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Upper-bound limit analysis based on the natural element method

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Acta Mechanica Sinica 2012年第5期28卷 1398-1415页

作者： shu-Tao zhou Ying-Hua Liu Department of Engineering Mechanics AMLTsinghua University

The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.

关键词： Upper bound limit analysis Meshless methodNatural neighbour interpolation Natural element methodMathematical programming Iteration algorithm

Asymptotic Behavior of Positive Solutions of Semilinear Elliptic Equations in R^n, Ⅱ

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Acta Mathematica Sinica,English Series 2010年第9期26卷 1723-1738页

作者： Bai shun LAI shu Qing zhou Institute of Contemporary Mathematics He 'nan University Kaifeng 475004 P. R. China School of Mathematics and Information Science He 'nan University Kaifeng 475004 P. R. China Department of Mathematics Hu'nan Normal University Changsha 410081 P. R. China

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in R^n by employing the Li＇s method of energy function.

关键词： Semilinear elliptic equation positive solutions asymptotic behavior

A New Inequality for Weakly (K_1,K_2)-Quasiregular Mappings

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Acta Mathematica Sinica,English Series 2007年第12期23卷 2241-2246页

作者： Hong Ya GAO shu Qing zhou ChinaCollege of Mathematics and Computer Hebei University Baoding 071002 P. R. Mathematical Study Center of Hebei Province Shijiazhuang 050016 P. R. China College of Mathematics and Computational Sciences Hu'nan Normal University Changsha 410081 P. R. China

We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.

关键词： (K1 K2)-Quasiregular mapping regularity McShane extension

Zero Extension for the Biharmonic Equation

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Acta Mathematica Sinica,English Series 2018年第10期34卷 1549-1562页

作者： Shao Peng XU shu Lin zhou School of Mathematical Sciences Peking University Beijing 100871 P. R. China LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

In this paper we present a necessary and sufficient condition to guarantee that the extended function of the solution by zero extension for the biharmonic equation in a smaller domain is still the solution of the corresponding extension problem in a larger domain. We prove the results under the frameworks of classical solutions and strong solutions.

关键词： Biharmonic zero extension

Functional protein microarray： an ideal platform for investigating protein binding property

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Frontiers in Biology 2012年第4期7卷 336-349页

作者： shu-Min zhou Shanghai Center for Systems Biomedicine Key Laboratory of Systems Biomedicine (Ministry of Education) Shanghai Jiao Tong University Shanghai 200240 China StateKey Laboratory of Oncogenes and Related Genes Shanghai 200240 China Department of Pharmacology and Molecular Sciences Johns Hopkins University School of Medicine Baltimore MD 21205 USA The High-Throughput Biology Center Johns Hopkins University School of Medicine Baltimore MD 21205 USA

Functional protein microarray is an important tool for high-throughput and large-scale systems biology studies. Besides the progresses that have been made for protein microarray fabrication, significant advancements have also been achieved for applying protein microarrays on determining a variety of protein biochemical activities. Among these applications, detection of protein binding properties, such as protein-protein interactions （PPIs）, protein-DNA interactions （PDIs）, protein-RNA interactions, and antigen-antibody interactions, are straightforward and have substantial impacts on many research fields. In this review, we will focus on the recent progresses in protein-protein, protein-DNA, protein-RNA, protein-small molecule, protein-lipid, protein-glycan, and antigen-antibody interactions. We will also discuss the challenges and future directions of protein microarray technologies. We strongly believe that protein microarrays will soon become an indispensible tool for both basic research and clinical applications.

关键词： lectin microarray protein microarray protein-cell interaction protein-DNA interaction (PDI) protein-proteininteraction (PPI)

Solitary Vortex Evolution in Two-Dimensional Harmonically Trapped Bose-Einstein Condensates

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Communications in Theoretical Physics 2018年第8期69卷 132-136页

作者： Ying Wang shu-Yu zhou School of Science Jiangsu University of Science and TechnologyZhenjiang 212003China Key Laboratory for Quantum Optics Shanghai Institute of Optics and Fine MechanicsChinese Academy of SciencesShanghai 201800China

We investigate solitary vortex evolution in two-dimensional Bose-Einstein condensates based on the GrossPitaevskii equation model. Through the variational method, together with the novel Gaussian ansatz incorporating asymmetric perturbation effects, we arrive at the analytical solitary vortex solution with two typical forms: a symmetric quasi-stable solution under certain parametric settings and a diverging propagation case arising from an initial asymmetric perturbation. The derived pictorial evolutionary patterns of the solitary vortices are compared with those from a pure numerical analysis, and by identifying the key qualitative features, we show the applicability of the theoretical treatment presented here.

关键词： solitary vortex Gross-Pitaevskii equation Bose-Einstein condensate

Existence of Positive Solutions for a Singular p-Laplacian Differential Equation

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Acta Mathematica Sinica,English Series 2008年第8期24卷 1331-1344页

作者： Xia LI Zheng An YAO Wen shu zhou Department of Mathematics Shenzhen University Shenzhen 518060 P. R. China Department of Mathematics Zhongshan University Guangzhou 510275 P. R. China Department of Mathematics Jilin University Changchun 130012 P. R. China

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r）〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.

关键词： p-Laplacian differential equation positive solution existence

Zero Extension Problem for the Heat Equation

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Acta Mathematica Sinica,English Series 2022年第11期38卷 1981-1997页

作者： Ge Yang DU Qiang XU shu Lin zhou School of Mathematical Sciences Peking UniversityBeijing 100871P.R.China School of Mathematics and Statistics Lanzhou UniversityLanzhou 730000P.R.China LMAM School of Mathematical SciencesPeking UniversityBeijing 100871P.R.China

In this paper we present a necessary and sufficient condition to guarantee that the zeroextended function of the solution for the heat equation in a smaller cylinder is still the solution of the corresponding extension problem in a larger *** prove the results under the frameworks of classical solutions,strong solutions and weak ***,we generalize these results to uniformly parabolic equations of divergence form.

关键词： Heat equation zero extension initial-boundary value problem

Blow-up of p-Laplacian evolution equations with variable source power

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Science China Mathematics 2017年第3期60卷 469-490页

作者： ZHENG Zhi QI Yuan Wei zhou shu Lin School of Mathematical Sciences Peking University Department of Mathematics University of Central Florida

We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power where Ω is either a bounded domain or the whole space RN and q（x） is a positive and continuous function defined in with 0 〈 q- infq（x） = q（x）〈 ∞supq（x） = q＋〈 ∞. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of q（x） and the structure of spatial domain Ω, compared with the case of constant source power. For the case that is a bounded domain, the exponent p - 1 plays a crucial role. If q＋〉 p - 1, there exist blow-up solutions, while if q＋ p - 1, all the solutions are global. If q-〉 p - 1, there exist global solutions, while for given q- 〈 p - 1 〈 q＋, there exist some function q（x） and such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. For the case Ω = RN the Fujita phenomenon occurs if 1 q＋ q＋ ≤p--1＋p/N, while if q_ 〉 p -- 1 ＋p/N there exist global solutions.

关键词： p-Laplacian blow-up variable source power