In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predi...In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup {S}(n>0) is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991).展开更多
Marine mobile buoy（MMB） have many potential applications in the maritime industry and ocean science.Great progress has been made,however the technology in this area is far from maturity in theory and faced with many...Marine mobile buoy（MMB） have many potential applications in the maritime industry and ocean science.Great progress has been made,however the technology in this area is far from maturity in theory and faced with many difficulties in application.A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB,especially with consideration of hydrodynamic force.The principle of wave-driven propulsion mechanism is briefly introduced.To set a theory foundation for study on the MMB,a dynamic model of the propulsion mechanism of the MMB is obtained.The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations.A simplified form of the motion equations is reached by omitting terms with high order small values.The relationship among the heave motion of the buoy,stiffness of the elastic components,and the forward speed can be obtained by using these simplified equations.The dynamic analysis show the following：The angle of displacement of foil is fairly small with the biggest value around 0.3 rad;The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy;The relationship among heaven motion,stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle,therefore,the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant.The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.展开更多
文摘In this paper, a mean-field equation of motion which is derived by Penrose (1991) for the dynamic Ising model with Glauber dynamics is considered. Various finite difference schemes such as explicit Euler scheme, predictor-corrector scheme and some implicit schemes are given and their convergence, stabilities and dynamical properties are discussed. Moreover, a Lyapunov functional for the discrete semigroup {S}(n>0) is constructed. Finally, numerical examples are computed and analyzed. it shows that the model is a better approximation to Cahn-Allen equation which is mentioned in Penrose (1991).
基金Supported by National Natural Science Foundation of China(Grant No.51175484)Program for New Century Excellent Talents in University,China(Grant No.NCET-12-0500)+1 种基金Program of Introducing Talents of Discipline to Universities,China(Grant No.B14028)Fundamental Research Funds for the Central Universities,China(Grant No.841513053)
文摘Marine mobile buoy（MMB） have many potential applications in the maritime industry and ocean science.Great progress has been made,however the technology in this area is far from maturity in theory and faced with many difficulties in application.A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB,especially with consideration of hydrodynamic force.The principle of wave-driven propulsion mechanism is briefly introduced.To set a theory foundation for study on the MMB,a dynamic model of the propulsion mechanism of the MMB is obtained.The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations.A simplified form of the motion equations is reached by omitting terms with high order small values.The relationship among the heave motion of the buoy,stiffness of the elastic components,and the forward speed can be obtained by using these simplified equations.The dynamic analysis show the following：The angle of displacement of foil is fairly small with the biggest value around 0.3 rad;The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy;The relationship among heaven motion,stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle,therefore,the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant.The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.
