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THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 1998年第3期16卷 275-288页

作者： lu, BN wan, GH Guo, BL Xiangtan Univ Inst Computat & Appl Math Xiangtan 411105 Peoples R China Inst Appl Phys & Computat Math Lab Computat Phys Beijing 100088 Peoples R China Shaanzi Normal Univ Dept Math Xian 710062 Peoples R China Inst Appl Phys & Computat Math Ctr Nonlinear Studies Beijing 100088 Peoples R China

In this paper, the initial value problem of nonlinear reaction-diffusion equation is considered. The Dufort-Frankel finite difference approximation for the long time scheme is given for the d-dimensional reaction-diffusion equation with the two different cases. The global solution and global attractor are discussed for the Dufort-Frankel scheme. Moreover properties of the solution are studied. The error estimate is presented in a finite time region and in the global time region for some special cases. Finally the numerical results for the equation are investigated for Allen-Cahn equation and some other equations and the homoclinic orbit is simulated numerically.

关键词： global Dufort-Frankel method reaction-diffusion equation global attractor error estimate numerical experiments

The Impact of Nonlinear Stochastic Perturbation on Dynamical Behavior of an HIV Infection System

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Journal of Systems Science & Complexity 2023年第2期36卷 632-655页

作者： sun Guanzhen lu Chun Department of Environmental Science School of Environment and Municipal EngineeringQingdao University of TechnologyQingdao 266520China Department of Mathematics Qingdao University of TechnologyQingdao266520China

In this paper,the authors develop and study an HIV infection system with two distinct cell subsets and nonlinear stochastic ***,the authors obtain that the solution of the system is positive and ***,for the corresponding linear case,the authors derive a critical condition R0S similar to deterministic *** R0S>1,the authors establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution to the stochastic system,***,the authors give sufficient criterions for extinction of the *** proposed work provides a new method in overcoming difficulty conduced by nonlinear stochastic perturbation.

关键词： HIV model nonlinear stochastic perturbation stationary distribution two distinct cell subsets

改进K-SMOTE随机森林算法在地震信息发布安全风险评估中的应用研究

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地震工程学报 2025年第1期47卷 168-177页

作者：李亚龙何琳万杰潘丹孙静安徽省地震局安徽合肥230031 安徽蒙城地球物理国家野外科学观测研究站安徽蒙城233527

为有效地提高地震监测、预警、灾情评估等信息发布的安全性提出一种改进型K-SMOTE随机森林(RF)方法构建地震信息安全风险评估模型。该模型通过改进K-SMOTE算法中运用混合采样获得均衡度高的样本集,然后使用随机K折交叉验证方法进行样本... 详细信息

为有效地提高地震监测、预警、灾情评估等信息发布的安全性提出一种改进型K-SMOTE随机森林(RF)方法构建地震信息安全风险评估模型。该模型通过改进K-SMOTE算法中运用混合采样获得均衡度高的样本集,然后使用随机K折交叉验证方法进行样本划分与模型优化,最终实现目标安全风险等级评估。对实际地震信息发布案例进行评测,文章所提方法构建模型评估准确率为92%,模型精确率和查全率分别为0.81和0.92,模型泛化能力强,能有效用于地震信息发布安全风险评估。本研究为完善地震信息发布安全评估体系、改进地震信息发布环境、降低安全风险提供了参考。

关键词：地震信息发布风险等级评估改进K-SMOTE 随机森林随机K折交叉验证

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

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Applied Mathematics and Mechanics(English Edition) 2017年第5期38卷 723-736页

作者： Chao ZHANG Zhenhua wan Dejun sun Department of Modern Mechanics University of Science and Technology of ChinaHefei 230027China

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

关键词： supersonic cavity flow reduced-order model (ROM) proper orthogonal decomposition (POD) Galerkin projection

Mode transition and oscillation suppression in supersonic cavity flow

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Applied Mathematics and Mechanics(English Edition) 2016年第7期37卷 941-956页

作者： Chao ZHANG Zhenhua wan Dejun sun Department of Modern Mechanics University of Science and Technology of China

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition （DMD） approach are consistent with the local power spectral density （PSD） analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.

