The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of th...The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.展开更多
The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Ham...The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.展开更多
The free-gradient is proposed for cellcentered total variation diminishing finite difference schemes of inviscid aerodynamic equations with high order of accuracy to eradicate the negative effects of the mesh skewness...The free-gradient is proposed for cellcentered total variation diminishing finite difference schemes of inviscid aerodynamic equations with high order of accuracy to eradicate the negative effects of the mesh skewness on the flux limiter. This paper demonstrates that it can satisfies the free-stream and free-gradient simultaneously and keeps the accuracy order of the schemes by assigning the Jacobe of transformation on the cell surfce as 1 for Harten and osher-Chakravarthy schemes. It also shows that Yee-Harten schemes do not satisfy the free-gradient, thus a modification is conducted to make them work better on skewed meshes.展开更多
In this paper we describe how the capacitated user equilibrium can be approximated by sequential uncapacitated models by the use of a penalty function. The efficiency of the method is governed by the algorithmic perfo...In this paper we describe how the capacitated user equilibrium can be approximated by sequential uncapacitated models by the use of a penalty function. The efficiency of the method is governed by the algorithmic performance of the uncapacitated model. A skew gradient-based Newton method is used to solve the capacitated user equilibrium within the feasible region of path flows. In the path-flow region, the straight gradient is defined as the derivative of the objective function with respect to the flow of the corresponding path, while the skew gradient is defined for each particular origin destination pair and is characterized by the average cost of all the paths for that pair. Instead of movement of flow toward the shortest path, in the equilibration procedure path flows below the average decrease and path flows above the average increase. The characteristics of the Newton method with the column generation procedure are combined to achieve the efficient determination of the equilibrium point. Numerical experiments demonstrate the excellent performance of the proposed method and highlight its potential applications.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China(Nos.10932002 and 11272050)
文摘The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.
文摘The free-gradient is proposed for cellcentered total variation diminishing finite difference schemes of inviscid aerodynamic equations with high order of accuracy to eradicate the negative effects of the mesh skewness on the flux limiter. This paper demonstrates that it can satisfies the free-stream and free-gradient simultaneously and keeps the accuracy order of the schemes by assigning the Jacobe of transformation on the cell surfce as 1 for Harten and osher-Chakravarthy schemes. It also shows that Yee-Harten schemes do not satisfy the free-gradient, thus a modification is conducted to make them work better on skewed meshes.
基金Supported by the National Natural Science Foundation of China (No. 50678037)the National Key Basic Research and Development (973) Program of China (No. 2006CB705500)
文摘In this paper we describe how the capacitated user equilibrium can be approximated by sequential uncapacitated models by the use of a penalty function. The efficiency of the method is governed by the algorithmic performance of the uncapacitated model. A skew gradient-based Newton method is used to solve the capacitated user equilibrium within the feasible region of path flows. In the path-flow region, the straight gradient is defined as the derivative of the objective function with respect to the flow of the corresponding path, while the skew gradient is defined for each particular origin destination pair and is characterized by the average cost of all the paths for that pair. Instead of movement of flow toward the shortest path, in the equilibration procedure path flows below the average decrease and path flows above the average increase. The characteristics of the Newton method with the column generation procedure are combined to achieve the efficient determination of the equilibrium point. Numerical experiments demonstrate the excellent performance of the proposed method and highlight its potential applications.
