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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 1.0084, china department of Mathematical Sciences, tsinghua university, beijing 1.0084, 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

Truncation error calculation based on Richardson extrapolation for variable-step collaborative simulation

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Science china(Information Sciences) 2011年第6期54卷 1238-1250页

作者： ZHANG HeMing 1 , LIANG SiLu 2 , SONG ShiJi 1 & WANG HongWei 3 1 department of automation, TNList, tsinghua university, beijing 1.0084, china 2 Computer and Information Management Center, tsinghua university beijing 1.0084, china 3 Engineering Design Centre, Engineering department, Cambridge university, Cambridge CB2 1PZ, UK 1. department of automation TNList Tsinghua University Beijing 100084 China2. Computer and Information Management Center Tsinghua University Beijing 100084 China3. Engineering Design Centre Engineering Department Cambridge University Cambridge CB2 1PZ UK

Collaborative simulation is an effective approach to performing simulation analysis for complex systems by integrating models developed for different engineering disciplines. Collaborative simulation issues include the modeling of coupled multidisciplinary systems, and the simulation running time integration of these models that are solved parallelly. Estimation of the local truncation error of coupling models is the key to solve multidisciplinary collaborative simulation problem, which is actually used to restrict the simulation step. This paper presents a variable-step method based on Richardson extrapolation for calculating the local truncation error to solve collaborative simulation problem of multidisciplinary coupling models. Formulas for estimating the local truncation error are derived through theoretical analysis by using integration methods and interpolation technologies, respectively. The simulation experiments are illustrated to validate the accuracy and efficiency of proposed collaborative simulation algorithm in comparison with the usual combinative algorithm.

关键词： multidisciplinary systems collaborative simulation variable-step algorithm error estimation

REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO department of Applied Mathematics, tsinghua university, beijing 1.0084, china. TSING HUA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

TRACE AVERAGING DOMAIN DECOMPOSITION METHOD WITH NONCONFORMING FINITE ELEMENTS

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Journal of Computational Mathematics 1996年第1期14卷 40-53页

作者： J. Gu X. Hu(department of Applied Mathematics, tsinghua university, beijing, china) TSING HUA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. We show its geometric convergence and present the dependence of the convergence factor on the relaxation factor, the subdomain diameter H and the mesh parameter h. In essence;, this method is equivalent to the simple iterative method for the preconditioned capacitance equation. The preconditioner implied in this iteration is easily invertible and can be applied to preconditioning the capacitance matrix with the condition number no more than O((1 + In H/h)max(1 + H-2, 1 + In H/h)).

关键词： Math TRACE AVERAGING DOMAIN DECOMPOSITION METHOD WITH NONCONFORMING FINITE ELEMENTS

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 1.0084, 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

A user-space file system for on-demand legacy desktop software

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Science china(Information Sciences) 2011年第6期54卷 1142-1150页

作者： ZHANG YouHui 1,2 , SU GeLin 1,2 & ZHENG WeiMin 1,2 1 department of Computer Science and Technology, tsinghua university, beijing 1.0084, china 2 tsinghua National Laboratory for Information Science and Technology, tsinghua university, beijing 1.0084, china 1. department of Computer Science and Technology Tsinghua University Beijing 100084 China2. Tsinghua National Laboratory for Information Science and Technology Tsinghua University Beijing 100084 China

Some user-level virtualization technologies have been used to convert legacy software (like the existing Windows desktop applications) into the on-demand software without any modification. To give the client a friendly and compatible method to access on-demand legacy software across the Internet, this paper presents a clientend file system for this usage case. It is a Windows user-space file system based on the cloud storage (where the on-demand software is stored), which converts the local file system accesses into remote visits. Quite a few optimizations are adopted and adjusted to suit the file-access-pattern of on-demand software, including the local cache, metadata/data/software prefetch and content-addressable storage (CAS), to decrease the number of remote visits and/or to overlap IO (input/output) operations with software execution. Detailed access-pattern analyses are also presented. This file system has been implemented and tests show that it is practical for much daily-used software-a local cache of limited size can provide up to 80% hit ratio and the corresponding overhead of running-time is about 37%. Owing to this method, on any compatible and networked computer, a user can use his/her personalized software conveniently although it does not exist on the local host.

