In this paper,we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes.We introduce a new nonlinear app...In this paper,we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes.We introduce a new nonlinear approach to construct the conservative flux,that is,a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method.Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns,so it can deal with the problem with general discontinuous coefficients.Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.展开更多
In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys....In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.展开更多
A new algorithm called homotopy iteration method based on the homotopy function is studied and improved. By the improved homotopy iteration method, Polynomial systems with high Order and deficient can be solved fast a...A new algorithm called homotopy iteration method based on the homotopy function is studied and improved. By the improved homotopy iteration method, Polynomial systems with high Order and deficient can be solved fast and efficiently comparing to the original homotopy iteration method. Numerical examples for the ninepoint path synthesis of four-bar linkages show the advantages and efficiency of the improved homotopy iteration method.展开更多
A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended i...A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.展开更多
This paper sets up a framework for analyzing the policies of the US and the People＇s Republic of China toward the Republic of China （Taiwan）. It surveys how the two powers＇ policies have evolved during the period ...This paper sets up a framework for analyzing the policies of the US and the People＇s Republic of China toward the Republic of China （Taiwan）. It surveys how the two powers＇ policies have evolved during the period 1949-2009 and makes numerical evaluations of the degree of ＂supportiveness＂ of American policy toward the ROC and the degree of ＂aggressiveness＂ of the PRC＇s policies. The evaluations are charted. The paper observes that the US and the PRC have been engaged in a kind of ＂ negotiation-by-move-and-countermove＂ over this period. This form of interaction is found to be slow-motion and not very effective for resolving differences between the two sides. However, the need for a formal resolution of the island＇s political-legal status becomes less important as the trade, investment, and people-to-people linkages between the two Chinese entities increase. There appears to be a huge potential for an ever-greater convergence of the two powers＇ economic desires for Taiwan even while the issue of their respective stances towards its legal-political-military status may not be resolved for quite a while.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11971069,12071045)the Scientific Research Foundation of NUAA No.YAH21109.
文摘In this paper,we construct a new cell-centered nonlinear finite volume scheme that preserves the extremum principle for heterogeneous anisotropic diffusion equation on distorted meshes.We introduce a new nonlinear approach to construct the conservative flux,that is,a linear second order flux is firstly given and a nonlinear conservative flux is then constructed by using an adaptive method and a nonlinear weighted method.Our new scheme does not need to use the convex combination of the cell-center unknowns to approximate the auxiliary unknowns,so it can deal with the problem with general discontinuous coefficients.Numerical results show that our new scheme performs more robust than some existing schemes on highly distorted meshes.
基金supported by the Science and Technology Development foundation of China Academy of Engineering Physics(Grant Nos.2015B0202041,2015B0202040)the Science and Technology Development foundation of China Academy of Engineering Physics(Grant 2015B0202040)+2 种基金the Science and Technology Development foundation of China Academy of Engineering Physics(Grant No.2015B0202033)for LiNSFC(Grant No.11371068)for SunNSFC(Grant No.11371068)for Zeng
文摘In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.
文摘A new algorithm called homotopy iteration method based on the homotopy function is studied and improved. By the improved homotopy iteration method, Polynomial systems with high Order and deficient can be solved fast and efficiently comparing to the original homotopy iteration method. Numerical examples for the ninepoint path synthesis of four-bar linkages show the advantages and efficiency of the improved homotopy iteration method.
基金supported by the National Natural Science Foundation of China (No. 10772051)the ScienceFoundation for the Excellent Youth Scholars of Higher Education of Shanghai (No. 571215)the Research Fund for the Doctoral Program of University of Shanghai for Science and Technology(No. 10D214)
文摘A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.
文摘This paper sets up a framework for analyzing the policies of the US and the People＇s Republic of China toward the Republic of China （Taiwan）. It surveys how the two powers＇ policies have evolved during the period 1949-2009 and makes numerical evaluations of the degree of ＂supportiveness＂ of American policy toward the ROC and the degree of ＂aggressiveness＂ of the PRC＇s policies. The evaluations are charted. The paper observes that the US and the PRC have been engaged in a kind of ＂ negotiation-by-move-and-countermove＂ over this period. This form of interaction is found to be slow-motion and not very effective for resolving differences between the two sides. However, the need for a formal resolution of the island＇s political-legal status becomes less important as the trade, investment, and people-to-people linkages between the two Chinese entities increase. There appears to be a huge potential for an ever-greater convergence of the two powers＇ economic desires for Taiwan even while the issue of their respective stances towards its legal-political-military status may not be resolved for quite a while.