关键词： supersonic cavity flow pressure oscillation mode transition vortex-corner interaction

Fabrication of cellulose aerogel from wheat straw with strong absorptive capacity

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Frontiers of Agricultural Science and Engineering 2014年第1期1卷 39-45页

作者： Jian LI Caichao wan Yun lu Qingfeng sun Material Science and Engineering College Northeast Forestry UniversityHarbin 150040China

An effectively mild solvent solution containing NaOH/PEG was employed to dissolve the cellulose extracted from the wheat *** further combined regeneration process and freeze-drying,the cellulose aerogel was successfully *** electron microscope,X-ray diffraction technique,Fourier transform infrared spectroscopy,and Brunauer-Emmett-Teller were used to characterize this cellulose aerogel of low density(about 40 mg·cm^(–3))and three-dimensional network with large specific surface area(about 101 m2·g^(–1)).Additionally,with a hydrophobic modification by trimethylchlorosilane,the cellulose aerogel showed a strong absorptive capacity for oil and dye solutions.

关键词： cellulose aerogel absorptive capacity waste wheat straw freeze-drying

Cramer-Rao bound of joint estimation of target location and velocity for coherent MIMO radar

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Journal of Systems Engineering and Electronics 2014年第4期25卷 566-572页

作者： Peilin sun Jun Tang Shuang wan Department of Electronic Engineering Tsinghua University

The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.

关键词： Cramer-Rao bound (CRB) joint estimation coherentmultiple input multiple output (MIMO) radar.

Template synthesis of imine-based covalent organic framework core-shell structure and hollow sphere:a case of COFTTA-DHTA

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Science China Chemistry 2017年第8期60卷 1098-1102页

作者： sun,Bing wang,Dong wan,Lijun Key Laboratory of Molecular Nanostructure and Nanotechnology Institute of Chemistry Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China

Controllably synthesizing well-dispersed covalent organic frameworks （COFs） with uniform both morphology and size is still a challenge. Herein, we report the template-directed synthesis of ***-based core-shell hybrids under solvothermal conditions by using amino-functionalized SiO2 microspheres as templates coupled with stepwise addition of initial monomer molecules. The modified amino groups on the surfaces of SiO2 templates play an important role in the formation of well-defined NH2-f-SiO2@COFTTA-DHXA core-shell hybrids. COFTTA-DHTA hollow spheres can be obtained by etching SiO2 cores of NH2-f-SiO2@COFTTA-DHTA. Both the NH2-f-SiO2@COFTTA-I）HTA and COFxTA-DHVA hollow spheres possess the well-defined morphology, high crystallinity and porosity, excellent dispersion property and high chemical stability. The template synthesis method demonstrated in this work provides a general method for the shape-controlled synthesis of COF-based materials, which is important for the further applications in the fields such as energy storage, drug delivery and catalysis.

关键词： covalent organic framework template synthesis organic porous material core-shell structure hollow sphere

Dynamic Accuracy Design Method of Ultra-precision Machine Tool

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Chinese Journal of Mechanical Engineering 2018年第1期31卷 167-175页

作者： Guo-Da Chen Ya-Zhou sun Fei-Hu Zhang Li-Hua lu wan-Qun Chen Nan Yu Center for Precision Engineering Harbin Institute of Technology Key Laboratory of E&M Ministry of Education & Zhejiang Province Zhejiang University of Technology Precision Engineering Institute Cranfield University

Ultra-precision machine tool is the most important physical tool to machining the workpiece with the frequency domain error requirement, in the design process of which the dynamic accuracy design(DAD) is indispensable and the related research is rarely available. In light of above reasons, a DAD method of ultra-precision machine tool is proposed in this paper, which is based on the frequency domain error *** basic procedure and enabling knowledge of the DAD method is introduced. The application case of DAD method in the ultra-precision flycutting machine tool for KDP crystal machining is described to show the procedure detailedly. In this case, the KDP workpiece surface has the requirements in four different spatial frequency bands, and the emphasis for this study is put on the middle-frequency band with the PSD specifications. The results of the application case basically show the feasibility of the proposed DAD method. The DAD method of ultra-precision machine tool can effectively minimize the technical risk and improve the machining reliability of the designed machine tool. This paper will play an important role in the design and manufacture of new ultra-precision machine tool.

关键词： Dynamic accuracy design Ultra-precision machine tool Frequency domain Error allocation