This paper outlines the significance of enhancing the instantaneous protection reliability of low voltage circuit breakers and describes their main failure modes. The instantaneous failure mechanism of low voltage cir...This paper outlines the significance of enhancing the instantaneous protection reliability of low voltage circuit breakers and describes their main failure modes. The instantaneous failure mechanism of low voltage circuit breakers was analyzed so that measures to improve instantaneous protection reliability can be determined. Furthermore, the theory of the instantaneous characteristics calibration device for low voltage circuit breakers and the method of eliminating the non-periodic component of test current are given in detail. Finally, the test results are presented.展开更多
Multi-focus parallel scanning can effectively increase laser fabrication throughput.However,the conventional approach of using a spatial light modulator(SLM)to generate multi-foci and scan this fixed number of foci wi...Multi-focus parallel scanning can effectively increase laser fabrication throughput.However,the conventional approach of using a spatial light modulator(SLM)to generate multi-foci and scan this fixed number of foci with galvanometer scanners can only achieve a periodic scanning trajectory due to the low switching speed of the SLM.Here we demonstrate a multifocus non-periodic scanning method for femtosecond lasers by using,instead,a fast-switching digital micromirror device(DMD)to generate a dynamic number of foci.The number of effective foci is quickly switched by introducing aberration to the undesired focus.In this way,the intensity allocated to each focus will not be affected by the number of foci,and a uniformity of 98%with different numbers of foci is achieved without adjusting the total laser energy.Finally,we validate the effectiveness of this scanning method by demonstrating corneal flap fabrication of porcine cornea in vitro.展开更多
This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and de...This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.展开更多
We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without res...We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.展开更多
Competitive systems defined by Lotka-Volterra equations where ri>0, aij>0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phen...Competitive systems defined by Lotka-Volterra equations where ri>0, aij>0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phenomenon, or May-type trajectory as it is called by some authors, since the discovery of that kind of trajectories in competitive LotkaVolterra systems made by May and Leonard[2] . Recently, the same phenomenon was reported to be existing in prey-predator systems. In this paper it is clear that one can expect the appearance of such phenomenon in a broader class of Lotka-Volterra systems, namely quasi-competitive systems (i.e. ri >0, (aij/ajj)+(aji/aii)>0 in (I)), which cover both competitive and some prey-predator systems in addition to others. Conditions are established in terms of the parameters of the systems for the existence of stable equilibrium, periodic oscillation and non-periodic oscillation.展开更多
In this paper,we establish the model of a finite,irreducible non-periodic and ergodic Markov chain for the sampling scheme without discotinuing state,then calculate and analyse the composite characteristics of a three...In this paper,we establish the model of a finite,irreducible non-periodic and ergodic Markov chain for the sampling scheme without discotinuing state,then calculate and analyse the composite characteristics of a three-level skip-lot sampling scheme.展开更多
The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocat...The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.展开更多
基金Project (No. 043804411) supported by the Tianjin Natural ScienceFoundation, China
文摘This paper outlines the significance of enhancing the instantaneous protection reliability of low voltage circuit breakers and describes their main failure modes. The instantaneous failure mechanism of low voltage circuit breakers was analyzed so that measures to improve instantaneous protection reliability can be determined. Furthermore, the theory of the instantaneous characteristics calibration device for low voltage circuit breakers and the method of eliminating the non-periodic component of test current are given in detail. Finally, the test results are presented.
基金This work was supported by the National Key Research and Development Program of China(No.2022YFC2404500)the National Natural Science Foundation of China(NSFC)(No.62075077)the Hubei Province Science and Technology Plan Project(No.2022BCA049).
文摘Multi-focus parallel scanning can effectively increase laser fabrication throughput.However,the conventional approach of using a spatial light modulator(SLM)to generate multi-foci and scan this fixed number of foci with galvanometer scanners can only achieve a periodic scanning trajectory due to the low switching speed of the SLM.Here we demonstrate a multifocus non-periodic scanning method for femtosecond lasers by using,instead,a fast-switching digital micromirror device(DMD)to generate a dynamic number of foci.The number of effective foci is quickly switched by introducing aberration to the undesired focus.In this way,the intensity allocated to each focus will not be affected by the number of foci,and a uniformity of 98%with different numbers of foci is achieved without adjusting the total laser energy.Finally,we validate the effectiveness of this scanning method by demonstrating corneal flap fabrication of porcine cornea in vitro.
基金supported by Fundamental Research Funds for the Central Universities (Grant No. 2010B02614)Natural Science Foundation of Hohai University (Grant No. 2009423511)+1 种基金National Natural Science Foundation of China (Grant No. 4176008)Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.
文摘We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.
文摘Competitive systems defined by Lotka-Volterra equations where ri>0, aij>0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phenomenon, or May-type trajectory as it is called by some authors, since the discovery of that kind of trajectories in competitive LotkaVolterra systems made by May and Leonard[2] . Recently, the same phenomenon was reported to be existing in prey-predator systems. In this paper it is clear that one can expect the appearance of such phenomenon in a broader class of Lotka-Volterra systems, namely quasi-competitive systems (i.e. ri >0, (aij/ajj)+(aji/aii)>0 in (I)), which cover both competitive and some prey-predator systems in addition to others. Conditions are established in terms of the parameters of the systems for the existence of stable equilibrium, periodic oscillation and non-periodic oscillation.
文摘In this paper,we establish the model of a finite,irreducible non-periodic and ergodic Markov chain for the sampling scheme without discotinuing state,then calculate and analyse the composite characteristics of a three-level skip-lot sampling scheme.
文摘The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.
