Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

Theoretical calculation of the quadratic Zeeman shift coefficient of the^(3)P_(0)^(o)clock state for strontium optical lattice clock

In the weak-magnetic-field approximation,we derived an expression of quadratic Zeeman shift coefficient of^(3)P_(0)^(o)clock state for^(88)Sr and^(87)Sr atoms.By using this formula and the multi-configuration Dirac-Hartree-Fock theory,the quadratic Zeeman shift coefficients were calculated.The calculated values C_(2)=-23.38(5)MHz/T^(2) for^(88)Sr and the^(3)p_(0)^(o),F=9/2,M_(F)=±9/2 clock states for^(87)Sr agree well with the other available theoretical and experimental values,especially the most accurate measurement recently.In addition,the calculated values of the^(3)p_(0)^(o),F=9/2,M_(F)=±9/2 clock states were also determined in our^(87)Sr optical lattice clock.The consistency with measurements verifies the validation of our calculation model.Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition,for example,the new proposed^(1)S_(0),F=9/2,M_(F)=±5/2-^(3)P_(0)^(o),F=9/2,M_(F)=±3/2 transitions.

Uphillshift decision strategy of an AMT off-road vehicle based on generalized road resistance coefficient

In order to improve the shift decision strategy for an off-road vehicle with automated manual transmission（AMT）,the generalized road resistance coefficient is defined based on the longitudinal dynamics analysis.Vehicle mass and generalized road resistance coefficient are estimated using the recursive least square（RLS）method with multiple forgetting factors.The improved shift schedule is designed based on the generalized road resistance coefficient under uphill road condition.The simulation and real vehicle test verify the effectiveness of improved shift strategy and the improvement of vehicle dynamic performance.

Contact surface fatigue life for roller rack pinion system

A roller rack pinion(RRP)system,which consists of a rack-bar and a cam pinion,transforms a rotation motion into linear motion.The rack-bar has a series of roller train and meshes with the cam pinion.First,the exact tooth profile of the cam pinion and the non-undercut condition to satisfy the required performance have been proposed with the introduction of the profile shift coefficient.Then,the load stress factors are investigated under the variation of the shape design parameters to predict the gear surface fatigue limit which is strongly related to the gear noise and vibration at the contact patch.The results show that the pitting life can be extended significantly with the increase of the profile shift coefficient.