Let G =(V, E) be a locally finite connected weighted graph, and ? be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ?u + f(u) on G. The blow-up p...Let G =(V, E) be a locally finite connected weighted graph, and ? be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ?u + f(u) on G. The blow-up phenomenons for ut = ?u + f(u) are discussed in terms of two cases:(i) an initial condition is given;(ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.展开更多
Due to the large error of the traditional battery theoretical model during large-rate discharge for electromagnetic launch,the Shepherd derivative model considering the factors of the pulse cycle condition,temperature...Due to the large error of the traditional battery theoretical model during large-rate discharge for electromagnetic launch,the Shepherd derivative model considering the factors of the pulse cycle condition,temperature,and life is proposed by the Naval University of Engineering.The discharge rate of traditional lithium-ion batteries does not exceed 10C,while that for electromagnetic launch reaches 60C.The continuous pulse cycle condition of ultra-large discharging rate causes many unique electrochemical reactions inside the cells.The traditional model cannot accurately describe the discharge characteristics of the battery.The accurate battery theoretical model is an important basis for system efficiency calculation,precise discharge control,and remaining capacity prediction.To this purpose,an experimental platform for electromagnetic launch is built,and discharge characteristics of the battery under different rate,temperature,and life decay are measured.Through the experimental test and analysis,the reason that the traditional model cannot accurately characterize the large-rate discharge process is analyzed.And a novel battery theoretical model is designed with the help of genetic algorithm,which is integrated with the electromagnetic launch topology.Numerical simulation is compared with the experimental results,which verifies the modeling accuracy for the large-rate discharge.On this basis,a variety of discharge conditions are applied to test the applicability of the model,resulting in better results.Finally,with the continuous cycle-pulse condition in the electromagnetic launch system,the stability and accuracy of the model are confirmed.展开更多
基金supported by the National Science Foundation of China(11671401)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(17XNH106)
文摘Let G =(V, E) be a locally finite connected weighted graph, and ? be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ?u + f(u) on G. The blow-up phenomenons for ut = ?u + f(u) are discussed in terms of two cases:(i) an initial condition is given;(ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.
基金This study was supported by the National Natural Science Foundation of China(Nos.51607187,51877214,51907203,51925704,and 52107235)the Hubei Provincial Natural Science Foundation of China(Nos.2019CFB371 and 2019CFB373)partially by No.12 Special Financial 349 Aid to China Postdoctoral Science Foundation(No.2019T120972).
文摘Due to the large error of the traditional battery theoretical model during large-rate discharge for electromagnetic launch,the Shepherd derivative model considering the factors of the pulse cycle condition,temperature,and life is proposed by the Naval University of Engineering.The discharge rate of traditional lithium-ion batteries does not exceed 10C,while that for electromagnetic launch reaches 60C.The continuous pulse cycle condition of ultra-large discharging rate causes many unique electrochemical reactions inside the cells.The traditional model cannot accurately describe the discharge characteristics of the battery.The accurate battery theoretical model is an important basis for system efficiency calculation,precise discharge control,and remaining capacity prediction.To this purpose,an experimental platform for electromagnetic launch is built,and discharge characteristics of the battery under different rate,temperature,and life decay are measured.Through the experimental test and analysis,the reason that the traditional model cannot accurately characterize the large-rate discharge process is analyzed.And a novel battery theoretical model is designed with the help of genetic algorithm,which is integrated with the electromagnetic launch topology.Numerical simulation is compared with the experimental results,which verifies the modeling accuracy for the large-rate discharge.On this basis,a variety of discharge conditions are applied to test the applicability of the model,resulting in better results.Finally,with the continuous cycle-pulse condition in the electromagnetic launch system,the stability and accuracy of the model are confirmed.