This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical...This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].展开更多
There are three basic methods in radiative transfer calculations, i.e., line-by-line （LBL） integration, correlated k-distribution method, and band model. The LBL integration is the most accurate of all, in which, th...There are three basic methods in radiative transfer calculations, i.e., line-by-line （LBL） integration, correlated k-distribution method, and band model. The LBL integration is the most accurate of all, in which, there are two quadrature algorithms named in this paper as integration by lines and by sampling points when calculating atmospheric transmittance in the considered wavenumher region. Because the LBL integration is the most expensive of all, it is necessary and important to save calculation time hut increase calculation speed when it is put into use in the daily operation in atmospheric remote sensing and atmospheric sounding. A simplified LBL method is given in this paper on the basis of integration by lines, which increases computational speed greatly with keeping the same accuracy. Then, we discuss the effects of different cutoff schemes on atmospheric absorption coefficient, transmittance, and cooling rate under both of accurate and simplified LBL methods in detail. There are four cutoff schemes described in this paper, i.e., CUTOFFs 1, 2, 3, and 4. It is shown by this numerical study that the way to cut off spectral line-wing has a great effect on the accuracy and speed of radiative calculations. The relative errors of the calculated absorption coefficients for CUTOFF 2 are the largest under different pressures, while for CUTOFF 1, they are less than 2% at most of sampling points and for CUTOFFs 3 or 4, they are almost less than 5% in the calculated spectral region, however, the calculation time is reduced greatly. We find in this study that the transmittance in the lower atmosphere is not sensitive to different LBL methods and different cutoff schemes. Whereas for the higher atmosphere, the differences of transmittance results between CUTOFF 2 and each of other three cutoff schemes are the biggest of all no matter for the accurate LBL or for the simplified LBL integrations. By comparison, the best and optimized cutoff scheme is given in this paper finally.展开更多
Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation （HHG）. A transition rate formula for HHG is obtained. Applying this formula, we cal- culate the spectra of h...Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation （HHG）. A transition rate formula for HHG is obtained. Applying this formula, we cal- culate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the ＂3.17＂ cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy Up and the ionization potential energy Ip, is 3.34Up 1.83Ip. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.展开更多
基金supported by the Fundamental Research Funds for the Central Universities
文摘This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].
基金the National Natural Science Foundation of China under Grant No.40775006the National Basic Research Program of China under Grant No.2006CB403707the Public Meteorology Special Foundation of China under Grant No.GYHY200706036.
文摘There are three basic methods in radiative transfer calculations, i.e., line-by-line （LBL） integration, correlated k-distribution method, and band model. The LBL integration is the most accurate of all, in which, there are two quadrature algorithms named in this paper as integration by lines and by sampling points when calculating atmospheric transmittance in the considered wavenumher region. Because the LBL integration is the most expensive of all, it is necessary and important to save calculation time hut increase calculation speed when it is put into use in the daily operation in atmospheric remote sensing and atmospheric sounding. A simplified LBL method is given in this paper on the basis of integration by lines, which increases computational speed greatly with keeping the same accuracy. Then, we discuss the effects of different cutoff schemes on atmospheric absorption coefficient, transmittance, and cooling rate under both of accurate and simplified LBL methods in detail. There are four cutoff schemes described in this paper, i.e., CUTOFFs 1, 2, 3, and 4. It is shown by this numerical study that the way to cut off spectral line-wing has a great effect on the accuracy and speed of radiative calculations. The relative errors of the calculated absorption coefficients for CUTOFF 2 are the largest under different pressures, while for CUTOFF 1, they are less than 2% at most of sampling points and for CUTOFFs 3 or 4, they are almost less than 5% in the calculated spectral region, however, the calculation time is reduced greatly. We find in this study that the transmittance in the lower atmosphere is not sensitive to different LBL methods and different cutoff schemes. Whereas for the higher atmosphere, the differences of transmittance results between CUTOFF 2 and each of other three cutoff schemes are the biggest of all no matter for the accurate LBL or for the simplified LBL integrations. By comparison, the best and optimized cutoff scheme is given in this paper finally.
文摘Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation （HHG）. A transition rate formula for HHG is obtained. Applying this formula, we cal- culate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the ＂3.17＂ cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy Up and the ionization potential energy Ip, is 3.34Up 1.83Ip. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.
