Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic m...Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.展开更多
In this study,by means of the experiments for desulfurization of model diesel through oxidative extraction,the changes associated with the rate of desulfurization of diesel and the mechanism for oxidation of sulfides ...In this study,by means of the experiments for desulfurization of model diesel through oxidative extraction,the changes associated with the rate of desulfurization of diesel and the mechanism for oxidation of sulfides in diesel were explored. Through studying the mechanism for oxidation of sulfides and the principle of solvent extraction,the kinetic equation of desulfurization via oxidative extraction were determined. By means of the evaluation of model parameters and curve fitting,the reaction order between organic sulfide and sulfone,the intrinsic oxidation rate constant of organic sulfide and sulfone,and the equilibrium constant between sulfone in model diesel and extractive solvent were determined. The experimental values of the desulfurization rate and the theoretical values of the corresponding model equation had closely demonstrated that the desulfurization reaction rate had high accuracy. And the reaction kinetics could provide an important basis for diesel desulfurization process in the future.展开更多
Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined a...Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined at 900℃ using a thermo-gravimetric (TG) analyzer connected to a flue gas analyzer and this equation. The equation was simplified for specific coals, including high ash content, low ash content, and low ash fusibility ones. The results show that 1) the apparent reaction rate constant increases with an increase in volatile matter value as dry ash-free basis,2) the effective coefficient of diffusion decreases with an increase in ash as dry basis, and 3) the mass transfer coefficient is independent of coal quality on the whole. The apparent reaction rate constant, mass-transfer coefficient and effective coefficient of diffusion of six char samples range from 7.51×104 m/s to 8.98×104 m/s, 3.05×106 m/s to 3.23×106 m/s and 5.36×106 m2/s to 8.23×106 m2/s at 900℃, respectively.展开更多
We have proposed a general numerical framework for plasma simulations on graphics processing unit clusters based on microscopic kinetic equations with full collision terms.Our numerical algorithm consistently deals wi...We have proposed a general numerical framework for plasma simulations on graphics processing unit clusters based on microscopic kinetic equations with full collision terms.Our numerical algorithm consistently deals with both long-range(classical forces in the Vlasov term)and short-range(quantum processes in the collision term)interactions.Providing the relevant particle masses,charges and types(classical,fermionic or bosonic),as well as the external forces and the matrix elements(in the collisional integral),the algorithm consistently solves the coupled multi-particle kinetic equations.Currently,the framework is being tested and applied in the field of relativistic heavy-ion collisions;extensions to other plasma systems are straightforward.Our framework is a potential and competitive numerical platform for consistent plasma simulations.展开更多
Metal evaporation on the basis of the kinetic model equations(BGK and S-model) and the direct simulation Monte Carlo(DSMC) method was investigated computationally under the circumstances of collimators existing or not...Metal evaporation on the basis of the kinetic model equations(BGK and S-model) and the direct simulation Monte Carlo(DSMC) method was investigated computationally under the circumstances of collimators existing or not. Numerical data of distributions of number density, bulk velocity and temperature were reported over a wide range of evaporation rate.It was shown that these results reached a good agreement for the case of small evaporation rate, while the deviations became increasingly obvious with the increase of evaporation rate, especially when the collimators existed. Moreover, the deposition thickness over substrate obtained from the kinetic model equations were inaccurate even though the evaporation rate was small. All of the comparisons showed the reliability of the kinetic model equations, which require less computational cost at small evaporation rate and simple structure.展开更多
The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the ...The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field(Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma(Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma.Terms are highlighted that account for these oscillations in the kinetic equations of the abovementioned highly informative wave drift scenarios.展开更多
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic...In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.展开更多
To understand the aging effects on detonation performances of explosives,an accelerated aging mechanism and effect of explosives were analyzed.Based on the thermo-gravimetric(TG) curves of explosives under the heat ra...To understand the aging effects on detonation performances of explosives,an accelerated aging mechanism and effect of explosives were analyzed.Based on the thermo-gravimetric(TG) curves of explosives under the heat rate of 5,10 and 20 K·min-1,the thermal decomposition activation energy,pre-exponential factor,mechanism function and kinetic equation of the explosives were calculated by Ozawa's equation and decomposition extents.Then,according to the derived kinetic equation,the density,composition and heat of formation of GI-1,PBX-1 and PBX-2 explosive in different decomposition extents were calculated at accelerated aging temperatures of 70 ℃ and 75 ℃,respectively.Furthermore,the detonation parameters of GI-1,PBX-1 and PBX-2 explosives were found out by means of VLWR code.The results show that after accelerated aging,the density are decrease,the detonation velocity and pressure are all decreased slightly.展开更多
A study is conducted to determine the effect of a kind of high-pressure arc discharge plasma on the degradation rate and kinetic equations of chlorpyrifos in different solvents with the treated times and concentration...A study is conducted to determine the effect of a kind of high-pressure arc discharge plasma on the degradation rate and kinetic equations of chlorpyrifos in different solvents with the treated times and concentrations as variables. The degradation rate was sorted in different solvents as water, methanol, acetone and then acetoacetate. The tendencies of the degradation rates with treated time in water and methanol were optimally fitted with first-order kinetics equations while those in acetone and acetoacetate were fitted with zeroth-order kinetics equations. The difference was attributed to the stronger polarity of water and methanol. The weak correlation of the degradation rates with time was mainly because the high-temperature of the arc discharge tube and the chemically-active species generated by the discharge. The degradation half-life was extended with increase of chlorpyrifos concentration. A degradation half-life less than 3 min was achieved for chlorpyrifos in water and methanol when the initial concentration was less than 300 μg/ml.展开更多
This paper gives the kinetic formation of multi-dimensional conservation laws and proves the compactness of velocity averages by employing the compactness theorem in L(loc)(1)(R(n) x R(t)). As a by product, the existe...This paper gives the kinetic formation of multi-dimensional conservation laws and proves the compactness of velocity averages by employing the compactness theorem in L(loc)(1)(R(n) x R(t)). As a by product, the existence and uniqueness of the generalized solution is obtained.展开更多
文摘Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.
