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ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS

Journal of computational mathematics 2025年第3期43卷 731-770页

作者： Ying Yang Ya Liu Yang Liu Shi Shu School of Mathematics and Computational Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationCenter for Applied Mathematics of Guangxi(GUET)Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105China

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion *** presenting the semi-discrete scheme,the optimal H1 norm error estimates are presented for the time-dependent PNP equations,which are based on some error estimates of a virtual element energy *** Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element *** numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.

关键词： Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration

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Asymmetry and Condition Number of an Elliptic-Parabolic System for Biological Network Formation

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应用数学与计算数学学报 2025年第1期7卷 78-94页

作者： Clarissa Astuto Daniele Boffi Jan Haskovec Peter Markowich Giovanni Russo Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics"F.Casorati" University of Pavia27100 PaviaItaly Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics University of Vienna1090 ViennaAustria Department of Mathematics and Computer Science University of Catania95125 CataniaItaly

We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r＞0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.

关键词： Bionetwork formation Cai-Hu model Leaf venation Asymmetry Conditioning number Finite-difference scheme Semi-implicit Symmetric alternating direction implicit(ADI) Wasserstein distance

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Effect of order–disorder transition on thermodynamic and electronic properties of σ and χ phases in W–Re alloy: the first-principles calculation

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Tungsten 2025年第1期7卷 195-213页

作者： Zhi-Peng Zhu Dian Jia William Yi Wang Jun-Lei Yin Xing-Yu Gao Shu-Feng Yang Hai-Feng Song Jin-Shan Li State Key Laboratory of Solidification Processing Northwestern Polytechnical University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics School of Metallurgical and Ecological Engineering University of Science and Technology Beijing

The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aerospace,electronics,and nuclear *** constituents of the topologically close-packed(TCP) phases,the sigma phase(σ) and chi phase(χ) formed within W-Re alloys wield considerable influence on the mechanical properties and the stability of the *** calculations were utilized in the present work to explore the structural,thermodynamic,and electronic properties of both ordered and disordered configurations within the σ and χ phases,culminating in a systematic elucidation of the higher phase stability exhibited by the ordered *** is found that the bulk modulus of these two phases is directly proportional to the concentration of Re in the alloy,while the equilibrium volume is inversely *** thermodynamic parameters of the σ and χ phases are calculated via the mean-field potential *** similar trends observed in the isobaric heat capacity,enthalpy increment,and entropy change curves for these two phases suggest they possess comparable thermodynamic *** is noteworthy that the contribution of ionic vibrations predominantly affects the isobaric heat capacity,while the contribution of thermal electronic excitations increases linearly with *** the structure and thermodynamic properties of TCP phases in W-Re alloys at low temperatures has profound significance for optimizing material performance,microstructures features,establishing theoretical foundations,and predicting material behavior.

关键词： First-principles calculations Phase stability Thermodynamic properties W-Re alloy TCP phases

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Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network

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IEEE Transactions on Information Theory 2025年第4期71卷 2955-2981页

作者： Ding, Zhao Duan, Chenguang Jiao, Yuling Yang, Jerry Zhijian Wuhan University School of Mathematics and Statistics Hubei Wuhan430072 China Wuhan University School of Artificial Intelligence National Center for Applied Mathematics in Hubei Hubei Key Laboratory of Computational Science School of Mathematics and Statistics Hubei Wuhan430072 China Wuhan University National Center for Applied Mathematics in Hubei Wuhan Institute for Math & Al School of Mathematics and Statistics Hubei Key Laboratory of Computational Science Hubei Wuhan430072 China

We propose SDORE, a Semi-supervised Deep SObolev REgressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm regularization, allowing the approximation of the regularization term by unlabeled data. Our study includes a thorough analysis of the convergence rates of SDORE in L2-norm, achieving the minimax optimality. Further, we establish a convergence rate for the associated plug-in gradient estimator, even in the presence of significant domain shift. These theoretical findings offer valuable insights for selecting regularization parameters and determining the size of the neural network, while showcasing the provable advantage of leveraging unlabeled data in semi-supervised learning. To the best of our knowledge, SDORE is the first provable neural network-based approach that simultaneously estimates the regression function and its gradient, with diverse applications such as nonparametric variable selection. The effectiveness of SDORE is validated through an extensive range of numerical simulations. © 1963-2012 IEEE.

关键词： Self-supervised learning

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Soliton resolution for the energy-critical wave equation with an inverse-square potential in the radial case

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science China mathematics 2025年

作者： Xuanying Li Changxing Miao Lifeng Zhao School of Mathematical Sciences University of Science and Technology of China Institute of Applied Physics and Computational Mathematics

In this paper, we present the soliton resolution for the energy-critical wave equation with an inverse square potential in the radial case and all dimensions N≥3. A crucial ingredient of our analysis involves the energy channel for the linearized wave equation with inverse square potentials, which incorporates the distorted Hankel transform.

