Micro-displacement measurement based on self-mixing interference using a fiber laser system was demonstrated. The sinusoidal phase modulation technique was introduced into the fiber laser self-mixing interference meas...Micro-displacement measurement based on self-mixing interference using a fiber laser system was demonstrated. The sinusoidal phase modulation technique was introduced into the fiber laser self-mixing interference measurement system to improve the measurement resolution. The phase could be demodulated by the Fourier analysis method. Error sources were evaluated in detail, and the system was experimentally applied to reconstruct the motion of a high-precision commercial piezoelectric ceramic transducer （PZT）. The displacement measurement resolution was well beyond a half-wavelength. It provides a practical solution for displacement measurement based on all optical-fiber sensing applications with high precision.展开更多
In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give t...In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.展开更多
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey pa...Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant No. 91123015, 51405240）, the Specialized Research Fund for the Doctoral Program of Higher Education （20113207110004）, and the Natural Science Foundation of Jiangsu Province（BK20140925）. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author（s） and source are credited.
文摘Micro-displacement measurement based on self-mixing interference using a fiber laser system was demonstrated. The sinusoidal phase modulation technique was introduced into the fiber laser self-mixing interference measurement system to improve the measurement resolution. The phase could be demodulated by the Fourier analysis method. Error sources were evaluated in detail, and the system was experimentally applied to reconstruct the motion of a high-precision commercial piezoelectric ceramic transducer （PZT）. The displacement measurement resolution was well beyond a half-wavelength. It provides a practical solution for displacement measurement based on all optical-fiber sensing applications with high precision.
文摘In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.
文摘Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
