The Effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical fiat plate have been investigated. The results are obtained by transforming the governing system of boundary layer ...The Effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical fiat plate have been investigated. The results are obtained by transforming the governing system of boundary layer equations into a system of non-dimensional equations and by applying implicit finite difference method together with Newton＇s linearization approximation. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction co-efficient and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters.展开更多
The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 2230...The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001 （2015）] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be＋, Mg＋, and Ca＋ in the field strength range of 0.0-6×10-5 a.u.. The scalar and tensor polarizabilities （α0, α2） and hyperpolarizabilities （Y0,Y2, 74） were deduced. The results of the hyperpolarizabilities for Be＋ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities, which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca＋ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca＋ in the optical dipole trap are estimated using quasi-electrostatic approximation.展开更多
文摘The Effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical fiat plate have been investigated. The results are obtained by transforming the governing system of boundary layer equations into a system of non-dimensional equations and by applying implicit finite difference method together with Newton＇s linearization approximation. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction co-efficient and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters.
基金supported by the National Natural Science Foundation of China (Grant No. 91536102)the National Basic Research Program of China (Grant No. 2012CB821305)
文摘The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001 （2015）] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be＋, Mg＋, and Ca＋ in the field strength range of 0.0-6×10-5 a.u.. The scalar and tensor polarizabilities （α0, α2） and hyperpolarizabilities （Y0,Y2, 74） were deduced. The results of the hyperpolarizabilities for Be＋ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities, which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca＋ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca＋ in the optical dipole trap are estimated using quasi-electrostatic approximation.
