For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transfor...For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determining equations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.展开更多
The fidelity scheme of physical conservation laws has been applied in the dynamic framework of a global spectral model. In this study, a set of diabatic physical processes are also involved. Based on six 30-day numeri...The fidelity scheme of physical conservation laws has been applied in the dynamic framework of a global spectral model. In this study, a set of diabatic physical processes are also involved. Based on six 30-day numerical integrations of real-time data, we show that the full model is able to reproduce the primary features of global energy cycle and hydrological distribution. Additionally, the root-mean-square error is dramatically decreased when diabatic processes are considered. Another advantage is that the false structure of ＂double Intertropical Convergence Zone （ITCZ）＂ is not seen in the result, although the orecioitation rate becomes lower.展开更多
文摘For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determining equations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China under Grant Nos. 40775067 and 40475026
文摘The fidelity scheme of physical conservation laws has been applied in the dynamic framework of a global spectral model. In this study, a set of diabatic physical processes are also involved. Based on six 30-day numerical integrations of real-time data, we show that the full model is able to reproduce the primary features of global energy cycle and hydrological distribution. Additionally, the root-mean-square error is dramatically decreased when diabatic processes are considered. Another advantage is that the false structure of ＂double Intertropical Convergence Zone （ITCZ）＂ is not seen in the result, although the orecioitation rate becomes lower.
