The high-accuracy, wide-range frequency estimation algorithm for multi-component signals presented in this paper, is based on a numerical differentiation and central Lagrange interpolation. With the sample sequences, ...The high-accuracy, wide-range frequency estimation algorithm for multi-component signals presented in this paper, is based on a numerical differentiation and central Lagrange interpolation. With the sample sequences, which need at most 7 points and are sampled at a sample frequency of 25600 Hz, and computation sequences, using employed a formulation proposed in this paper, the frequencies of each component of the signal are all estimated at an accuracy of 0.001% over 1 Hz to 800 kHz with the amplitudes of each component of the signal varying from 1 V to 200 V and the phase angle of each component of the signal varying from 0° to 360°. The proposed algorithm needs at most a half cycle for the frequencies of each component of the signal under noisy or non-noisy conditions. A testing example is given to illustrate the proposed algorithm in Matlab environment.展开更多
A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordin...A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.展开更多
When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. I...When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation.展开更多
The motion of micro-particles with different mass flow rate in the planer turbulent jet flow has been simulated, using LES method to obtain the flow vorticity evolution and Lagrangian method to track micro-particles. ...The motion of micro-particles with different mass flow rate in the planer turbulent jet flow has been simulated, using LES method to obtain the flow vorticity evolution and Lagrangian method to track micro-particles. The re- suits showed that when the flow rate is small, the particles more likely to present in the vortex periphery, the dis- tribution pattern is similar to the flow pattern. When the flow rate is high, some particles will escape from the mo- tion region to the original static region, so that in the jet region, particles are relatively evenly distributed. When the flow field is full developed, the particles average concentration in the y direction affected by the mass flow rate relative slightly, the normalized mean particles concentrations at different flow rate were similar to Gaussian shape.展开更多
Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was ...Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet.The five distinct flow regimes of the kerosene-water system,previously identified in the experiments from Zhao et al.,were reproduced.The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method.The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model.This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels,and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.展开更多
The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （...The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.展开更多
文摘The high-accuracy, wide-range frequency estimation algorithm for multi-component signals presented in this paper, is based on a numerical differentiation and central Lagrange interpolation. With the sample sequences, which need at most 7 points and are sampled at a sample frequency of 25600 Hz, and computation sequences, using employed a formulation proposed in this paper, the frequencies of each component of the signal are all estimated at an accuracy of 0.001% over 1 Hz to 800 kHz with the amplitudes of each component of the signal varying from 1 V to 200 V and the phase angle of each component of the signal varying from 0° to 360°. The proposed algorithm needs at most a half cycle for the frequencies of each component of the signal under noisy or non-noisy conditions. A testing example is given to illustrate the proposed algorithm in Matlab environment.
基金The National Natural Science Foundation of China (No10471023)
文摘A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.
基金the State Key Project of Fundamental Research of China under
文摘When one wants to calculate all the three components of magnetization of Heisenberg model under random phase approximation, at least one of the components should be the solution of an ordinary differential equation. In this paper such an equation is established. It is argued that the general expressions of magnetization for any spin quantum number S suggested before are the solution of the ordinary differential equation.
基金supported by National Natural Science Foundation of China (Grant No. 50976107 and 51206149)National Key Technology R&D Program of China (Grant No. 2009BAF39B01)Zhejiang Science Technology Project (Grant No. 2011C11073)
文摘The motion of micro-particles with different mass flow rate in the planer turbulent jet flow has been simulated, using LES method to obtain the flow vorticity evolution and Lagrangian method to track micro-particles. The re- suits showed that when the flow rate is small, the particles more likely to present in the vortex periphery, the dis- tribution pattern is similar to the flow pattern. When the flow rate is high, some particles will escape from the mo- tion region to the original static region, so that in the jet region, particles are relatively evenly distributed. When the flow field is full developed, the particles average concentration in the y direction affected by the mass flow rate relative slightly, the normalized mean particles concentrations at different flow rate were similar to Gaussian shape.
基金supported by Corning Incorporated, the National Natural Science Foundation of China (20990224, 20976177)National Science Fund for Distinguished Young Scholars (21025627)the National Basic Research Program of China (2009CB623406)
文摘Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet.The five distinct flow regimes of the kerosene-water system,previously identified in the experiments from Zhao et al.,were reproduced.The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method.The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model.This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels,and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.
文摘The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.
