High-order Laguerre–Gaussian(LG)petal-like beams have become a topic of significant interest due to their potential application in next-generation optical trapping,quantum optics,and materials processing technologies...High-order Laguerre–Gaussian(LG)petal-like beams have become a topic of significant interest due to their potential application in next-generation optical trapping,quantum optics,and materials processing technologies.In this work,we demonstrate the generation of high-order LG beams with petal-like spatial profiles and tunable orbital angular momentum(OAM)in the mid-infrared wavelength region.These beams are generated using idler-resonant optical parametric oscillation(OPO)in a KTiOAsO_(4)(KTA)crystal.By adjusting the length of the resonant cavity,the OAM of the mid-infrared idler field can be tuned and we demonstrate tuning in the range of 0 to10.When using a maximum pump energy of 20.2 mJ,the maximum output energy of high-order modes LG_(0.45),LG_(0.48),and LG_(0.410) were 0.8,0.53,and 0.46 mJ,respectively.The means by which high-order LG modes with petal-like spatial profiles and tunable OAM were generated from the OPO is theoretically modeled by examining the spatial overlap efficiency of the beam waists of the pump and resonant idler fields within the center of the KTA crystal.The methodology presented in this work offers a simple and flexible method to wavelength-convert laser emission and generate high-order LG modes.展开更多
Using real-time data and the WRF mesoscale model,a heavy rain event in the process of Mesoscale Convective Complex(MCC) turning into banded Mesoscale Convective Systems(MCSs) during 18-19 June 2010 is simulated and an...Using real-time data and the WRF mesoscale model,a heavy rain event in the process of Mesoscale Convective Complex(MCC) turning into banded Mesoscale Convective Systems(MCSs) during 18-19 June 2010 is simulated and analyzed in this paper.The results indicated that the formation and maintenance of a southwest vortex and shear line at 850 h Pa was the mesoscale system that affected the production of this heavy rain.The low-vortex heavy rain mainly happened in the development stage of MCC,and the circular MCC turned into banded MCSs in the late stage with mainly shear line precipitation.In the vicinity of rainfall area,the intense horizontal vorticity due to the vertical shear of u and v caused the rotation,and in correspondence,the ascending branch of the vertical circulation triggered the formation of heavy rain.The different distributions of u and v in the vertical direction produced varying vertical circulations.The horizontal vorticity near the low-vortex and shear line had obvious differences which led to varying reasons for heavy rain formation.The low-vortex heavy rain was mainly caused by the vertical shear of v,and the shear line rainfall formed owing to the vertical shear of both u and v.In this process,the vertical shear of v constituted the EW-trending rain band along the shear line,and the latitudinal non-uniformity of the vertical shear in u caused the vertical motion,which was closely related to the generation and development of MCSs at the shear line and the formation of multiple rain clusters.There was also a similar difference in the positively-tilting term(conversion from horizontal vorticity to vertical positive vorticity) near the rainfall center between the low-vortex and the shear line.The conversion in the low vortex was mainly determined by бv/бp<0,while that of the shear line by бu/бp<0.The scale of the conversion from the horizontal vorticity to vertical vorticity was relatively small,and it was easily ignored in the averaged state.The twisting term was mainly conducive to the reinforcement of precipitation,whereas its contribution to the development of southwest vortex and shear line was relatively small.展开更多
We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field ...We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.展开更多
To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence ra...To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.展开更多
This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through...This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.展开更多
The complete form of the vertical vorticity tendency equation （the complete-form vorticity equation） is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new comp...The complete form of the vertical vorticity tendency equation （the complete-form vorticity equation） is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new complete-form vorticity equation, which has the same form as the original complete-form vorticity equation, is deduced from the absolute vorticity vector equation combined with the continuity equation and the expression of three-dimensional （3D） entropy gradient. By comparing the complete-form vorticity equation with the classical vertical vorticity equation, it is found that regardless of whether or not the isentropic surface is tilting, the two vorticity equations are in essence the same. The ＂baroclinic term＂ of the complete-form vorticity equation is exactly equal to the solenoidal term of the classical one, and there is a significant amount of cancellation between the two baroclinic items （the ＂slantwise term＂ and the horizontal vorticity change term） in the complete-form vorticity equation. In operational weather analysis, the tilt of the isentropic surface can be diagnosed according to the density of the isotherm on the upper-level isobaric map. For synoptic-scale motion, the vertical vorticity produced by the tilt of the isentropic surface is due to the contribution of atmospheric baroclinicity, which is measured by the solenoid. The 3D solenoid is parallel to the isentropic surface, so the more tilted the isentropic surface, the bigger the projection of the 3D solenoid in the vertical direction. The baroclinic contribution can be interpreted based on the PV thinking theory, but the relationship between the vorticity field and the potential vorticity field is not immediate.展开更多
We design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions.We obtain excellent numerical stability due to some new elements in the algorithm.The schemes are based on...We design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions.We obtain excellent numerical stability due to some new elements in the algorithm.The schemes are based on three-and five-wave approximate Riemann solvers of the HLL-type,with the novelty that we allow a varying normal magnetic field.This is achieved by considering the semiconservative Godunov-Powell form of the MHD equations.We show that it is important to discretize the Godunov-Powell source term in the right way,and that the HLL-type solvers naturally provide a stable upwind discretization.Second-order versions of the ENO-and WENO-type reconstructions are proposed,together with precise modifications necessary to preserve positive pressure and density.Extending the discrete source term to second order while maintaining stability requires non-standard techniques,which we present.The first-and second-order schemes are tested on a suite of numerical experiments demonstrating impressive numerical resolution as well as stability,even on very fine meshes.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12264049 and 11664041)the Xinjiang Normal University Young Outstanding Talent Programme(Grant No.XJNUQB2022-17).
