Nonlinear instability in electrically charged jets is studied using the governing electro-hydrodynamic equations describing stretching and thinning of a liquid jet. A jet flow system subject to both space and time evo...Nonlinear instability in electrically charged jets is studied using the governing electro-hydrodynamic equations describing stretching and thinning of a liquid jet. A jet flow system subject to both space and time evolving disturbances is considered. At the linear stage, the Rayleigh and conducting jet flow instability modes are uncovered.Nonlinear instability in the flow is explored via triad resonant waves which uncover favorable operating modes not previously detected in the linear study of the problem. In particular, the jet radius is significantly reduced, and the electric field of the jet is properly oriented under the nonlinear study. It is found that taking into account the resonance triad modes provides a better mathematical description of a jet that stretches and thins due to tangential electric field effects. Both linear and nonlinear instability results in the jet flow system are presented and discussed.展开更多
A theoretical model which describes the small-scale irregularities excited by powerful high frequency （3–30 MHz） electromagnetic wave in ionosphere heating is investigated quantitatively in this paper. The model is...A theoretical model which describes the small-scale irregularities excited by powerful high frequency （3–30 MHz） electromagnetic wave in ionosphere heating is investigated quantitatively in this paper. The model is based on the transport equation in magnetic plasma and mode conversion from electromagnetic wave to electrostatic wave in ionospheric modification.Threshold electric field for exciting small-scale （meter scale） irregularities and spatial spectra of irregularities are analytically calculated by this model. The results indicate that background electron density and geomagnetic field play an important role for the threshold electric field and the spatial scale of the electron density irregularities. The results demonstrate that the electric field threshold increases with the decrease of the spatial scale of the irregularities. For exciting meter scale irregularities, the threshold electric field is about tens of mV m^（-1）. The theoretical results are consistent with those of the experiments.展开更多
In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example...In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.展开更多
基金Project supported by the National Science Foundation of U.S.A.(No.DMS-0946431)
文摘Nonlinear instability in electrically charged jets is studied using the governing electro-hydrodynamic equations describing stretching and thinning of a liquid jet. A jet flow system subject to both space and time evolving disturbances is considered. At the linear stage, the Rayleigh and conducting jet flow instability modes are uncovered.Nonlinear instability in the flow is explored via triad resonant waves which uncover favorable operating modes not previously detected in the linear study of the problem. In particular, the jet radius is significantly reduced, and the electric field of the jet is properly oriented under the nonlinear study. It is found that taking into account the resonance triad modes provides a better mathematical description of a jet that stretches and thins due to tangential electric field effects. Both linear and nonlinear instability results in the jet flow system are presented and discussed.
基金supported by National Natural Science Foundation of China(NSFC grants 41204111,4157414641774162 and 41704155)China Postdoctoral Science Foundation(2017M622504)
文摘A theoretical model which describes the small-scale irregularities excited by powerful high frequency （3–30 MHz） electromagnetic wave in ionosphere heating is investigated quantitatively in this paper. The model is based on the transport equation in magnetic plasma and mode conversion from electromagnetic wave to electrostatic wave in ionospheric modification.Threshold electric field for exciting small-scale （meter scale） irregularities and spatial spectra of irregularities are analytically calculated by this model. The results indicate that background electron density and geomagnetic field play an important role for the threshold electric field and the spatial scale of the electron density irregularities. The results demonstrate that the electric field threshold increases with the decrease of the spatial scale of the irregularities. For exciting meter scale irregularities, the threshold electric field is about tens of mV m^（-1）. The theoretical results are consistent with those of the experiments.
文摘In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.
