A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existin...A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existing approaches,the pGHQ scheme has the following advantages:extremely concise algorithm,unifies the constructing procedure for symmetric and asymmetric on-node lattices,and covers a full-range quadrature degree of a given discrete velocity set.We employ the pGHQ scheme to search the local optimal and asymmetric lattices for{n=3,4,5,6,7}moment degree equilibrium distribution discretization on the range[-10,10].The search reveals a surprising abundance of available lattices.Through a brief analysis,the discrete velocity set shows a significant influence on the positivity of equilibrium distributions,which is considered as one of the major impacts of the numerical stability of the LB method.Hence,the results of the p GHQ scheme lay a foundation for further investigations to improve the numerical stability of the LB method by modifying the discrete velocity set.It is also worth noting that pGHQ can be extended into the entropic LB model,even though it was proposed for the Hermite polynomial expansion LB theory.展开更多
Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncat...Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.展开更多
Spatial quantum optics and quantum information based on the high order transverse mode are of importance for the super-resolution measurement beyond the quantum noise level. We demonstrated experimentally the transver...Spatial quantum optics and quantum information based on the high order transverse mode are of importance for the super-resolution measurement beyond the quantum noise level. We demonstrated experimentally the transverse plane TEM01 Hermite Gauss quantum squeezing. The squeezed TEM01 mode is generated in a degenerate optical parametric amplifier with the nonlinear crystal of periodically poled KTiOPO4. The level of 2.2-dB squeezing is measured using a spatial balance homodyne detection system.展开更多
Spatial quantum optics based on the high-order transverse mode is important for the super-resolution measurement and quantum image beyond the shot noise level. Quantum entanglement of the transverse plane Hermite–Gau...Spatial quantum optics based on the high-order transverse mode is important for the super-resolution measurement and quantum image beyond the shot noise level. Quantum entanglement of the transverse plane Hermite–Gauss TEM（01） mode has been demonstrated experimentally in this paper. Two squeezed TEM（01） modes, which are generated by a pair of degenerate optical parametric amplifiers（DOPA） with the nonlinear crystals of periodically poled KTi OPO4, have been combined to produce TEM（01） mode entanglement using a beam splitter. The 1.5 dB for the sum of amplitude and 1.2 dB for the difference of phase below shot-noise level is achieved with the measurement system of a Bell state detection.展开更多
基金Project supported by the National Science and Technology Major Project,China(Grant No.2017ZX06002002)
文摘A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate system.Compared with the existing approaches,the pGHQ scheme has the following advantages:extremely concise algorithm,unifies the constructing procedure for symmetric and asymmetric on-node lattices,and covers a full-range quadrature degree of a given discrete velocity set.We employ the pGHQ scheme to search the local optimal and asymmetric lattices for{n=3,4,5,6,7}moment degree equilibrium distribution discretization on the range[-10,10].The search reveals a surprising abundance of available lattices.Through a brief analysis,the discrete velocity set shows a significant influence on the positivity of equilibrium distributions,which is considered as one of the major impacts of the numerical stability of the LB method.Hence,the results of the p GHQ scheme lay a foundation for further investigations to improve the numerical stability of the LB method by modifying the discrete velocity set.It is also worth noting that pGHQ can be extended into the entropic LB model,even though it was proposed for the Hermite polynomial expansion LB theory.
文摘Recently there have been researches about new efficient nonlinear filtering techniques in which the nonlinear filters generalize elegantly to nonlinear systems without the burdensome lineafization steps. Thus, truncation errors due to linearization can be compensated. These filters include the unscented Kalman filter （UKF）, the central difference filter （CDF） and the divided difference filter （DDF）, and they are also called Sigma Point Filters （SPFs） in a unified way. For higher order approximation of the nonlinear function. Ito and Xiong introduced an algorithm called the Gauss Hermite Filter, which is revisited in [5]. The Gauss Hermite Filter gives better approximation at the expense of higher computation burden, although it＇s less than the particle filter. The Gauss Hermite Filter is used as introduced in [5] with additional pruning step by adding threshold for the weights to reduce the quadrature points.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10774096, 60708010, and 60978008)the National Basic Research Program of China (Grant No. 2010CB923102)the Specialized Research Fund for the Doctoral Program of China (Grant No. 200801080004)
文摘Spatial quantum optics and quantum information based on the high order transverse mode are of importance for the super-resolution measurement beyond the quantum noise level. We demonstrated experimentally the transverse plane TEM01 Hermite Gauss quantum squeezing. The squeezed TEM01 mode is generated in a degenerate optical parametric amplifier with the nonlinear crystal of periodically poled KTiOPO4. The level of 2.2-dB squeezing is measured using a spatial balance homodyne detection system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504218 and 61108003)the Natural Science Foundation of Shanxi Province,China(Grant No.2013021005-2)
文摘Spatial quantum optics based on the high-order transverse mode is important for the super-resolution measurement and quantum image beyond the shot noise level. Quantum entanglement of the transverse plane Hermite–Gauss TEM（01） mode has been demonstrated experimentally in this paper. Two squeezed TEM（01） modes, which are generated by a pair of degenerate optical parametric amplifiers（DOPA） with the nonlinear crystals of periodically poled KTi OPO4, have been combined to produce TEM（01） mode entanglement using a beam splitter. The 1.5 dB for the sum of amplitude and 1.2 dB for the difference of phase below shot-noise level is achieved with the measurement system of a Bell state detection.
