This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis...This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.展开更多
Ion specificity of Na＋ and C1- ions for NaCI solution confined in silicon nanochannels is investigated with molecular dynamics （MD） simulations. The MD simulation results demonstrate that ion specificity for Na＋ a...Ion specificity of Na＋ and C1- ions for NaCI solution confined in silicon nanochannels is investigated with molecular dynamics （MD） simulations. The MD simulation results demonstrate that ion specificity for Na＋ and C1- ions exhibits clearly in na- nochannels with high surface charge density. The two types of ions show different density distributions perpendicular to the channel surface due to the ion specificity when they act as countefions near negatively and positively charged surfaces, respec- tively. Both the two counterion distributions cannot be predicted by Poisson-Boltzmann equation within 0.75 nm near the sur- face. In addition, the ion specificity is also demonstrated through affecting the water density distributions. In the nanochannel with negatively charged surfaces, the presence of the Na＋ ions reduces the number of water peaks in water density distribution profile. In comparison, when the C1- ions act as counterions near positively charged surfaces, they do not affect the number of the water peaks. Besides the influence on the water density distribution, ion specificity also exhibits through affecting the wa- ter molecule orientation in the adsorbed layer. It is found that C1- ions make the water molecules in the adsorbed layer align more orderly than Na~ ions do when the two types of ions act as the counterions near the positively and negatively charged surfaces with the same surface charge density.展开更多
An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equ...An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.展开更多
Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. Th...Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.展开更多
Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stim...Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stimulated scattering effects.The resulting Kompaneets equation depends explicitly on the electron cyclotron frequency and the incidence angle of the incoming photons relative to the direction of the magnetic field.The evolutionary behavior of the photon spectrum and energy density is highly anisotropic with respect to the static external magnetic field.Possible applications of our results to the X-ray emission from compact and massive stellar objects are discussed in detail and those to the interaction of the microwave background radiation with the hot electrons in galactic clusters are discussed briefly.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 91016027 and 91130018)
文摘This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.
基金supported by the National Basic Research Program of Chi-na(Grant Nos.2011CB707601,2011CB707605)the National Natural Science Foundation of China(Grant No.50925519)+3 种基金the Research Funding for the Doctor Program from China Educational Ministry(Grant No.20100092110051)the Innovative Project for Graduate Students of Jiangsu Province(Grant No.CXZZ13_0087)the Scientific Research Founda-tion of Graduate School of Southeast University(Grant No.YBJJ1322)The calculations were performed on Tianhe-1A at National Supercomputing Center in Tianjin,China
文摘Ion specificity of Na＋ and C1- ions for NaCI solution confined in silicon nanochannels is investigated with molecular dynamics （MD） simulations. The MD simulation results demonstrate that ion specificity for Na＋ and C1- ions exhibits clearly in na- nochannels with high surface charge density. The two types of ions show different density distributions perpendicular to the channel surface due to the ion specificity when they act as countefions near negatively and positively charged surfaces, respec- tively. Both the two counterion distributions cannot be predicted by Poisson-Boltzmann equation within 0.75 nm near the sur- face. In addition, the ion specificity is also demonstrated through affecting the water density distributions. In the nanochannel with negatively charged surfaces, the presence of the Na＋ ions reduces the number of water peaks in water density distribution profile. In comparison, when the C1- ions act as counterions near positively charged surfaces, they do not affect the number of the water peaks. Besides the influence on the water density distribution, ion specificity also exhibits through affecting the wa- ter molecule orientation in the adsorbed layer. It is found that C1- ions make the water molecules in the adsorbed layer align more orderly than Na~ ions do when the two types of ions act as the counterions near the positively and negatively charged surfaces with the same surface charge density.
文摘An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11274378 and 10404037
文摘Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.
基金supported by the National Natural Science Foundation of China (Grant Nos. Y011091001,11003023 and 10833003)
文摘Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stimulated scattering effects.The resulting Kompaneets equation depends explicitly on the electron cyclotron frequency and the incidence angle of the incoming photons relative to the direction of the magnetic field.The evolutionary behavior of the photon spectrum and energy density is highly anisotropic with respect to the static external magnetic field.Possible applications of our results to the X-ray emission from compact and massive stellar objects are discussed in detail and those to the interaction of the microwave background radiation with the hot electrons in galactic clusters are discussed briefly.
