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MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

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Acta Mechanica Solida Sinica 2003年第3期16卷 231-239页

作者： Lou Luliang zeng Pan (department of Mechanical Engineering,tsinghua university,beijing 100084,china. department of Mechanical Engineering Tsinghua University Beijing 100084 China

A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation *** domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack *** each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked *** J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this *** meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method.

关键词： meshless method crack propagation mixed-mode crack Voronoi cell

THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

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Journal of Computational mathematics 2003年第4期21卷 435-450页

作者： Hou-de Han Xin Wen (department of Mathematical Sciences, tsinghua university, beijing 100084, china. department of Mathematical Sciences Tsinghua University Beijing 100084 China

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.

关键词： Ship wave Potential flow Global artificial boundary condition Finite element method.

THE INVARIANT CONTINUOUS-TRACE C*-ALGEBRAS BY THE ACTIONS OF COMPACT ABELIAN GROUPS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 489-498页

作者： FANG XIAOCHUN (department of applied mathematics, Tonaii university, Shanghai, 200092, china.) Tongji Univ Dept Appl Math Shanghai 200092 Peoples R China

The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant　continuous trace property. For separable C*-dynamic system (A, G, α) with G compact and　abelian,A liminal, αt ∈ AutCb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.

关键词： Continuous-Trace Action of Group C*-Algebra

Maximal regularity of second order delay equations in Banach spaces

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Science china.mathematics 2010年第1期53卷 51-62页

作者： BU ShangQuan ? & FANG Yi department of Mathematical Sciences, tsinghua university, beijing 100084, china.department of Mathematical Sciences, tsinghua university, beijing 100084, china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(*** ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).

关键词： maximal regularity second order delay equations Lebesgue-Bochner spaces Besov spaces Triebel-Lizorkin spaces

Quantum and Non-Causal Stochastic Calculus

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Acta Mathematica Sinica,English Series 1998年第3期14卷 289-294页

作者： Liang Zongxia Zheng Mingli department of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University 100084 Beijing China

In this paper, using the Guichardet space technique, the relationship between Fermion quantum stochastic calculus and non-causal calculus in Segal space L^2(H) is discussed, and an anticipating quantum stochastic calc... 详细信息

关键词： Non-causal stochastic analysis Quantum stochastic analysis Guichardet space

MARKOV FUZZY CRITERION DECISION MODELS

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Systems Science and Mathematical Sciences 2000年第3期13卷 309-320页

作者： WU Congbin LIN Yuanlie(department of applied mathematics, tsinghua university, beijing 100084, china. 清华大学应用数学系北京 100084 清华大学应用数学系北京

This paper investigates non-stationary discrete time Markov decision models with Borel state spaces and action sets, in which fuzzy criterion functions are employed to be a measure of performance. A class of Markov fuzzy criterion decision models is formulated. Under certain conditions, it is proved that the optimal equations hold and there exists a deterministic Markov optimal policy and the structure properties and the stability theorem of optimal policy are obtained. For models where transition laws are determined by system state equations, two conditions to be verified easily are presented and two applied examples are given.

关键词： Markov decision model fuzzy criterion function optimal policy

Numerical Simulation of Nonlinear Radiation Water Surface Wave Caused by Large-Amplitude Oscillation of A Cylinder

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 24-28页

作者： Wuzhou HE (department of Hydraulic Engineering, tsinghua university, beijing 100084, china. department of Hydraulic Engineering Tsinghua University Beijing 100084 China

The BEM combined with the time-stepping scheme is employed in the nonlinear numerical simulation of the development process of radiation wave profile and hydrodynamic force caused by large amplitude oscillating cylinder. To ensure stability and accuracy of the simulation, special consideration is paid on a series of difficulties in numerical modeling, such as the compatibility of free surface and body surface conditions at the intersection point and the open boundary condition problem. Numerical calculation is carried out for some study cases of different shaped cylinders undergoing large amplitude oscillating motions with distinct modes, the results show. some nonlinear phenomena and indicate the feasibility of the numerical approach.

关键词： 2-D water surface wave boundary element method time-stepping scheme

PARALLE DOMAIN DECOMPOSITION ALGORITHMS FOR A GENERALIZED STOKES PROBLEM

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Systems Science and Mathematical Sciences 1994年第2期7卷 153-168页

作者： CHU Delin ZHOU Fangjun(department of applied mathematics, tsinghua university, beijing 100084, china.

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关键词： Domain decomposition trace average operator convergence condition number a generalized Stokes problem.

MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (department of mathematics, Capital Normal university, beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem