Using quasi time dependent semiclassical transport theory, within relaxation time approximation, we obtained coupled electronic current equations in the presence of time varying field, and based on general scattering ...Using quasi time dependent semiclassical transport theory, within relaxation time approximation, we obtained coupled electronic current equations in the presence of time varying field, and based on general scattering mechanism,. In the vicinity of Dirac points, we find that a characteristic exponent?corresponds to acoustic phonon scattering,?long range Coulomb scattering mechanism and?is short range (delta or contact potential) scattering in which the conductivity is constant of temperature. The?case is the ballistic regime. In the low energy dynamics of Dirac electrons in graphene, the effect of the time dependent electric field is to alter just the electron charge by?making electronic conductivity nonlinear. The effect of constant magnetic field at finite temperature is also considered.展开更多
In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the...In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.展开更多
This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation a...This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation and the assumption of the e-V relaxation through a continuous series of Boltzmann distributions over the vibrational states,an analytic approach is derived from the proposed scaling relation of e-V transition rates.A full kinetic model is then investigated by numerically solving the state-to-state master equation for all vibrational levels.The analytical approach leads to a Landau-Teller（LT）-type equation for relaxation of vibrational energy,and predicts the relaxation time on the right order of magnitude.By comparison with the kinetic model,the LT-type equation is valid in typical electron temperatures in gas discharge.However,the analytical approach is not capable of describing the vibrational distribution function during the e-V process in which a full kinetic model is required.展开更多
Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especi...Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.展开更多
文摘Using quasi time dependent semiclassical transport theory, within relaxation time approximation, we obtained coupled electronic current equations in the presence of time varying field, and based on general scattering mechanism,. In the vicinity of Dirac points, we find that a characteristic exponent?corresponds to acoustic phonon scattering,?long range Coulomb scattering mechanism and?is short range (delta or contact potential) scattering in which the conductivity is constant of temperature. The?case is the ballistic regime. In the low energy dynamics of Dirac electrons in graphene, the effect of the time dependent electric field is to alter just the electron charge by?making electronic conductivity nonlinear. The effect of constant magnetic field at finite temperature is also considered.
基金Supported by the Chinese Postdoctoral Science Foundation, the Young Scientists Funds of NSF of China (10401019)the Tsinghua Basic Research Foundation.
文摘In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.
基金supported by National Natural Science Foundation of China(No.11505015)the National High-Tech Research and Development Program of China(863 Program)
文摘This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation and the assumption of the e-V relaxation through a continuous series of Boltzmann distributions over the vibrational states,an analytic approach is derived from the proposed scaling relation of e-V transition rates.A full kinetic model is then investigated by numerically solving the state-to-state master equation for all vibrational levels.The analytical approach leads to a Landau-Teller（LT）-type equation for relaxation of vibrational energy,and predicts the relaxation time on the right order of magnitude.By comparison with the kinetic model,the LT-type equation is valid in typical electron temperatures in gas discharge.However,the analytical approach is not capable of describing the vibrational distribution function during the e-V process in which a full kinetic model is required.
文摘Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.
