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A Hierarchy of Multidimensional Hénon-Heiles Systems

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Acta Mathematica Sinica,English Series 2000年第3期16卷 527-534页

作者： Yunbo Zeng dep.r.ment of Mathematical Sciences,tsinghua university,beijing 100084 P.r.china dep.r.ment of Mathematical Sciences Tsinghua University Bejing 100084 P. R. China

A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV *** Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV *** using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed.

关键词： Higher-order constrained flow Multidimensional Hénon-Heiles systems Lax representation Jacobi inversion problem

Multi-swingby optimization of mission to Saturn using global optimization algorithms

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Acta Mechanica Sinica 2009年第6期25卷 839-845页

作者： Kaijian Zhu Junfeng Li Hexi Baoyin School of Aerospace, tsinghua university,100084 beijing, china School of Aerospace Tsinghua University 100084 Beijing China

Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories ofEJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms： DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be supe- rior to other non-hybrid algorithms in the trajectory optimi- zation problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is vali- dated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.

关键词： Swingby trajectory . Global optimization .Hybrid algorithm . Mission design

Thermodynamic Significance of Human Basal Metabolism

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Journal of Thermal Science 1993年第2期2卷 81-86页

作者： Wang Cuncheng Thermal Engineering dep.r.ment tsinghua university, beijing 100084, P.r. china 1. Thermal Engineering dep.r.ment tsinghua university 100084 Beijing P.R. China

The human basal state,a non-equilibrium steady state,is analysed in this paper in the light of the First and Second Laws of Thermodynamics whereby the thermodynamic significance of the basal metabolic rate and its distinction to the dissipation function and exergy loss are *** analysis demonstrates the correct expression of the effects of the blood flow on the heat balance in a human-body bio-heat model and the relationship between the basal metabolic rate and the blood perfusion.

关键词： thermodynamic laws basal metabolism blood perfusion dissipation function exergy loss

Explicit Classification for Torsion Subgroups of rational Points of Elliptic Curves

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Acta Mathematica Sinica,English Series 2002年第3期18卷 539-548页

作者： De rong QIU Center for Advanced Study, tsinghua university, beijing 100084. P. r. china Xian Ke ZHANG dep.r.ment of Mathematical Sciences, tsinghua university, beijing 100084, P. r. china Center for Advanced Study Tsinghua University Beijing P. R. China dep.r.ment of Mathematical Sciences Tsinghua University Beijing P. R. China

We study the classification of elliptic curves E over the rationals Q according to the torsion subgroups E_(tors)(Q). More precisely, we classify those elliptic curves with E_(tors)(Q) being cyclic with even orders. We also give explicit formulas for generators of E_(tors)(Q). These results, together with the recent results of K. Ono for the non-cyclic E_(tors)(Q), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.

关键词： Elliptic curve rational point Torsion group Mordell group Parameterization

Modeling of Mold Filling and Solidification in Lost Foam Casting

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Journal of Materials Science & Technology 2003年第5期19卷 395-397页

作者： Fengjun LI, Houfa SHEN and Baicheng LIUdep.r.ment of Mechanical Engineering, tsinghua university, beijing 100084, china dept. of Mech. Eng. Tsinghua Univ. Beijing 100084 China

Based on the characteristics of the lost foam casting (LFC) and the artificial neural network technique, a mathematical model for the simulation of the melt-pattern interface movement during the mold filling of LFC has been proposed and experimentally verified. The simulation results are consistent with the experiments in both the shapes of melt front and filling sequences. According to the calculated interface locations, the fluid flow and the temperature distributions during the mold filling and solidification processes were calculated, and the shrinkage defect of a lost foam ductile iron casting was predicted by considering the mold wall movement in LFC. The simulation method was applied to optimize the casting design of lost foam ductile iron castings. It is shown that the model can be used for the defects prediction and for casting design optimization in the practical LFC production.

关键词： Lost foam casting Numerical simulation Artificial neural network

3D Stochastic Modeling of Grain Structure for Aluminum Alloy Casting

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Journal of Materials Science & Technology 2003年第5期19卷 391-394页

作者： Qingyan XU, Weiming FENG and Baicheng LIUdep.r.ment of Mechanical Engineering, tsinghua university, beijing 100084, china dept. of Mech. Eng. Tsinghua Univ. Beijing 100084 China

A 3D stochastic modeling was carried out to simulate the dendritic grains during solidification of aluminum alloys, including time-dependent calculations for temperature field, solute redistribution in liquid, curvature of the dendritic tip, and growth anisotropy. The nucleation process was treated by continuous nucleation. A 3D simplified grain shape model was established to represent the equiaxed dendritic grain. Based on the Cellular Automaton method, a grain growth model was proposed to capture the neighbor cells of the nucleated cell. During growing, each grain continues to capture the nearest neighbor cells to form the final shape. When a neighbor cell was captured by other grains, the grain growth along this direction would be stopped. Three-dimensional calculations were performed to simulate the evolution of dendritic grain. In order to verify the modeling results, the predictions were compared with the observation on samples cast in the sand mold and the metal mold.

关键词： 3D stochastic modeling Nucleation Grain growth

A scheme to implement the Deutsch-Josza algorithm on a superconducting charge-qubit quantum computer

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Progress in Natural Science:Materials International 2006年第6期16卷 594-599页

作者： HUO Wenyi and LONG Guilu (Key Laboratory for Quantum Information and Measurements, and dep.r.ment of Physics, tsinghua university, beijing 100084, china Key Laboratory for Atomic and Molecular NanoSciences, tsinghua university, beijing 100084, china) [a]Key Laboratory for Quantum Information and Measurements and Department of Physics Tsinghua University Bejjing China [b]Key Laboratory for Atomic and Molecular NanoSciences Tsinghua University Bejing China

We have studied the implementation of the Deutsch-Josza quantum algorithm in a superconducting charge-qubit quantum computer. Different from previous studies, we have used the inductance coupled system of You et al. The detailed pulse sequences have been designed for the four possible functions in a 2-qubit system. The result is generalized to an arbitrary n-qubit system. This scheme will be useful for practical implementation of the algorithm.

关键词： superconducting quantum computer Deutsch-Josza algorithm.

Modularity of Calabi-Yau varieties and conformal field theory

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Science china Mathematics 2008年第6期51卷 1135-1146页

作者： TAN FuCheng dep.r.ment of Mathematical Sciences,tsinghua university,beijing 100084,china dep.r.ment of Mathematical Sciences Tsinghua University Beijing 100084 China

We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of *** express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.

关键词： L-function Calabi-Yau variety Gepner model 53C80

Numerical Simulation of Microporosity Evolution of Aluminum Alloy Castings

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Journal of Materials Science & Technology 2004年第1期20卷 23-26页

作者： Shuyong DONG, Shoumei XIONG and Baicheng LIUdep.r.ment of Mechanical Engineering, tsinghua university, beijing 100084, china dept. of Mech. Eng. Tsinghua Univ. Beijing 100084 China

A mathematical model to calculate the size and distribution of microporosities was studied and coupled with a stochastic microstructure evolution model. The model incorporates various solidification phenomena such as grain structure evolution, solidification shrinkage, interdendritic fluid flow and formation and growth of pores during solidification processes. The nucleation and growth of grains were modeled with a cellular automaton method that utilizes the results from a macro scale modeling of the solidification process. Experiments were made to validate the proposed models. The calculated results of aluminum alloy castings agreed with the experimental measurements.

关键词： Numerical simulation Microporosity evolution Aluminum alloy castings