In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuti...In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.展开更多
A Cr-Ni type of low transformation temperature（LTT）welding filler was devised in the present study.The LTT weld microstructures of the tungsten inert gas（TIG）and metal active gas（MAG）weldings were investigated b...A Cr-Ni type of low transformation temperature（LTT）welding filler was devised in the present study.The LTT weld microstructures of the tungsten inert gas（TIG）and metal active gas（MAG）weldings were investigated by using electron-backscattered diffraction and orientation imaging microscopy.The results showed that the LTT weld microstructures prepared by TIG and MAG weldings were primarily martensite with 17.5% and 8.0% retained austenite,respectively.The LTT weld metal using TIG welding had larger grain size than using MAG.In addition,based on the Taylor factor calculation,the weld metal using MAG welding was more competent in repressing fatigue crack initiation.Meanwhile,the high angle and coincidence site lattice grain boundaries were dominant in the LTT weld metal using MAG welding.Moreover,the hardness of the LTT weld metal using MAG welding was higher than that of using TIG.Based on heat input and phase transformation,finite element method was applied to analyzing the tensile residual stress（RS）reduction in welded joints prepared by both conventional and LTT welding fillers,respectively.The corresponding outcome confirmed that the LTT weld metal using MAG welding was more beneficial to tensile RS reduction.展开更多
In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one （Jumarie） has proposed rece...In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one （Jumarie） has proposed recently an alternative referred to as （local） modified Riemann-Liouville definition, which directly, provides a Taylor＇s series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional or- der. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to La- grange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation.展开更多
A multigrid-assisted solver tbr the three-dimensional time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes is developed. The spatial accuracy is third-order for the convective terms and fou...A multigrid-assisted solver tbr the three-dimensional time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes is developed. The spatial accuracy is third-order for the convective terms and fourth-order for the viscous terms, and a fractional-step strategy ensures second-order time accuracy. To achieve good time-wise efficiency a multigrid technique is used to solve the highly time-consuming pressure-Poisson equation that requires to be solved at every time step. The speed-up achieved by multigrid is shown in tabular form. The performance and accuracy of the code are first ascertained by computing the flow in a single-sided lid-driven cubic cavity with good grid-economy and comparing the results available in the literature. The code, thus validated, is then applied to a new test problem we propose and various transient and asymptotically obtained steady-state results are presented. Given the care taken to establish the credibility of the code and the good spatio-temporal accuracy of the discretization, these results are accurate and may be used for ascertaining the performance of any computational algorithm applied to this test problem.展开更多
文摘In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.
基金supported by National Natural Science Foundation of China(Grant No.51774213)
文摘A Cr-Ni type of low transformation temperature（LTT）welding filler was devised in the present study.The LTT weld microstructures of the tungsten inert gas（TIG）and metal active gas（MAG）weldings were investigated by using electron-backscattered diffraction and orientation imaging microscopy.The results showed that the LTT weld microstructures prepared by TIG and MAG weldings were primarily martensite with 17.5% and 8.0% retained austenite,respectively.The LTT weld metal using TIG welding had larger grain size than using MAG.In addition,based on the Taylor factor calculation,the weld metal using MAG welding was more competent in repressing fatigue crack initiation.Meanwhile,the high angle and coincidence site lattice grain boundaries were dominant in the LTT weld metal using MAG welding.Moreover,the hardness of the LTT weld metal using MAG welding was higher than that of using TIG.Based on heat input and phase transformation,finite element method was applied to analyzing the tensile residual stress（RS）reduction in welded joints prepared by both conventional and LTT welding fillers,respectively.The corresponding outcome confirmed that the LTT weld metal using MAG welding was more beneficial to tensile RS reduction.
文摘In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one （Jumarie） has proposed recently an alternative referred to as （local） modified Riemann-Liouville definition, which directly, provides a Taylor＇s series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional or- der. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to La- grange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation.
文摘A multigrid-assisted solver tbr the three-dimensional time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes is developed. The spatial accuracy is third-order for the convective terms and fourth-order for the viscous terms, and a fractional-step strategy ensures second-order time accuracy. To achieve good time-wise efficiency a multigrid technique is used to solve the highly time-consuming pressure-Poisson equation that requires to be solved at every time step. The speed-up achieved by multigrid is shown in tabular form. The performance and accuracy of the code are first ascertained by computing the flow in a single-sided lid-driven cubic cavity with good grid-economy and comparing the results available in the literature. The code, thus validated, is then applied to a new test problem we propose and various transient and asymptotically obtained steady-state results are presented. Given the care taken to establish the credibility of the code and the good spatio-temporal accuracy of the discretization, these results are accurate and may be used for ascertaining the performance of any computational algorithm applied to this test problem.