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Parameter Inference and Nonequilibrium Identification for Markov Networks Based on Coarse-Grained Observations

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Physical Review Letters 2025年第8期134卷 087103-087103页

作者： Bingjie Wu Chen Jia Applied and Computational Mathematics Division Beijing Computational Science Research Center Beijing 100193 China

Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on an infinitely long coarse-grained trajectory, we obtain a set of sufficient statistics that extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we set up a theoretical framework of parameter inference and nonequilibrium identification for a general Markov network with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can be used to identify whether the sufficient statistics are enough for empirical estimation of all unknown parameters and we can also provide a quantitative criterion that reveals nonequilibrium. Our nonequilibrium criterion generalizes the one obtained [J. Chem. Phys. 132, 041102 (2010)] for a three-state system with two coarse-grained clusters and is capable of detecting a larger nonequilibrium region compared to the classical criterion based on autocorrelation functions.

关键词： Coarse-grained modeling

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Hamiltonian boundary value methods applied to KdV-KdV systems

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applied Numerical mathematics 2025年 214卷 1-27页

作者： Luo, Qian Xiao, Aiguo Luo, Xuqiong Yan, Xiaoqiang School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan 411105 China School of Mathematics and Statistics Changsha University of Science and Technology Changsha410114 China National Center for Applied Mathematics in Hunan Xiangtan University Hunan 411105 China

In this paper, we propose a highly accurate scheme for two KdV systems of the Boussinesq type under periodic boundary conditions. The proposed scheme combines the Fourier-Galerkin method for spatial discretization with Hamiltonian boundary value methods for time integration, ensuring the conservation of discrete mass and energy. By expanding the system in Fourier series, the equations are firstly transformed into Hamiltonian form, preserving the original Hamiltonian structure. Applying the Fourier-Galerkin method for semi-discretization in space, we obtain a large-scale system of Hamiltonian ordinary differential equations, which is then solved using a class of energy-conserving Runge-Kutta methods, known as Hamiltonian boundary value methods. The efficiency of this approach is assessed, and several numerical examples are provided to demonstrate the effectiveness of the method. © 2025 IMACS

关键词： Ordinary differential equations

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Numerical modeling of the ion-acoustic solitary waves arising in nonlinear dispersive system

Numerical modeling of the ion-acoustic solitary waves arisin...

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作者： Nikan, Omid Yang, Yin Avazzadeh, Zakieh School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Hunan Xiangtan411105 China Department of Mathematical Sciences University of South Africa Florida South Africa

This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains the water wave phenomena in nonlinear dispersive system. The solution of the ZK-BBME is discretized by using hybridization of the finite difference and localized radial basis function based on partition of unity method. The association of this hybridization leads to a meshless method and it does not requires any linearization. In the initial step, the PDE is converted into a nonlinear ODE system by making use of radial kernels. In the next step, the obtained nonlinear ODE system is solved based on an ODE solver of high order. The global collocation technique imposes a large computational cost because a dense algebraic system must be calculated. This proposed strategy is based on decomposing the initial domain into a number of sub-domains using kernel approximation on each sub-domain. Three numerical examples are illustrated to clarify the efficiency and accuracy of the proposed strategy. © 2023 John Wiley & Sons, Ltd.

关键词： Water waves

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Predator Prey Scavenger Model using Holling’s Functional Response of Type III and Physics-Informed Deep Neural Networks

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International Journal of applied and computational mathematics 2025年第2期11卷 1-32页

作者： Panchal, Aneesh Beniwal, Kirti Kumar, Vivek Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore 560012 India Department of Applied Mathematics Delhi Technological University Delhi New Delhi 110042 India

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator–prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling’s functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden–Fletcher–Goldfarb–Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

关键词： Broyden–Fletcher–Goldfarb–Shanno optimization Physics-informed deep neural network Predator prey scavenger model Stability analysis

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Impact of Intraspecific Competition of Predator on Coexistence of a Predator-Prey Model with Additive Predation on Prey

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SIAM Journal on applied Dynamical Systems 2025年第2期24卷 1191-1230页

作者： Bai, Dingyong Xie, Mingming Wu, Jianhong Zheng, Bo Yu, Jianshe Kang, Yun School of Mathematics and Information Science Guangzhou University Guangzhou510006 China Guangzhou Center for Applied Mathematics Guangzhou University Guangzhou510006 China Laboratory for Industrial and Applied Mathematics York University TorontoONM3J 1P3 Canada Science and Mathematics Faculty College of Integrate Sciences and Arts Arizona State University MesaAZ85212 United States Simon A. Levin Mathematical Computational and Modeling Sciences Center Arizona State University TempeAZ85281 United States

We consider a predator-prey model incorporating intraspecific competition in the predator and additive predation on the prey. The additive predation can elicit strong/weak Allee effects in prey, leading to complex dynamics in the model. Our goal is to examine how predator competition affects the species' coexistence. Analyzing the model with the predator competition coefficient as the bifurcation parameter, we reveal the existence and stability of equilibria, and various bifurcation phenomena such as Hopf, saddle-node, and Bogdanov-Takens bifurcations, as well as heteroclinic and homoclinic bifurcations. These bifurcations identify critical thresholds in the competition coefficient, indicating behavioral transitions. Our findings indicate that the strong Allee effect heightens the extinction risk for both species, but predator intraspecific competition reduces this risk and promotes coexistence. Especially when the ratio of the predator's mortality to conversion rate is low, there are competition thresholds that trigger a range of initial values conducive to coexistence, which widens as competition intensifies. Additionally, our analysis shows that reducing the predation pressure on the prey from other potential predators can foster coexistence by inducing a weak Allee effect or eliminating the Allee effect altogether. © 2025 Society for Industrial and applied mathematics.

关键词： Abiotic

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