The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first repor...The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.展开更多
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method an...We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.展开更多
The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is propose...The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is proposed for DSR calculation in power injection space. The method identifies coherent generation groups by the developed K-medoids algorithm, taking a similarity matrix derived from the reachability Grammian as the index. As an experimental result, reachability Grammian matrices under local injections are approximately invariant. It indicates that the generator coherency identifications are nearly consistent for different injections. Then instability separation modes can be predicted at the normal operating point, while average initial acceleration is considered as the measure of the critical generator group to amend the error. Moreover, based on these predicted instability separation modes, a critical point search strategy for DSR calculation is illustrated in the reduced injection space of the critical generators. The proposed method was evaluated using New England Test System, and the computation accuracy and speed in determining the practical DSR were improved.展开更多
A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For ...A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For the balancing problem for the scenario-based robust assembly line with a finitely large number of potential scenarios, the direct solution methodology considering all potential scenarios is quite time-consuming. A scenario relaxation algorithm that embeds genetic al- gorithm is developed. This new algorithm guarantees termination at an optimal robust solution with relatively short running time, and makes it possible to solve robust problems with large quantities of potential scenarios. Extensive computational results are reported to show the efficiency and effectiveness of the proposed algorithm.展开更多
This article focuses on the study of stability of motion of the phase systems described by differential equations whose right-hand sides are periodic in the angular coordinate. The article deals with the mathematical ...This article focuses on the study of stability of motion of the phase systems described by differential equations whose right-hand sides are periodic in the angular coordinate. The article deals with the mathematical model which has been investigated for stability ＂in the large＂ using the second Lyapunov method. Based on the theoretical results obtained in the work,the computational experiments on concrete examples of electric power systems, which showedthe sufficient efficacy of the proposed method for the studied phase system, were conducted.展开更多
A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a sy...A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a systematic parallel decompositionof the problem (related to arbitrarily overlapping decomposition of domains) and on a penaltyargument.SPA is presented here for the case of linear parabolic equations, with distributed or boundarycontrol. It extends to practically all linear and non linear evolution equations, as it will bepresented in several other publications.展开更多
文摘The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.
基金supported by National Natural Science Foundation of China under Grant No. 1057400the Natural Science Foundation of Heilongjiang Province under Grant No. A200506
文摘We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.
基金Supported by National Natural Science Foundation of China (No.50595413)Special Fund of the National Fundamental Research of China(No.2004CB217904)+4 种基金US EPRI under Agreement EP-P29464/C9966Foundation for the Author of National Excellent Doctoral Disserta-tion (No.200439)Key Project of Ministry of Education of China(No.105047)Program for New Century Excellent Talents in University,Fok Ying Tung Education Foundation (No.104019)Innovation Fund of Tianjin Municipal (2006-09)
文摘The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is proposed for DSR calculation in power injection space. The method identifies coherent generation groups by the developed K-medoids algorithm, taking a similarity matrix derived from the reachability Grammian as the index. As an experimental result, reachability Grammian matrices under local injections are approximately invariant. It indicates that the generator coherency identifications are nearly consistent for different injections. Then instability separation modes can be predicted at the normal operating point, while average initial acceleration is considered as the measure of the critical generator group to amend the error. Moreover, based on these predicted instability separation modes, a critical point search strategy for DSR calculation is illustrated in the reduced injection space of the critical generators. The proposed method was evaluated using New England Test System, and the computation accuracy and speed in determining the practical DSR were improved.
基金Supported by the National High Technology Research and Development Programme of China （No. 2006AA04Z160） and the National Natural Science Foundation of China （ No. 60874066）.
文摘A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For the balancing problem for the scenario-based robust assembly line with a finitely large number of potential scenarios, the direct solution methodology considering all potential scenarios is quite time-consuming. A scenario relaxation algorithm that embeds genetic al- gorithm is developed. This new algorithm guarantees termination at an optimal robust solution with relatively short running time, and makes it possible to solve robust problems with large quantities of potential scenarios. Extensive computational results are reported to show the efficiency and effectiveness of the proposed algorithm.
文摘This article focuses on the study of stability of motion of the phase systems described by differential equations whose right-hand sides are periodic in the angular coordinate. The article deals with the mathematical model which has been investigated for stability ＂in the large＂ using the second Lyapunov method. Based on the theoretical results obtained in the work,the computational experiments on concrete examples of electric power systems, which showedthe sufficient efficacy of the proposed method for the studied phase system, were conducted.
文摘A new algorithm for the stabilization or (possibly turbulent, chaotic) distributed systems,governed by linear or non linear systems of equations is presented.The SPA (Stabilization Parallel Algorithm) is based on a systematic parallel decompositionof the problem (related to arbitrarily overlapping decomposition of domains) and on a penaltyargument.SPA is presented here for the case of linear parabolic equations, with distributed or boundarycontrol. It extends to practically all linear and non linear evolution equations, as it will bepresented in several other publications.