文摘High-order Laguerre–Gaussian(LG)petal-like beams have become a topic of significant interest due to their potential application in next-generation optical trapping,quantum optics,and materials processing technologies.In this work,we demonstrate the generation of high-order LG beams with petal-like spatial profiles and tunable orbital angular momentum(OAM)in the mid-infrared wavelength region.These beams are generated using idler-resonant optical parametric oscillation(OPO)in a KTiOAsO_(4)(KTA)crystal.By adjusting the length of the resonant cavity,the OAM of the mid-infrared idler field can be tuned and we demonstrate tuning in the range of 0 to10.When using a maximum pump energy of 20.2 mJ,the maximum output energy of high-order modes LG_(0.45),LG_(0.48),and LG_(0.410) were 0.8,0.53,and 0.46 mJ,respectively.The means by which high-order LG modes with petal-like spatial profiles and tunable OAM were generated from the OPO is theoretically modeled by examining the spatial overlap efficiency of the beam waists of the pump and resonant idler fields within the center of the KTA crystal.The methodology presented in this work offers a simple and flexible method to wavelength-convert laser emission and generate high-order LG modes.
基金National Program on Basic Research Project(973 Program)(2009CB421503,2013CB430103)National Natural Science Foundation of China(40975037)Construction of Advantageous Disciplines for Higher Education in Jiangsu Province,Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘Using real-time data and the WRF mesoscale model,a heavy rain event in the process of Mesoscale Convective Complex(MCC) turning into banded Mesoscale Convective Systems(MCSs) during 18-19 June 2010 is simulated and analyzed in this paper.The results indicated that the formation and maintenance of a southwest vortex and shear line at 850 h Pa was the mesoscale system that affected the production of this heavy rain.The low-vortex heavy rain mainly happened in the development stage of MCC,and the circular MCC turned into banded MCSs in the late stage with mainly shear line precipitation.In the vicinity of rainfall area,the intense horizontal vorticity due to the vertical shear of u and v caused the rotation,and in correspondence,the ascending branch of the vertical circulation triggered the formation of heavy rain.The different distributions of u and v in the vertical direction produced varying vertical circulations.The horizontal vorticity near the low-vortex and shear line had obvious differences which led to varying reasons for heavy rain formation.The low-vortex heavy rain was mainly caused by the vertical shear of v,and the shear line rainfall formed owing to the vertical shear of both u and v.In this process,the vertical shear of v constituted the EW-trending rain band along the shear line,and the latitudinal non-uniformity of the vertical shear in u caused the vertical motion,which was closely related to the generation and development of MCSs at the shear line and the formation of multiple rain clusters.There was also a similar difference in the positively-tilting term(conversion from horizontal vorticity to vertical positive vorticity) near the rainfall center between the low-vortex and the shear line.The conversion in the low vortex was mainly determined by бv/бp<0,while that of the shear line by бu/бp<0.The scale of the conversion from the horizontal vorticity to vertical vorticity was relatively small,and it was easily ignored in the averaged state.The twisting term was mainly conducive to the reinforcement of precipitation,whereas its contribution to the development of southwest vortex and shear line was relatively small.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10734080,11074263,60978013,60921004,and 10874194)the Doctor Fund of Henan Polytechnic University (Grant No. B2011-076)
文摘We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.
基金supported by the National Natural Science Foundation of China(No.11601517)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.
文摘This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.
基金Supported by the National Natural Science Foundation of China(41475042 and 41175043)China Meteorological Administration Special Public Welfare Research Fund(GYHY201406002)
文摘The complete form of the vertical vorticity tendency equation （the complete-form vorticity equation） is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new complete-form vorticity equation, which has the same form as the original complete-form vorticity equation, is deduced from the absolute vorticity vector equation combined with the continuity equation and the expression of three-dimensional （3D） entropy gradient. By comparing the complete-form vorticity equation with the classical vertical vorticity equation, it is found that regardless of whether or not the isentropic surface is tilting, the two vorticity equations are in essence the same. The ＂baroclinic term＂ of the complete-form vorticity equation is exactly equal to the solenoidal term of the classical one, and there is a significant amount of cancellation between the two baroclinic items （the ＂slantwise term＂ and the horizontal vorticity change term） in the complete-form vorticity equation. In operational weather analysis, the tilt of the isentropic surface can be diagnosed according to the density of the isotherm on the upper-level isobaric map. For synoptic-scale motion, the vertical vorticity produced by the tilt of the isentropic surface is due to the contribution of atmospheric baroclinicity, which is measured by the solenoid. The 3D solenoid is parallel to the isentropic surface, so the more tilted the isentropic surface, the bigger the projection of the 3D solenoid in the vertical direction. The baroclinic contribution can be interpreted based on the PV thinking theory, but the relationship between the vorticity field and the potential vorticity field is not immediate.
文摘We design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions.We obtain excellent numerical stability due to some new elements in the algorithm.The schemes are based on three-and five-wave approximate Riemann solvers of the HLL-type,with the novelty that we allow a varying normal magnetic field.This is achieved by considering the semiconservative Godunov-Powell form of the MHD equations.We show that it is important to discretize the Godunov-Powell source term in the right way,and that the HLL-type solvers naturally provide a stable upwind discretization.Second-order versions of the ENO-and WENO-type reconstructions are proposed,together with precise modifications necessary to preserve positive pressure and density.Extending the discrete source term to second order while maintaining stability requires non-standard techniques,which we present.The first-and second-order schemes are tested on a suite of numerical experiments demonstrating impressive numerical resolution as well as stability,even on very fine meshes.
