Article
Physics, Multidisciplinary
Yu Tan, Xiao-Lin Li
Summary: An improved moving least square meshless method is developed for solving the numerical nonlinear improved Boussinesq equation. Nonlinear systems of discrete algebraic equations are solved using an iterative algorithm, and shifted and scaled basis functions are incorporated to ensure convergence and stability. Numerical examples demonstrate high convergence rate and computational accuracy of the method.
Article
Mathematics
Jufeng Wang, Fengxin Sun, Rongjun Cheng
Summary: The DS-IMLS method utilizes dimension splitting to reduce matrix dimension and computational complexity in calculating shape functions, achieving high accuracy in approximations and derivatives. It is utilized in an improved IEFG method for two-dimensional potential problems, resulting in high accuracy in numerical solutions.
Article
Engineering, Multidisciplinary
Marziye Ramezani Lashkariani, Ali Rahmani Firoozjaee
Summary: An improved node moving technique based on spring analogy was developed for solving flow problems adaptively. By applying the Collocated Discrete Least Squares Meshless (CDLSM) method, considerable improvement was achieved compared to previous works.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Fengxin Sun, Jufeng Wang, Qi Wei, Yong Wu
Summary: In this paper, an improved element-free Galerkin method (IEFGM) is proposed to solve two-dimensional elasticity problems. The IEFGM utilizes the dimension-splitting moving least squares (DS-MLS) method for constructing trial functions and the Galerkin variational weak form with integral coordinate transformation to obtain discrete equations for the elastic problems. The DS-MLS method, developed from dimensional splitting and moving least squares approximation, reduces the dimension and complexity of matrix operations, thus improving calculation efficiency. Several examples demonstrate the effectiveness of the improved meshless method in terms of reduced CPU time and higher accuracy solution compared to the EFG method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Qiang Wu, PiaoPiao Peng, YuMin Cheng
Summary: The paper introduces the IEFG method for solving 2D elastic large deformation problems, which provides higher computational efficiency and accuracy compared to the traditional EFG method, thanks to its ability to apply displacement boundary conditions directly.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Zhijuan Meng, Yuye Ma, Lidong Ma
Summary: A fast interpolating meshless (FIM) method is introduced for solving three-dimensional heat conduction equations. The method employs the dimension splitting method to transform the 3D problem into relevant 2D problems and utilizes the improved interpolating moving least-squares method for obtaining accurate approximation functions. Finite difference method is used for time domain and direction splitting. The FIM method overcomes difficulties caused by singular weight functions and can directly implement Dirichlet boundary conditions. Numerical examples demonstrate that the FIM method effectively improves computation speed and accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics
Yajie Deng, Xingkeng Shen, Jixiao Tao, Ying Dai
Summary: A numerical model for the two-dimensional nonlinear elastic-plastic problem has been proposed based on the IICVEFG method and incremental tangent stiffness matrix method. The viability of the model has been verified through three elastic-plastic examples, showing good convergence and higher computing precision and efficiency compared to non-interpolating meshless methods. The solutions obtained using the IICVEFG method are consistent with those from finite element methods using ABAQUS program.
Article
Mathematics, Applied
Jiangshuang Wan, Xiaolin Li
Summary: This paper analyzes the computational formulas, properties, and theoretical error of the recursive MLS approximation, revealing that the high-order derivatives of the approximation have the same convergence order as the first-order derivative. Numerical results confirm the superconvergence of the recursive MLS approximation.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Showkat Ahmad Lone, Sadia Anwar, Tabassum Naz Sindhu, Fahd Jarad
Summary: This study discusses the challenge of estimating the parameters of mixture models from a frequentist perspective. It compares the three frequentist approaches, namely maximum likelihood, ordinary, and weighted least squares, and demonstrates the model's applicability through simulated and real-world data, achieving promising results in terms of enhanced estimation.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Xiang Rao, Wentao Zhan, Hui Zhao, Yunfeng Xu, Deng Liu, Weixin Dai, Ruxiang Gong, Fei Wang
Summary: This paper used a meshless method to study water-gas flow in a dual-medium shale gas reservoir model. The method was validated through a numerical reservoir model with a rectangular boundary shape, and parametric analysis was performed to investigate the impact of reservoir physical parameters on shale gas production.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Mechanical
S. K. Lohit, Amar K. Gaonkar, Tejas P. Gotkhindi
Summary: The Interpolating Modified Moving Least Squares (IMMLS) based element-free Galerkin method (EFGM) is a technique that addresses the limitations of classical methods and has been well-demonstrated in tissue deformation. However, its use in fracture mechanics has not been explored. This study investigates the application of IMMLS in isotropic and orthotropic thermoelastic Linear Elastic Fracture Mechanics (LEFM) cases as well as an isotropic Elastoplastic Fracture Mechanics (EPFM) case. The results show that IMMLS has a close correspondence with the finite element method (FEM) results and offers advantages in enforcing boundary conditions, nodal configuration, and computational time, making it a potential tool for fracture mechanics.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2022)
Article
Engineering, Multidisciplinary
P. Areias, L. Fernandes, R. Melicio