关键词： on-demand software software as a service user-space file system cloud storage

Research on dual-stator winding multi-phase high-speed induction generator with rectifier load

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Science china(Technological Sciences) 2008年第6期51卷 683-692页

作者： WANG XiangHeng1 & WU XinZhen2 1 department of Electrical Engineering, tsinghua university, beijing 1.0084, china 2.department of Electrical Engineering, Qingdao university, Qingdao 266071, china 1. department of Electrical Engineering Tsinghua University Beijing 100084 China 2. department of Electrical Engineering Qingdao University Qingdao 266071 China

Based on analysis and calculation of the relation between current harmonics and MMF harmonics in the dual-stator winding multi-phase high-speed induction gen-erator with a rectifier load, a new idea, which divides the generator system into two sub-systems to be analyzed individually, is presented. For the sub-system of the 12-phase power winding with a rectifier load, the loop current method is used to establish network equation set in terms of the network graph theory. The numerical stability problem is solved by alternating use of fixed time-step and varied time-step, and the voltage and current with their fundamental components of the power winding are obtained. For the other sub-system of the induction generator with dual-stator winding and solid cage rotor, the electromagnetic field analysis method and the multi-variable optimization approach are combined to get the con-trol winding current and stator frequency. Calculated results well match experiment results, indicating that the new proposed method is of effectiveness and high ac-curacy.

关键词： dual-stator winding induction generator rectifier load MMF analysis loop current method finite element method optimization approach

Dense coding scheme using superpositions of Bell-states and its NMR implementation

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Science china(Physics,Mechanics & Astronomy) 2005年第1期48卷 57-67页

作者： ZHANG Jingfu, XIE Jingyi, DENG Zhiwei & LU Zhiheng Key Laboratory for Quantum Information and Measurements, department of Physics, tsinghua university, beijing 1.0084, china Center for Quantum Information, tsinghua university, beijing 1.0084, china department of Materials Science and Engineering, beijing Normal university, beijing 100875, china Testing and Analytical Center, beijing Normal university, beijing 100875, china department of Physics, beijing Normal university, beijing 100875, china 1. Key Laboratory for Quantum Information and Measurements Department of Physics Tsinghua University 100084 Beijing China 2. Center for Quantum Information Tsinghua University 100084 Beijing China 3. department of Materials Science and Engineering Beijing Normal University 100875 Beijing China 4. Testing and Analytical Center Beijing Normal University 100875 Beijing China 5. department of Physics Beijing Normal University 100875 Beijing China

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR)quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.

关键词： dense coding, superpositions of Bell-states, generalized Grover's algorithm, nuclear magnetic res-onance, quantum computer.

Investigation on extremal and critical characteristics of ignition time for H_2/O_2 combustion system and their applications

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Science china(Technological Sciences) 2009年第5期52卷 1161-1166页

作者： CHEN JianHua1,ZHANG HuiQiang2,LI ZhuoYi2 & ZHANG GuiTian1 1 School of Aerospace,North Western Polytechnical university,Xi’an 710072,china 2.department of Engineering Mechanics,tsinghua university,beijing 1.0084,china School of Aerospace North Western Polytechnical University Xi’an 710072 China department of Engineering Mechanics Tsinghua University Beijing 100084 China

The L,H and C curves in P-T phase are proposed to describe the minimal,maximal and critical char-acteristics of ignition time of H2/O2 combustion system,*** features of H2/O2(Air) com-bustion system,including explosion or not as well as the time delay to achieve its explosion status,can be well shown by explosion limits and these proposed *** curves can be described by 1.2k1=ks[Ms],(k11/k10+1)k1=ks[Ms],and 2k1=ks[Ms],respectively,which provide a physical explanation for these curves and give another way to establish *** on the contour of ignition time,the Z-type explosion limits can be explained by thermal explosion ***,the ignition distance of supersonic combustion is predicted according to the ignition time obtained in a Semenov system,which is very reasonable.

关键词： ignition time thermal explosion detailed reaction mechanism Semenov system supersonic combustion