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-Ha...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.展开更多
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)...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.展开更多
For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators ...For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.展开更多
The influence of self-heating on the millimeter-wave(mm-wave)and terahertz(THz)performance of double-drift region(DDR)impact avalanche transit time(IMPATT)sources based on silicon(Si)has been investigated in this pape...The influence of self-heating on the millimeter-wave(mm-wave)and terahertz(THz)performance of double-drift region(DDR)impact avalanche transit time(IMPATT)sources based on silicon(Si)has been investigated in this paper.The dependences of static and large-signal parameters on junction temperature are estimated using a non-sinusoidal voltage excited(NSVE)large-signal simulation technique developed by the authors,which is based on the quantum-corrected drift-diffusion(QCDD)model.Linear variations of static parameters and non-linear variations of large-signal parameters with temperature have been observed.Analytical expressions representing the temperature dependences of static and large-signal parameters of the diodes are developed using linear and 2nd degree polynomial curve fitting techniques,which will be highly useful for optimizing the thermal design of the oscillators.Finally,the simulated results are found to be in close agreement with the experimentally measured data.展开更多
The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure.However,the linear damping is frequently underestimated,especially for the natural frequency.To investigate ...The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure.However,the linear damping is frequently underestimated,especially for the natural frequency.To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure(VLFS),this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests.Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank.Corresponding model tests are also implemented to verify and validate against the numerical solutions.The effects of the sloping seafloor,as well as the water depth,on the hydrodynamic coefficients are investigated based on the validated CFD modeling.Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches.For the case studied in present paper,the identification errors introduced by the conventional method are 1.5%while they are 0.5%using the direct integration method.The quadratic damping coefficient for heave mode decreases about 10.4%when the sloping angle increases from 0 to 6 deg.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61775220)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB21030100)+1 种基金the Key Research Project of Frontier Science of the Chinese Academy of Sciences(Grant No.QYZDB-SSW-JSC004)the West Light Foundation of the Chinese Academy of Sciences(Grant No.XAB2018B17)。
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No.61775220)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB21030100)the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No.QYZDB-SSW-JSC004)。
文摘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.
文摘For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.
文摘The influence of self-heating on the millimeter-wave(mm-wave)and terahertz(THz)performance of double-drift region(DDR)impact avalanche transit time(IMPATT)sources based on silicon(Si)has been investigated in this paper.The dependences of static and large-signal parameters on junction temperature are estimated using a non-sinusoidal voltage excited(NSVE)large-signal simulation technique developed by the authors,which is based on the quantum-corrected drift-diffusion(QCDD)model.Linear variations of static parameters and non-linear variations of large-signal parameters with temperature have been observed.Analytical expressions representing the temperature dependences of static and large-signal parameters of the diodes are developed using linear and 2nd degree polynomial curve fitting techniques,which will be highly useful for optimizing the thermal design of the oscillators.Finally,the simulated results are found to be in close agreement with the experimentally measured data.
基金the support of the National Natural Science Foundation of China(Grant No.51979167,51179103)the Ministry of Industry and Information Technology(Grant No.[2018]473)+1 种基金the China Scholarship Council(Grant 201806230206)the Hainan Provincial Joint Project of Sanya Bay Science and Technology City(Grant No.520LH051).
文摘The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure.However,the linear damping is frequently underestimated,especially for the natural frequency.To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure(VLFS),this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests.Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank.Corresponding model tests are also implemented to verify and validate against the numerical solutions.The effects of the sloping seafloor,as well as the water depth,on the hydrodynamic coefficients are investigated based on the validated CFD modeling.Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches.For the case studied in present paper,the identification errors introduced by the conventional method are 1.5%while they are 0.5%using the direct integration method.The quadratic damping coefficient for heave mode decreases about 10.4%when the sloping angle increases from 0 to 6 deg.
