In this paper, we introduce new invariant sets, and the invariant sets and exact solutions to general reactiondiffusion equation are discussed. It is shown that there exist a class of exact solutions to the equations ...In this paper, we introduce new invariant sets, and the invariant sets and exact solutions to general reactiondiffusion equation are discussed. It is shown that there exist a class of exact solutions to the equations that belong to the invariant sets.展开更多
The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volu...The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing （TVD） Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure （LWDG） based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.展开更多
The analysis of accuracy for superposition of squeezed states （SSSs） in lossless and loss case has been performed in this study. In lossless case, time accuracies of SSSs with mean photon number ns have a scaling of...The analysis of accuracy for superposition of squeezed states （SSSs） in lossless and loss case has been performed in this study. In lossless case, time accuracies of SSSs with mean photon number ns have a scaling of ns-2 in two limits of large and small squeezing. With the help of photon loss model, the dissipative channel will degrade accuracies has been proved. In the limit of large squeezing, the accuracy will slowly decrease with the reduction of transmittance η. In the limit of small squeezing, time accuracy scales as 1/（η4n2） and will decrease much faster along with η decreases.展开更多
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030 and 10502042the Natural Science Foundation of Shanxi Province under Grant No.2003A03
文摘In this paper, we introduce new invariant sets, and the invariant sets and exact solutions to general reactiondiffusion equation are discussed. It is shown that there exist a class of exact solutions to the equations that belong to the invariant sets.
基金supported by the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations,NSFC grant 10671091,SRF for ROCS,SEM and JSNSF BK2006511.
文摘The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing （TVD） Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure （LWDG） based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.
基金supported by the National Natural Science Foundation of China (Grant No. 61075014)the Science Foundation of Xi’an University of Posts and Telecommunications for Young Teachers (Grant No.ZL2010-11)the Science Foundation of Shaanxi Provincial Department of Education (Grant No. 11JK0902)
文摘The analysis of accuracy for superposition of squeezed states （SSSs） in lossless and loss case has been performed in this study. In lossless case, time accuracies of SSSs with mean photon number ns have a scaling of ns-2 in two limits of large and small squeezing. With the help of photon loss model, the dissipative channel will degrade accuracies has been proved. In the limit of large squeezing, the accuracy will slowly decrease with the reduction of transmittance η. In the limit of small squeezing, time accuracy scales as 1/（η4n2） and will decrease much faster along with η decreases.
