In this paper, we establish a few existence results of nonoscillatory solutions to second-order nonlinear neutral delay differential equations, construct several Manntype iterative approximation schemes for these nono...In this paper, we establish a few existence results of nonoscillatory solutions to second-order nonlinear neutral delay differential equations, construct several Manntype iterative approximation schemes for these nonoscillatory solutions, and give some error estimates between the approximate solutions and the nonoscillatory solutions. And finally we give an example to illustrate our results.展开更多
With the raise of voltage level in electric power grid,the phenomena of high voltage gas insulation has received extensive attention from all over the world.The research on the breakdown mechanism of vacuum which is t...With the raise of voltage level in electric power grid,the phenomena of high voltage gas insulation has received extensive attention from all over the world.The research on the breakdown mechanism of vacuum which is the main insulation gas in high voltage level is one of the most important issues.It is also important to the study of vacuum arc in vacuum switch.But for the limitations of available method used in analyzing the breakdown mechanism of vacuum,the main research on vacuum breakdown is macroscopic experiment.The experiments are greatly influenced by environmental factors and high vacuum degree is difficult to be ensured.So the data from the experiments are dispersive and the complex physical change in vacuum breakdown can not be revealed.The purpose of this work is to analyze the mechanism of vacuum breakdown quantitatively by microscopic numerical simulation.The particle in cell and Monte Carlo methods are used here to solve microscopic dynamic equation of gas.Based on the field emission theory in vacuum,electrons produced by the cathode and ions produced by the collision between electron and metal vapor molecule are the objects of this study.The motions of microscopic particles which are at the functions of the applied and self-consistent electric filed are traced in time and two space dimensions.Mont Carlo method is used here to cope with the collisions between electrons and metal vapor molecules.The cross sections of the collision which is related with the energy are all from the experiments.The secondary electron emission,exciting,elastic and ionizing collisions between electrons and metal vapor molecules have been considered in this paper.By the simulation,the number densities of electron and ion are acquired and the microscopic dynamic electric field produced by space charge is also calculated. The effect of vacuum degree on discharge voltage is also discussed here.According to the simulation data,we draw the conclusion that the main reason for vacuum arc formation is metal vapor ionization and large amount of metal gas is from high energy electrons' collision with the anode.展开更多
Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can ...Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can be modeled accurately by solving the Navier–Stokes(NS)equations;however,the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo(DSMC)method or the solution of the Boltzmann equation.The Boltzmann equation and the general solution approach,using the splitting method,will be introduced in this paper.Details of the method used for solving both the classical Boltzmann equation(CBE)and the generalized Boltzmann equation(GBE)are also provided.The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases.In particular,the method is applied to simulate two of the three primary constituents of air(N_(2),O_(2),and Ar)in a binary mixture at 1:1 density ratio at Mach 2 and 5,with gases in translational,rotational and vibrational non-equilibrium.展开更多
基金supported by the National Natural Science Foundation of China(No.10771001)Doctoral Fund of Ministry of Education of China(No.20093401110001)Nature Science Foundation of Anhui Province(No.KJ2013B276)
文摘In this paper, we establish a few existence results of nonoscillatory solutions to second-order nonlinear neutral delay differential equations, construct several Manntype iterative approximation schemes for these nonoscillatory solutions, and give some error estimates between the approximate solutions and the nonoscillatory solutions. And finally we give an example to illustrate our results.
基金Supported by National Natural Science Foundation of China(50877048)Program for New Century Excellent Talents in University of China(NECT-08-0863)Key Scientific and Technological project of Liaoning Science and Technology Department (2010219016)
文摘With the raise of voltage level in electric power grid,the phenomena of high voltage gas insulation has received extensive attention from all over the world.The research on the breakdown mechanism of vacuum which is the main insulation gas in high voltage level is one of the most important issues.It is also important to the study of vacuum arc in vacuum switch.But for the limitations of available method used in analyzing the breakdown mechanism of vacuum,the main research on vacuum breakdown is macroscopic experiment.The experiments are greatly influenced by environmental factors and high vacuum degree is difficult to be ensured.So the data from the experiments are dispersive and the complex physical change in vacuum breakdown can not be revealed.The purpose of this work is to analyze the mechanism of vacuum breakdown quantitatively by microscopic numerical simulation.The particle in cell and Monte Carlo methods are used here to solve microscopic dynamic equation of gas.Based on the field emission theory in vacuum,electrons produced by the cathode and ions produced by the collision between electron and metal vapor molecule are the objects of this study.The motions of microscopic particles which are at the functions of the applied and self-consistent electric filed are traced in time and two space dimensions.Mont Carlo method is used here to cope with the collisions between electrons and metal vapor molecules.The cross sections of the collision which is related with the energy are all from the experiments.The secondary electron emission,exciting,elastic and ionizing collisions between electrons and metal vapor molecules have been considered in this paper.By the simulation,the number densities of electron and ion are acquired and the microscopic dynamic electric field produced by space charge is also calculated. The effect of vacuum degree on discharge voltage is also discussed here.According to the simulation data,we draw the conclusion that the main reason for vacuum arc formation is metal vapor ionization and large amount of metal gas is from high energy electrons' collision with the anode.
文摘Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can be modeled accurately by solving the Navier–Stokes(NS)equations;however,the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo(DSMC)method or the solution of the Boltzmann equation.The Boltzmann equation and the general solution approach,using the splitting method,will be introduced in this paper.Details of the method used for solving both the classical Boltzmann equation(CBE)and the generalized Boltzmann equation(GBE)are also provided.The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases.In particular,the method is applied to simulate two of the three primary constituents of air(N_(2),O_(2),and Ar)in a binary mixture at 1:1 density ratio at Mach 2 and 5,with gases in translational,rotational and vibrational non-equilibrium.
