Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear...Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.展开更多
This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than one.The value ...This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than one.The value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel functions.Strong consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the system.Thenumerical simulation is consistent with the theoretical analysis.展开更多
The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of t...The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.展开更多
基金supported by the National Science Foundation(No. DMS-0915066)
文摘Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.
基金supported by the National Natural Science Foundation of China under Grant Nos. 60821091and 60874001Grant from the National Laboratory of Space Intelligent ControlGuozhi Xu Posdoctoral Research Foundation
文摘This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than one.The value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel functions.Strong consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the system.Thenumerical simulation is consistent with the theoretical analysis.
基金supported by a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Programme(No. MTKD-CT-2004-013389)
文摘The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.
