A Chinese satellite gravity mission called SAGM (Space Advanced Gravity Measurements) is now taken into consideration.To meet its designed requirement,the measurement precision of the laser ranging system used to meas...A Chinese satellite gravity mission called SAGM (Space Advanced Gravity Measurements) is now taken into consideration.To meet its designed requirement,the measurement precision of the laser ranging system used to measure the inter-satellite distance change has to be better than l00nm/Hz1/2 within a broad bandwidth from 0.1mHz to 1Hz.An equal arm heterodyne Mach-Zehnder interferometer has been built on ground to demonstrate the measurement principle of a laser ranging system,which potentially can be used for both SAGM and future GW (gravitational wave) space antennas.Because of the equal arm length,the laser frequency noise has been significantly suppressed in the interferometer.Thus,the sensitivity better than 1nm/Hz1/2 in a frequency range of 0.15 mHz-0.375 Hz has been achieved.The result shows that the proposed methodology has very promising feasibility to meet the requirements of SAGM and of GW space antennas as well.展开更多
Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(R...We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.展开更多
基金Supported by the Space Science Research Projects in Advance,Chinese Academy of Sciences.
文摘A Chinese satellite gravity mission called SAGM (Space Advanced Gravity Measurements) is now taken into consideration.To meet its designed requirement,the measurement precision of the laser ranging system used to measure the inter-satellite distance change has to be better than l00nm/Hz1/2 within a broad bandwidth from 0.1mHz to 1Hz.An equal arm heterodyne Mach-Zehnder interferometer has been built on ground to demonstrate the measurement principle of a laser ranging system,which potentially can be used for both SAGM and future GW (gravitational wave) space antennas.Because of the equal arm length,the laser frequency noise has been significantly suppressed in the interferometer.Thus,the sensitivity better than 1nm/Hz1/2 in a frequency range of 0.15 mHz-0.375 Hz has been achieved.The result shows that the proposed methodology has very promising feasibility to meet the requirements of SAGM and of GW space antennas as well.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
基金supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104)。
文摘We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.
