The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability ...The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.展开更多
Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth qu...Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.展开更多
The orientation angle is an important parameter that reflects the structure of molecules at interfaces. In order to obtain this parameter, second order nonlinear spectroscopic techniques including second harmonic gene...The orientation angle is an important parameter that reflects the structure of molecules at interfaces. In order to obtain this parameter, second order nonlinear spectroscopic techniques including second harmonic generation （SHG） and sum frequency generation-vibrational spec- troscopy （SFG-VS） have been successfully applied through analysis of the nonlinear signal from various polarizations. In some SHG and SFG-VS experiments, total internal reflection （TIR） configuration has been adopted to get enhanced signals. However, the reports on the detailed procedure of the polarization analysis and the calculation of the orientation angle of interracial molecules under TIR configuration are still very few. In this paper, we mea- sured the orientation angles of two molecules at the hexadecane-water interface under TIR and Non-TIR experimental configurations. The results measured from polarization analysis in TIR configuration consist with those obtained from Non-TIR configuration. This work demonstrates the feasibility and accuracy of polarization analysis in the determination of the orientation angle of molecules at the interfaces under TIR-SHG configuration.展开更多
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear glob...An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Mamlousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis （MVA） in complex areas.展开更多
The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Ray...The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.展开更多
In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the e...In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.展开更多
文摘The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.
文摘Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.
文摘The orientation angle is an important parameter that reflects the structure of molecules at interfaces. In order to obtain this parameter, second order nonlinear spectroscopic techniques including second harmonic generation （SHG） and sum frequency generation-vibrational spec- troscopy （SFG-VS） have been successfully applied through analysis of the nonlinear signal from various polarizations. In some SHG and SFG-VS experiments, total internal reflection （TIR） configuration has been adopted to get enhanced signals. However, the reports on the detailed procedure of the polarization analysis and the calculation of the orientation angle of interracial molecules under TIR configuration are still very few. In this paper, we mea- sured the orientation angles of two molecules at the hexadecane-water interface under TIR and Non-TIR experimental configurations. The results measured from polarization analysis in TIR configuration consist with those obtained from Non-TIR configuration. This work demonstrates the feasibility and accuracy of polarization analysis in the determination of the orientation angle of molecules at the interfaces under TIR-SHG configuration.
基金This work is supported by National Natural Science Foundation of China （Grant No.40839905）.
文摘An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Mamlousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis （MVA） in complex areas.
基金supported by the National Natural Science Foundation of China(Grant Nos.61178016 and 10974179)Zhejiang Provincial Natural Science Foundation of China(Grant No.Y1090073)
文摘The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.
文摘In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.
