By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations ...By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm.Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.展开更多
Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplificat...Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear（2＋1）-dimensional displacement shallow water wave equation（FN2DDSWWE）. The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.展开更多
Based on Lee-Low-Pines(LLP) unitary transformation, this article adopts the variational method of the Pekar type and gets the energy and wave functions of the ground state and the first excited state of strong-couplin...Based on Lee-Low-Pines(LLP) unitary transformation, this article adopts the variational method of the Pekar type and gets the energy and wave functions of the ground state and the first excited state of strong-coupling bipolaron in two-dimensional quantum dot in electric field, thus constructs a bipolaron qubit. The numerical results represent that the time oscillation period T0 of probability density of the two electrons in qubit decreases with the increasing electric field intensity F and dielectric constant ratio of the medium η; the probability density Q of the two electrons in qubit oscillates periodically with the increasing time t; the probability of electron appearing near the center of the quantum dot is larger, while that appearing away from the center of the quantum dot is much smaller.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11472124,11572145,11202090,and 11301350)the Doctor Research Start-up Fund of Liaoning Province,China(Grant No.20141050)+1 种基金the China Postdoctoral Science Foundation(Grant No.2014M560203)the General Science and Technology Research Plans of Liaoning Educational Bureau,China(Grant No.L2013005)
文摘By using the discrete variational method,we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework,and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm.Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11272076 and 51609034)China Postdoctoral Science Foundation(Grant No.2016M590219)
文摘Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear（2＋1）-dimensional displacement shallow water wave equation（FN2DDSWWE）. The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.
基金supported by the Natural Science Foundation of Hebei Province(No.E2013407119)the Items of Institution of Higher Education Scientific Research of Hebei Province(Nos.ZD20131008 and Z2015149)
文摘Based on Lee-Low-Pines(LLP) unitary transformation, this article adopts the variational method of the Pekar type and gets the energy and wave functions of the ground state and the first excited state of strong-coupling bipolaron in two-dimensional quantum dot in electric field, thus constructs a bipolaron qubit. The numerical results represent that the time oscillation period T0 of probability density of the two electrons in qubit decreases with the increasing electric field intensity F and dielectric constant ratio of the medium η; the probability density Q of the two electrons in qubit oscillates periodically with the increasing time t; the probability of electron appearing near the center of the quantum dot is larger, while that appearing away from the center of the quantum dot is much smaller.
