检索结果-内蒙古大学图书馆

arXiv 2023年

作者： Song, Teng Liu, Bin Department of Mathematics Wuhan University of Technology China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper discusses the discrete-time mean-field stochastic linear quadratic optimal control problems, whose weighting matrices in the cost functional are not assumed to be definite. The open-loop solvability is characterized by the existence of the solution to a mean-field forward-backward stochastic difference equations with a convexity condition and a stationary condition. The closed-loop solvability is presented by virtue of the existences of the regular solution to the generalized Riccati equations and the solution to the linear recursive equation, which is also shown by the uniform convexity of the cost functional. Moreover, based on a family of uniformly convex cost functionals, the finiteness of the problem is characterized. Also, it turns out that a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem. Finally, some examples are given to illustrate the theory *** Codes 93E20, 93C55, 49N10 Copyright © 2023, The Authors. All rights reserved.

关键词： Riccati equations

来源：评论

学校读者我要写书评

暂无评论

Invariant foliations for stochastic dynamical systems with multiplicative stable Lévy noise

arXiv

引用

arXiv 2018年

作者： Chao, Ying Wei, Pingyuan Yuan, Shenglan School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Lévy noise. We first establish the existence of stable and unstable foliations for this kind of system via the Lyapunov-Perron method. Then we examine the geometric structure of the invariant foliations, and their relation with invariant manifolds. Finally, we illustrate our results in an example. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

来源：评论

学校读者我要写书评

暂无评论

Simulation of nitrogen transport in a surficial aquifer and estimation of nitrogen load from septic systems in the Indian River Lagoon Area, Florida

Simulation of nitrogen transport in a surficial aquifer and ...

引用

World Environmental and Water Resources Congress 2015: Floods, Droughts, and Ecosystems

作者： Sayemuzzaman, Mohammad Ye, Ming Zhu, Yun Hicks, Richard Shi, Liangsheng Department of Scientific Computing Florida State University United States State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan Hubei China Florida Department of Environmental Protection TallahasseeFL United States

ISBN: (数字)9780784479162

ISBN: (纸本)9780784479162

Onsite sewage treatment and disposal system (OSTDS) or septic systems, is one of the significant sources of nitrogen in groundwater and surface water, poseing serious threats to human health and the environment. The ArcGIS-based Nitrate Load Estimation Toolkit (ArcNLET) has been used to simulate nitrogen transport and estimate nitrogen load from septic systems to surface waterbodies through the surficial aquifer. It is based on a simplified conceptual model of groundwater flow and nitrogen transport. This study utilizes the ArcNLET tool for the Main-South Canal (MSC) drainage basins of Indian River County (IRC) area which discharge to the Indian River Lagoon (IRL), FL. The purpose of this study is to estimate the nitrogen load from 12,735 septic systems to the IRL and other surface waterbodies in MSC drainage basins. This study found, all the waterbodies(574 in number) including the IRL have been receiving a total nitrogen load of 13,742 lbs/yr. Twenty out of the 574 watebodies receive 50.5% (6,802 lbs/yr) of the total load. Among the 12,735 septic systems, only 358 septic systems contributed nitrogen load directly to the IRL, which is 2.01% (271 lbs/yr) of the total load. It is also found that the estimated ground water load of nitrogen to the southern drainage basin is greater than the estimated septic tank load to the main drainage basin. The estimation of nitrogen load exhibits spatial variability, which is useful to facilitate decisions on the sewering of residential areas served by OSTDS to reduce nitrogen load to the canals and the IRL. The modeling results may change when new data are available for model calibration. © 2015 ASCE.

关键词： Aquifers

来源：评论

学校读者我要写书评

暂无评论

The Exploration of Neural Collapse under Imbalanced Data

arXiv

引用

arXiv 2024年

作者： Liu, Haixia School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the L-extended unconstrained feature model with a bias term and provide a theoretical analysis of global minimizer. Our findings include: (1) Features within the same class converge to their class mean, similar to both the balanced case and the imbalanced case without bias. (2) The geometric structure is mainly on the left orthonormal transformation of the product of L linear classifiers and the right transformation of the class-mean matrix. (3) Some rows of the left orthonormal transformation of the product of L linear classifiers collapse to zeros and others are orthogonal, which relies on the singular values of Ŷ = (IK − 1/Nn1TK)D, where K is class size, n is the vector of sample size for each class, D is the diagonal matrix whose diagonal entries are given by √n. Similar results are for the columns of the right orthonormal transformation of the product of class-mean matrix and D. (4) The i-th row of the left orthonormal transformation of the product of L linear classifiers aligns with the i-th column of the right orthonormal transformation of the product of class-mean matrix and D. (5) We provide the estimation of singular values about Ŷ . Our numerical experiments support these theoretical *** Codes ***, *** Copyright © 2024, The Authors. All rights reserved.

