基于等腰劈光学等倾干涉原理,利用CMOS(complementary metal oxide semiconductor,互补金属氧化物半导体)图像传感器,设计了一种可测量流体折射率微小变化的传感器系统。该系统使用具有高频率像素时钟的CMOS图像传感器对等腰劈中出射光...基于等腰劈光学等倾干涉原理,利用CMOS(complementary metal oxide semiconductor,互补金属氧化物半导体)图像传感器,设计了一种可测量流体折射率微小变化的传感器系统。该系统使用具有高频率像素时钟的CMOS图像传感器对等腰劈中出射光信号进行测量,将携带信息的光信号转换成电信号,再经过一块现场可编程门阵列(field programmable gate array,FPGA)芯片采集数字图像,通过极值计数法处理数据获得光学信息,从而计算流体折射率微变量。该传感器系统的理论测量精度达2.75×10^-6,可应用于大气测量和材料研究等领域。展开更多
Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as t...Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.展开更多
A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and ...A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and unified tensor-product representation of LRL vector is also deduced by using an effective single-body description.Some properties of the vector are numerated and proved.Conservation of this vector is demonstrated in the tensor-product form.The energy formula for a bound-state elliptic orbit is simply derived via a novel approach.For a two-body system,the R-test rules for every kinds of Kepler＇s motion are discussed in detail.展开更多
Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution...Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.展开更多
基金Supported by the National Natural Science Foundation of China (10775105)
文摘Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.
基金Supported by the National Teaching Team Foundation(202276003)
文摘A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and unified tensor-product representation of LRL vector is also deduced by using an effective single-body description.Some properties of the vector are numerated and proved.Conservation of this vector is demonstrated in the tensor-product form.The energy formula for a bound-state elliptic orbit is simply derived via a novel approach.For a two-body system,the R-test rules for every kinds of Kepler＇s motion are discussed in detail.
基金Supported by the National Natural Science Foundation of China(10775105)
文摘Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.
