We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold pertu...We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.展开更多
This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method(EBM) and the iteration perturbation method(IPM).To assess the accuracy of solutions,we...This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method(EBM) and the iteration perturbation method(IPM).To assess the accuracy of solutions,we compare the results with the harmonic balance method(HBM).The obtained results from EBM and IPM are in excellent agreement with HBM results.The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.展开更多
Curved channels are ubiquitous in microfluidic systems.The pressure-driven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under th...Curved channels are ubiquitous in microfluidic systems.The pressure-driven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number.The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer(EDL)potential.The EDL potential at the outer side of the bend is larger than that at the inner side of the bend.The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow.Since the spanwise pressure gradient is dominant over the inertial force,the resulting axial velocity profile is skewed into the inner region of the curved channel.Furthermore,the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section.The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows.Remarkably,the curved geometry could be beneficial to improving the electrokinetic energy conversion(EKEC)efficiency.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11647071)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20160435)
文摘We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.
文摘This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method(EBM) and the iteration perturbation method(IPM).To assess the accuracy of solutions,we compare the results with the harmonic balance method(HBM).The obtained results from EBM and IPM are in excellent agreement with HBM results.The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.
基金Project supported by the National Natural Science Foundation of China(Nos.11902165 and 11772162)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2019BS01004)the Inner Mongolia Grassland Talent of China(No.12000-12102408)。
文摘Curved channels are ubiquitous in microfluidic systems.The pressure-driven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number.The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer(EDL)potential.The EDL potential at the outer side of the bend is larger than that at the inner side of the bend.The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow.Since the spanwise pressure gradient is dominant over the inertial force,the resulting axial velocity profile is skewed into the inner region of the curved channel.Furthermore,the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section.The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows.Remarkably,the curved geometry could be beneficial to improving the electrokinetic energy conversion(EKEC)efficiency.
