After presenting the infinite operator-sum form solution to the Milburn equation dp/dt=γ（UρU^f - ρ）=γU[p, Uf], where U=e^-iH/hγ, and verifying that this equation preserves the three necessary conditions of dens...After presenting the infinite operator-sum form solution to the Milburn equation dp/dt=γ（UρU^f - ρ）=γU[p, Uf], where U=e^-iH/hγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the yon Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then theproduct AB obeys （d/dt）（AB） = γU[AB, U^f]-（1/γ）（dA/dt）（dB/dt）, which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general展开更多
This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dyna...This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dynamic and static solutions of these equations can be applied to calculate quantitative relationships between the concentration ratio of precursors and secondary fine particles as well as the physical clearance power of the atmosphere,chemical reaction rate,and the scale of a contaminated area.The dynamic solution presented here therefore corresponds with a theoretical formula for calculating the overall rate constant for the oxidation reaction of reducing pollutants in the actual atmosphere based on their local concentrations and meteorological monitoring data.In addition,the static solution presented in this paper reveals the functional relationship between the concentration of secondary fine particles and precursor emission rate as well as atmospheric self-purification capacity.This result can be applied to determine the atmospheric environmental capacity of a precursor.Hourly records collected over the last 40 years from 378 weather stations in China's Mainland as well as the spatiotemporal distribution sequence of overall oxidation reaction rates from precursors show that when the reference concentration limit of secondary fine particles is100μmol m-3,the atmospheric environmental capacity of total precursors canbe calculated as 24890×1010 mol yr-1.Thus,when the annual average concentration limit of given fine particles is 35μg m-3 and the ratio of sulfate and nitrate to 30%and 20%of the total amount of fine particles,the capacities of SO2,NOx and NH3 are 1255,1344,and 832(1010g yr-1),respectively.The clearance density of precursors for different return periods across China's Mainland under above conditions are also provided in this study.展开更多
It is mathematically and thoroughly proved in this paper that the nonlinearstochastic ocean-atmosphere oscillator model possesses a stable limit cycle; then the modelequations are transformed into the Fokker-Planck eq...It is mathematically and thoroughly proved in this paper that the nonlinearstochastic ocean-atmosphere oscillator model possesses a stable limit cycle; then the modelequations are transformed into the Fokker-Planck equation (FPE), and the evolution of ElNino-Southern Oscillation (ENSO) from unstable state to stable state is studied from the point ofview of nonequilibrium system dynamics. The study results reveal that although the complex nonlinearocean-atmosphere oscillator model possesses multiequilibrium states, the real climatic systempossesses only a quasi-normal state and a strong ENSO cycle stable state. The first passage timebetween states is also given in this paper, and the theoretical computational results agree withobservational data.展开更多
文摘After presenting the infinite operator-sum form solution to the Milburn equation dp/dt=γ（UρU^f - ρ）=γU[p, Uf], where U=e^-iH/hγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the yon Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then theproduct AB obeys （d/dt）（AB） = γU[AB, U^f]-（1/γ）（dA/dt）（dB/dt）, which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general
基金supported by S & T Development Program (Grant No. CAMS 2018KJ026)
文摘This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dynamic and static solutions of these equations can be applied to calculate quantitative relationships between the concentration ratio of precursors and secondary fine particles as well as the physical clearance power of the atmosphere,chemical reaction rate,and the scale of a contaminated area.The dynamic solution presented here therefore corresponds with a theoretical formula for calculating the overall rate constant for the oxidation reaction of reducing pollutants in the actual atmosphere based on their local concentrations and meteorological monitoring data.In addition,the static solution presented in this paper reveals the functional relationship between the concentration of secondary fine particles and precursor emission rate as well as atmospheric self-purification capacity.This result can be applied to determine the atmospheric environmental capacity of a precursor.Hourly records collected over the last 40 years from 378 weather stations in China's Mainland as well as the spatiotemporal distribution sequence of overall oxidation reaction rates from precursors show that when the reference concentration limit of secondary fine particles is100μmol m-3,the atmospheric environmental capacity of total precursors canbe calculated as 24890×1010 mol yr-1.Thus,when the annual average concentration limit of given fine particles is 35μg m-3 and the ratio of sulfate and nitrate to 30%and 20%of the total amount of fine particles,the capacities of SO2,NOx and NH3 are 1255,1344,and 832(1010g yr-1),respectively.The clearance density of precursors for different return periods across China's Mainland under above conditions are also provided in this study.
基金Supported by the National Key Program for Developing Basic Sciences (2006CB400503).
文摘It is mathematically and thoroughly proved in this paper that the nonlinearstochastic ocean-atmosphere oscillator model possesses a stable limit cycle; then the modelequations are transformed into the Fokker-Planck equation (FPE), and the evolution of ElNino-Southern Oscillation (ENSO) from unstable state to stable state is studied from the point ofview of nonequilibrium system dynamics. The study results reveal that although the complex nonlinearocean-atmosphere oscillator model possesses multiequilibrium states, the real climatic systempossesses only a quasi-normal state and a strong ENSO cycle stable state. The first passage timebetween states is also given in this paper, and the theoretical computational results agree withobservational data.
