The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive m...The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.展开更多
Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice method...Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.展开更多
The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the co...The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.展开更多
文摘The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
基金co-supported by the National Natural Science Foundation of China(No.51375104)the Heilongjiang Province Funds for Distinguished Young Scientists(No.JC201405)+1 种基金the China Postdoctoral Science Foundation(No.2015M581433)the Postdoctoral Science Foundation of Heilongjiang Province(No.LBH-Z15038)
文摘Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.
基金supported by the National Natural Science Foundation of China(Grant No.11302110)the Public Project of Science and Technology Department of Zhejiang Province(Grant No.2015C31152)+1 种基金the Natural Science Foundation of Ningbo(Grant No.2014A610086)“Wang Weiming”Entrepreneurship Supporting Fund
文摘The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.