Summary: This paper introduces a finite element-based approach to element-free Galerkin discretization for finite strain, which uses simplifications and specialized techniques based on a Lagrangian kernel. A quadratic polynomial basis is used for discretization, and support is determined based on the number of preassigned nodes for each quadrature point. Quadrature points coincide with the centroids of tetrahedra. The use of a Lagrangian kernel allows for the adoption of recent developments in finite strain elasto-plastic constitutive modeling. Four 3D benchmark tests were successfully solved.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Chemistry, Multidisciplinary
Yunhan Yao, Ke Zhang
Summary: In this paper, an improved self-born weighted least square method (ISWLS) is proposed to enhance the stability and resistance to gross errors in geometric error evaluation. By updating the ordinal number information of the independent sets of equations, the influence of gross error data on the solution of the equations is minimized. Experimental results demonstrate the algorithm's strong resistance to gross differences and shorter operation time.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics, Applied
Xiaolin Li
Summary: This paper proposes a new numerical method for solving the nonlinear improved Boussinesq equation. The method has high accuracy and stable convergence in both spatial and temporal dimensions.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Tengyuan Liang, Benjamin Recht
Summary: This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The mistake bound and regularized variant for MNIC are derived using elementary properties of matrix inverses. Under the assumption of data being independently and identically distributed, it is shown that MNIC generalizes at a rate proportional to the norm of the interpolating solution and inversely proportional to the number of data points. Several plausible generative models are derived for the interpolating classifier, and the conditions under which MNIC generalizes with a fast rate are also discussed.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
Article
Geochemistry & Geophysics
Gang Ma, Jiangzhou Mei, Ke Gao, Jidong Zhao, Wei Zhou, Di Wang
Summary: Understanding the relationship between microslips and macroscopic stress fluctuations is crucial for gaining insights into geophysical processes such as earthquakes. This study uses discrete element method simulations and a machine learning approach to quantitatively connect microslips to stress fluctuations. The data-driven model successfully predicts the magnitude of stress fluctuation by incorporating the spatial distribution of microslips. The findings shed light on the mechanisms governing earthquake nucleation and the dynamics of earthquake cycles.
EARTH AND PLANETARY SCIENCE LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Yibo Zhang, Gang Ma, Longwen Tang, Wei Zhou
Summary: The study aims to establish a machine learning model that can identify the precursors of crystalline phases during the granular crystallization process. Through simulation experiments and the use of discrete element method, the study finds that the local volume fraction is an important structural signature in the generation of crystalline phases.
Article
Engineering, Geological
Wei Zhou, Shuhan Yang, Jiaying Liu, Gang Ma, Tianqi Qi, Mingchun Lin
Summary: Inter-particle friction is crucial for the mechanical behavior of granular materials, particularly under 3D non-axisymmetric loading conditions. The multiscale effects of inter-particle friction play a complex role in determining the behavior of granular materials. The evolution of strong contact network is found to be consistent with the overall stress tensor, regardless of the friction coefficient.
Article
Engineering, Geological
Yuxiong Zou, Gang Ma, Jiangzhou Mei, Jidong Zhao, Wei Zhou
Summary: The research explores the shape-dependent shear strength of granular materials and the influence of granular temperature on their properties. It is found that the nonlinearity of shear strength with particle shape and the coupling between rotational and translational particle dynamics are important factors affecting the macroscopic behavior of granular materials.
Article
Environmental Sciences
Chengqian Guo, Gang Ma, Haibin Xiao, Wei Zhou, Hongjie Chen, Zhiwei Zhou, Xiang Cheng
Summary: This article introduces the necessity and feasibility of using multi-source monitoring data in landslide displacement back analysis in reservoir areas. By utilizing surface InSAR and internal inclinometers, the article predicts landslide deformation through numerical modeling and evaluates the deformation state and stability of landslides, which is crucial for reservoir risk mitigation and the sustainable development of hydropower resources.
Article
Engineering, Geological
Gang Ma, Yihan Wang, Heng Zhou, Xi Lu, Wei Zhou
Summary: This study quantitatively investigates the morphology characteristics of fragments produced by crushing rock grains, showing that different-shaped grains yield different sizes of fragments, and there is no obvious relationship between the distribution of fragment shape descriptors and fragment size except for sphericity.
INTERNATIONAL JOURNAL OF GEOMECHANICS
(2022)
Article
Computer Science, Artificial Intelligence
Daren Zhang, Gang Ma, Zhuoran Deng, Qiao Wang, Guike Zhang, Wei Zhou
Summary: The aggregation of individuals facilitates information exchange and migration leads to dynamic community structure. Organisms' negative feedback regulation mechanism helps them in good living conditions. A novel particle swarm optimization algorithm with self-organizing topology and self-adaptive parameters (KGPSO) is proposed. K-Means clustering method divides the particle swarm into sub-swarms, and the optimal number of sub-swarms is determined. KGPSO maintains population diversity and uses adjusted parameters for dynamic balance between exploration and exploitation. Bayesian optimization tunes the hyperparameters of KGPSO. KGPSO performs best among tested PSO algorithms and shows excellent optimization capability in X-ray CT image enhancement.
