For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld inva...For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.展开更多
This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures loc...This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.展开更多
We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories： （I） theoretical, empirical and num...We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories： （I） theoretical, empirical and numerically based models and （Ⅱ） self-consistent multi-dimensional numerical magnetohydrodynamic （MHD） models. The models of Category I are used to sep- arately describe the solar wind solution in two plasma flows regions： transonic/trans-Alfvrnic and supersonic/super-Alfvenic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvrnic region into supersonic/super-Alfvrnic region. The Wang-Sheeley-Arge （WSA）/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme （BATS-R-US） code in SWMF （Space Weather Modeling Framework） and the solar-interplanetary conservative element solution element MHD （SIP-CESE MHD） model in SWIM （Space Weather Integrated Model） are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models＇ prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.展开更多
文摘For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.
文摘This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.
基金Work done by Shi Tsan WU was supported by National Science Foundation of USA(Grant No.AGS 1153323)
文摘We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories： （I） theoretical, empirical and numerically based models and （Ⅱ） self-consistent multi-dimensional numerical magnetohydrodynamic （MHD） models. The models of Category I are used to sep- arately describe the solar wind solution in two plasma flows regions： transonic/trans-Alfvrnic and supersonic/super-Alfvenic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvrnic region into supersonic/super-Alfvrnic region. The Wang-Sheeley-Arge （WSA）/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme （BATS-R-US） code in SWMF （Space Weather Modeling Framework） and the solar-interplanetary conservative element solution element MHD （SIP-CESE MHD） model in SWIM （Space Weather Integrated Model） are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models＇ prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.