关键词： Linear transformations

来源：评论

学校读者我要写书评

暂无评论

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

引用

Physical Review E 2018年第3期97卷 033309-033309页

作者： Hong Liang Jiangrong Xu Jiangxing Chen Huili Wang Zhenhua Chai Baochang Shi Department of Physics Hangzhou Dianzi University Hangzhou 310018 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

关键词： Interfacial flows Kelvin-Helmholtz instability Multiphase flows Rayleigh-Taylor instability Lattice-Boltzmann methods

来源：评论

学校读者我要写书评

暂无评论

Maxwell-Stefan-theory-based lattice Boltzmann model for diffusion in multicomponent mixtures

引用

Physical Review E 2019年第2期99卷 023312-023312页

作者： Zhenhua Chai Xiuya Guo Lei Wang Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Physics China University of Geosciences Wuhan 430074 China

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures and also perform a Chapman-Enskog analysis to show that the MS continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model and find that the results are in good agreement with the previous work. Besides, the reverse diffusion, osmotic diffusion, and diffusion barrier phenomena are also captured. Finally, compared to the kinetic-theory-based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

关键词： Lattice-Boltzmann methods

来源：评论

学校读者我要写书评

暂无评论

Phase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows

引用

Physical Review E 2020年第6期101卷 063310-063310页

作者： Xiaolei Yuan Hong Liang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China Department of Physics Hangzhou Dianzi University Hangzhou 310018 China

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase flows (N≥2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N−1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N≥2) immiscible incompressible flows.

关键词： Multiphase flows Lattice-Boltzmann methods

来源：评论

学校读者我要写书评

暂无评论

A unified framework for asymptotic analysis and computation of finite Hankel transform

arXiv

引用

arXiv 2018年

作者： Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this paper we present a unified framework for asymptotic analysis and computation of the finite Hankel transform. This framework enables us to derive asymptotic expansions of the transform, including the cases where the oscillator has zeros and stationary points. As a consequence, two efficient and affordable methods for computing the transform numerically are developed and a detailed analysis of their asymptotic error estimate is carried out. Numerical examples are provided to confirm our analysis.65D30, 65D32, 65R10, 41A60 Copyright © 2018, The Authors. All rights reserved.

关键词： Asymptotic analysis

来源：评论

学校读者我要写书评

暂无评论

Gradient Descent for Symmetric Tensor Decomposition

引用

Annals of Applied Mathematics 2022年第4期38卷 385-413页

作者： Jian-Feng Cai Haixia Liu Yang Wang Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina School of Mathematics and Statistics&Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhanHubei 430074China

Symmetric tensor decomposition is of great importance in *** studies have employed a greedy approach,where the main idea is to first find a best rank-one approximation of a given tensor,and then repeat the process to the residual tensor by subtracting the rank-one *** this paper,we focus on finding a best rank-one approximation of a given orthogonally order-3 symmetric *** give a geometric landscape analysis of a nonconvex optimization for the best rank-one approximation of orthogonally symmetric *** show that any local minimizer must be a factor in this orthogonally symmetric tensor decomposition,and any other critical points are linear combinations of the ***,we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem,and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable *** result,combined with the landscape analysis,reveals that the greedy algorithm will get the tensor CP low-rank *** results are provided to verify our theoretical results.

关键词： Gradient descent random initialization symmetric tensor decomposition CP decomposition linear convergence

来源：评论

学校读者我要写书评

暂无评论

Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

引用

Physical Review E 2019年第6期99卷 063316-063316页

作者： Xiuya Guo Zhenhua Chai Shengyong Pang Yong Zhao Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Material Processing and Die & Mould Technology Huazhong University of Science and Technology Wuhan 430074 China

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

关键词： Lattice-Boltzmann methods

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：