APPLIED SOFT COMPUTING
(2022)
Article
Environmental Sciences
Jia Zhang, Gang Ma, Zhibing Yang, Qirui Ma, Wenyu Zhang, Wei Zhou
Summary: This study systematically investigated the influence of pore structure on the flow characteristics of landslide materials and found that tortuosity and global efficiency are related to permeability. Pore size heterogeneity and connectivity significantly affect the flow characteristics.
WATER RESOURCES RESEARCH
(2022)
Article
Engineering, Geological
Ni An, Gang Ma, Heng Zhou, Di Wang, Xi Lu, Wei Zhou
Summary: The study investigates the scale effect mechanism of sandy gravel material from Dashixia rockfill dam in China using the discrete element method (DEM). The results show that particle breakage weakens the shear strength of the material, while the widening of particle size distribution increases the resistance to deformation.
Article
Engineering, Geological
Shaoheng Guan, Tongming Qu, Y. T. Feng, Gang Ma, Wei Zhou
Summary: In this article, a coupled finite element method and machine learning framework is proposed for simulating the mechanical responses of granular materials. Random loading paths and coupled simulations are used to generate training samples, and machine learning is employed to directly learn the constitutive relationship from the datasets. Active learning is used to evaluate the informativeness of data points and establish an effective resampling scheme.
Article
Engineering, Geological
Jialin Cheng, Gang Ma, Guike Zhang, Qiao Wang, Wei Zhou
Summary: The deterioration of rockfill materials affects the safety and workability of rockfill dams. This study investigates the mechanical property deterioration of rockfill materials under different wetting-drying cycles and wetting duration. It is found that cyclic wetting-drying results in more significant particle breakage and microstructural changes compared to wetting alone.
ROCK MECHANICS AND ROCK ENGINEERING
(2023)
Article
Geosciences, Multidisciplinary
Renjun Zhang, Zhibing Yang, Russell Detwiler, Dongqi Li, Gang Ma, Ran Hu, Yi-Feng Chen
Summary: This study reveals that the effect of liquid cohesion on particle clogging has been overlooked in previous studies. Visualized experiments show that even a tiny amount of additional immiscible wetting liquid can dramatically enhance clogging. An experimental phase diagram of clogging patterns is obtained, and the combined effect of suspension composition and hydrodynamic condition on the clogging behavior is analyzed. A theoretical model of agglomerate size is proposed to quantify the capillary cohesion effect. This work improves the understanding of fines migration and particle-clogging behaviors in the subsurface and paves the way for controlling particle transport and clogging in various applications.
GEOPHYSICAL RESEARCH LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jialin Cheng, Gang Ma, Guike Zhang, Xiaolin Chang, Wei Zhou
Summary: This study presents a theoretical model for analyzing the deterioration effect on the stress and deformation characteristics of rockfill materials during weathering. By introducing a deterioration coefficient, the stress and strain tensors before and after deterioration can be derived from granular matter mechanics and quantitatively evaluated using the Duncan-Chang EB model. The model predictions were verified through triaxial tests and showed good agreement with experimental results. The model can also predict the deteriorated stress and deformation characteristics after cyclic wetting-drying.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Materials Science, Multidisciplinary
Jiangzhou Mei, Gang Ma, Jiaying Liu, Francois Nicot, Wei Zhou
Summary: This paper investigates the transition between the solid and liquid phases of sheared granular materials from the perspective of the contact network. Persistent homology tools are used to quantify the dynamics of the contact network, and two important topological invariants, components and loops, are analyzed through numerical simulations. The study reveals the heterogeneous composition of the contact network and suggests a partition threshold for distinguishing strong and weak contact subnetworks. Mechanical precursors of the solid-liquid transition are identified during the shearing process. The study demonstrates the capability of the persistent homology method in bridging microscopic dynamics with macroscopic responses through the contact network.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Construction & Building Technology
Zhitao Ai, Gang Ma, Guike Zhang, Xiang Cheng, Quancheng Zou, Wei Zhou
Summary: The global construction of rockfill dams has reached a height of over 300 meters. However, monitoring techniques for high rockfill dams have not kept pace with dam design and construction. This study introduces the use of a shape accel array (SAA) for monitoring internal displacement in a 300-meter high earth core rockfill dam. Compared to conventional techniques, SAA is a data-intensive monitoring technique. The study also utilizes a parameter inversion method to predict rockfill dam deformation based on the intensive data obtained from SAA using a multiobjective optimization algorithm.
STRUCTURAL CONTROL & HEALTH MONITORING
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
