This paper introduces a practical solving scheme of gradetransition trajectory optimization(GTTO) problems under typical certificate-checking–updating framework. Due to complicated kinetics of polymerization,differen...This paper introduces a practical solving scheme of gradetransition trajectory optimization(GTTO) problems under typical certificate-checking–updating framework. Due to complicated kinetics of polymerization,differential/algebraic equations(DAEs) always cause great computational burden and system non-linearity usually makes GTTO non-convex bearing multiple optima. Therefore, coupled with the three-stage decomposition model, a three-section algorithm of dynamic programming(TSDP) is proposed based on the general iteration mechanism of iterative programming(IDP) and incorporated with adaptivegrid allocation scheme and heuristic modifications. The algorithm iteratively performs dynamic programming with heuristic modifications under constant calculation loads and adaptively allocates the valued computational resources to the regions that can further improve the optimality under the guidance of local error estimates. TSDP is finally compared with IDP and interior point method(IP) to verify its efficiency of computation.展开更多
An algorithm for precisely calculating the inductance of a three-section solenoid is presented, which is based on summing the layer self-inductances and the mutual inductances. A theoretical model with ex plicit expre...An algorithm for precisely calculating the inductance of a three-section solenoid is presented, which is based on summing the layer self-inductances and the mutual inductances. A theoretical model with ex plicit expressions is firstly developed to calculate the self-inductance of a single layer, and then numerical calcu lation of the mutual inductance between two layers is introduced. Using the presented computation method, the inductance of a solenoid designed in the experiment is successfully calculated （4.30 mH）, which has a difference of less than 1% from the experimental data.展开更多
By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the dis...By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the distribution of eddy transfer coefficient k is divided into three sections:k_1z(z_0≤z<h_1),k_2(h_1≤z<h_2), and k_3(h_2≤z).The results are in agreement with the observations.In particular,the wind profile in the surface layer(z_0≤z<h_1)coincides with the logarithmic distribution.The maximum angle between winds near the surface and at the bottom of the free atmosphere is only about 30°.This work improves the work of Wu and Blumen(1982)who introduced the geostrophic momentum approximation to the boundary layer.The solutions in barotropic and neutral conditions have been also extended to the baroclinic and stratified atmosphere.展开更多
基金Supported by the National Basic Research Program of China(2012CB720500)the National High Technology Research and Development Program of China(2013AA040702)
文摘This paper introduces a practical solving scheme of gradetransition trajectory optimization(GTTO) problems under typical certificate-checking–updating framework. Due to complicated kinetics of polymerization,differential/algebraic equations(DAEs) always cause great computational burden and system non-linearity usually makes GTTO non-convex bearing multiple optima. Therefore, coupled with the three-stage decomposition model, a three-section algorithm of dynamic programming(TSDP) is proposed based on the general iteration mechanism of iterative programming(IDP) and incorporated with adaptivegrid allocation scheme and heuristic modifications. The algorithm iteratively performs dynamic programming with heuristic modifications under constant calculation loads and adaptively allocates the valued computational resources to the regions that can further improve the optimality under the guidance of local error estimates. TSDP is finally compared with IDP and interior point method(IP) to verify its efficiency of computation.
文摘An algorithm for precisely calculating the inductance of a three-section solenoid is presented, which is based on summing the layer self-inductances and the mutual inductances. A theoretical model with ex plicit expressions is firstly developed to calculate the self-inductance of a single layer, and then numerical calcu lation of the mutual inductance between two layers is introduced. Using the presented computation method, the inductance of a solenoid designed in the experiment is successfully calculated （4.30 mH）, which has a difference of less than 1% from the experimental data.
文摘By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the distribution of eddy transfer coefficient k is divided into three sections:k_1z(z_0≤z<h_1),k_2(h_1≤z<h_2), and k_3(h_2≤z).The results are in agreement with the observations.In particular,the wind profile in the surface layer(z_0≤z<h_1)coincides with the logarithmic distribution.The maximum angle between winds near the surface and at the bottom of the free atmosphere is only about 30°.This work improves the work of Wu and Blumen(1982)who introduced the geostrophic momentum approximation to the boundary layer.The solutions in barotropic and neutral conditions have been also extended to the baroclinic and stratified atmosphere.
