针对 TiAl 基合金的显微组织控制,综述了 TiAl 基合金中几种常见的组织演变,着重论述了变形 TiAl基合金在热处理过程中的晶拉长大及动力学分析,TiAl 基合盒在冷却时层状组织的形成和全层状 TiAl 基合盒在高温时的非连续粗化这3种组织演...针对 TiAl 基合金的显微组织控制,综述了 TiAl 基合金中几种常见的组织演变,着重论述了变形 TiAl基合金在热处理过程中的晶拉长大及动力学分析,TiAl 基合盒在冷却时层状组织的形成和全层状 TiAl 基合盒在高温时的非连续粗化这3种组织演变的研究现状和面临的问题。展开更多
As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many o...As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.展开更多
The three-dimensional discontinuous deformation analysis(3D-DDA) is a promising numerical method for both static and dynamic analyses of rock systems. Lacking mature software, its popularity is far behind its ability....The three-dimensional discontinuous deformation analysis(3D-DDA) is a promising numerical method for both static and dynamic analyses of rock systems. Lacking mature software, its popularity is far behind its ability. To address this problem, this paper presents a new software architecture from a software engineering viewpoint. Based on 3D-DDA characteristics, the implementation of the proposed architecture has the following merits. Firstly, the software architecture separates data, computing, visualization, and signal control into individual modules. Secondly, data storage and parallel access are fully considered for different conditions. Thirdly, an open computing framework is provided which supports most numerical computing methods; common tools for equation solving and parallel computing are provided for further development. Fourthly, efficient visualization functions are provided by integrating a variety of visualization algorithms. A user-friendly graphical user interface is designed to improve the user experience. Finally, through a set of examples, the software is verified against both analytical solutions and the original code by Dr. Shi Gen Hua.展开更多
H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius＇s gradient estimate. If the coefficients are piecewise smooth and the homogeniz...H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius＇s gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O（e） in the HSlder norm; it is O（e） in W1,∞ based on the Avellaneda-Lin＇s gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.展开更多
基金Supported by National Natural Science Foundation of China (No.10871144)the Seed Foundation of Tianjin University (No.60302023)
文摘As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.
基金supported by the National Natural Science Foundation of China(Grant No.61471338)the Knowledge Innovation Program of the Chinese Academy of Sciences,Youth Innovation Promotion Association CAS,President Fund of UCASCRSRI Open Research Program(Grant No.CKWV2015217/KY)
文摘The three-dimensional discontinuous deformation analysis(3D-DDA) is a promising numerical method for both static and dynamic analyses of rock systems. Lacking mature software, its popularity is far behind its ability. To address this problem, this paper presents a new software architecture from a software engineering viewpoint. Based on 3D-DDA characteristics, the implementation of the proposed architecture has the following merits. Firstly, the software architecture separates data, computing, visualization, and signal control into individual modules. Secondly, data storage and parallel access are fully considered for different conditions. Thirdly, an open computing framework is provided which supports most numerical computing methods; common tools for equation solving and parallel computing are provided for further development. Fourthly, efficient visualization functions are provided by integrating a variety of visualization algorithms. A user-friendly graphical user interface is designed to improve the user experience. Finally, through a set of examples, the software is verified against both analytical solutions and the original code by Dr. Shi Gen Hua.
基金supported by National Natural Science Foundation of China (Grant No.90916027)Special Funds for National Basic Research Program of China (973 Program) (Grant No. 2010CB832702)the State Key Laboratory of Scientific and Engineering Computing
文摘H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius＇s gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O（e） in the HSlder norm; it is O（e） in W1,∞ based on the Avellaneda-Lin＇s gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.
