mechanical elements tandemly arranged along optical path. Here, we propose a fiber-integrated polarimeter with nano-thickness by vertically stacking three two-dimensional (2D) materials based photodetection units. We demonstrate a self-power-calibrated, ultrafast, unambiguous detection of linear (LP) and circular polarized (CP) light according to the symmetry broken induced linear photogalvanic effects (LPGE) and circular photogalvanic effects (CPGE) in black phosphorous (BP) units, which are twistedly stacked to substitute traditional mechanical rotation of polarizers. As a demonstration, we achieve Hadamard single-pixel polarimetric imaging by the polarimeter to recognize the polarization distributions, showing potential in high-speed polarization-division-multiplexed imaging and real-time polarized endoscopy. This work provides a new strategy for next-generation ultracompact optical and optoelectronic systems, and guides a way for developing high-resolution arrayed devices with multifunctional pixels.

physics.optics↗

arXiv2021

Local Existence and Uniqueness of Spatially Quasi-Periodic Solutions to the Generalized KdV Equation

In this paper, we study the existence and uniqueness of spatially quasi-periodic solutions to the generalized KdV equation (gKdV for short) on the real line with quasi-periodic initial data whose Fourier coefficients are exponentially decaying. In order to solve for the Fourier coefficients of the solution, we first reduce the nonlinear dispersive partial differential equation to a nonlinear infinite system of coupled ordinary differential equations, and then construct the Picard sequence to approximate them. However, we meet, and have to deal with, the difficulty of studying {\bf the higher dimensional discrete convolution operation for several functions}: \[\underbrace{c\times\cdots\times c}_{\mathfrak p~\text{times}}~(\text{total distance}):=\sum_{\substack{\clubsuit_1,\cdots,\clubsuit_{\mathfrak p}\in\mathbb Z^ν\\ \clubsuit_1+\cdots+\clubsuit_{\mathfrak p}=~\text{total distance}}}\prod_{j=1}^{\mathfrak p}c(\clubsuit_j).\] In order to overcome it, we apply a combinatorial method to reformulate the Picard sequence as a tree. Based on this form, we prove that the Picard sequence is exponentially decaying and fundamental ({\color{red}i.e., a} Cauchy sequence). We first give a detailed discussion of the proof of the existence and uniqueness result in the case $\mathfrak p=3$. Next, we prove existence and uniqueness in the general case $\mathfrak p\geq 2$, which then covers the remaining cases $\mathfrak p\geq 4$. As a byproduct, we recover the local result from \cite{damanik16}. We exhibit the most important combinatorial index $σ$ and obtain a relationship with other indices, which is essential to our proofs in the case of general $\mathfrak p$.

math.AP↗

arXiv2021

BUSIS: A Benchmark for Breast Ultrasound Image Segmentation

Breast ultrasound (BUS) image segmentation is challenging and critical for BUS Comput-er-Aided Diagnosis (CAD) systems. Many BUS segmentation approaches have been studied in the last two decades, but the performances of most approaches have been assessed using relatively small private datasets with different quantitative metrics, which results in a discrepancy in performance comparison. Therefore, there is a pressing need for building a benchmark to compare existing methods using a public dataset objectively, to determine the performance of the best breast tumor segmentation algorithm available today, and to investigate what segmentation strategies are valuable in clinical practice and theoretical study. In this work, a benchmark for B-mode breast ultrasound image segmentation is presented. In the benchmark, 1) we collected 562 breast ultrasound images, prepared a software tool, and involved four radiologists in obtaining accurate annotations through standardized procedures; 2) we extensively compared the performance of sixteen state-of-the-art segmentation methods and discussed their advantages and disadvantages; 3) we proposed a set of valuable quantitative metrics to evaluate both semi-automatic and fully automatic segmentation approaches; and 4) the successful segmentation strategies and possible future improvements are discussed in details.

cs.CV↗