文摘In this study,by means of the experiments for desulfurization of model diesel through oxidative extraction,the changes associated with the rate of desulfurization of diesel and the mechanism for oxidation of sulfides in diesel were explored. Through studying the mechanism for oxidation of sulfides and the principle of solvent extraction,the kinetic equation of desulfurization via oxidative extraction were determined. By means of the evaluation of model parameters and curve fitting,the reaction order between organic sulfide and sulfone,the intrinsic oxidation rate constant of organic sulfide and sulfone,and the equilibrium constant between sulfone in model diesel and extractive solvent were determined. The experimental values of the desulfurization rate and the theoretical values of the corresponding model equation had closely demonstrated that the desulfurization reaction rate had high accuracy. And the reaction kinetics could provide an important basis for diesel desulfurization process in the future.
基金Projects 59906014, 50276066 and 20207014 supported by National Natural Science Foundation of China
文摘Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined at 900℃ using a thermo-gravimetric (TG) analyzer connected to a flue gas analyzer and this equation. The equation was simplified for specific coals, including high ash content, low ash content, and low ash fusibility ones. The results show that 1) the apparent reaction rate constant increases with an increase in volatile matter value as dry ash-free basis,2) the effective coefficient of diffusion decreases with an increase in ash as dry basis, and 3) the mass transfer coefficient is independent of coal quality on the whole. The apparent reaction rate constant, mass-transfer coefficient and effective coefficient of diffusion of six char samples range from 7.51×104 m/s to 8.98×104 m/s, 3.05×106 m/s to 3.23×106 m/s and 5.36×106 m2/s to 8.23×106 m2/s at 900℃, respectively.
基金supported by National Natural Science Foundation of China(No.12105227)。
文摘We have proposed a general numerical framework for plasma simulations on graphics processing unit clusters based on microscopic kinetic equations with full collision terms.Our numerical algorithm consistently deals with both long-range(classical forces in the Vlasov term)and short-range(quantum processes in the collision term)interactions.Providing the relevant particle masses,charges and types(classical,fermionic or bosonic),as well as the external forces and the matrix elements(in the collisional integral),the algorithm consistently solves the coupled multi-particle kinetic equations.Currently,the framework is being tested and applied in the field of relativistic heavy-ion collisions;extensions to other plasma systems are straightforward.Our framework is a potential and competitive numerical platform for consistent plasma simulations.
文摘Metal evaporation on the basis of the kinetic model equations(BGK and S-model) and the direct simulation Monte Carlo(DSMC) method was investigated computationally under the circumstances of collimators existing or not. Numerical data of distributions of number density, bulk velocity and temperature were reported over a wide range of evaporation rate.It was shown that these results reached a good agreement for the case of small evaporation rate, while the deviations became increasingly obvious with the increase of evaporation rate, especially when the collimators existed. Moreover, the deposition thickness over substrate obtained from the kinetic model equations were inaccurate even though the evaporation rate was small. All of the comparisons showed the reliability of the kinetic model equations, which require less computational cost at small evaporation rate and simple structure.
文摘The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field(Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma(Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma.Terms are highlighted that account for these oscillations in the kinetic equations of the abovementioned highly informative wave drift scenarios.
文摘In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.
文摘To understand the aging effects on detonation performances of explosives,an accelerated aging mechanism and effect of explosives were analyzed.Based on the thermo-gravimetric(TG) curves of explosives under the heat rate of 5,10 and 20 K·min-1,the thermal decomposition activation energy,pre-exponential factor,mechanism function and kinetic equation of the explosives were calculated by Ozawa's equation and decomposition extents.Then,according to the derived kinetic equation,the density,composition and heat of formation of GI-1,PBX-1 and PBX-2 explosive in different decomposition extents were calculated at accelerated aging temperatures of 70 ℃ and 75 ℃,respectively.Furthermore,the detonation parameters of GI-1,PBX-1 and PBX-2 explosives were found out by means of VLWR code.The results show that after accelerated aging,the density are decrease,the detonation velocity and pressure are all decreased slightly.
基金supported by the National Natural Science Foundation of China(No.5017700)Provincial Nature Science Foundation of Shanxi(No.20051078)
文摘A study is conducted to determine the effect of a kind of high-pressure arc discharge plasma on the degradation rate and kinetic equations of chlorpyrifos in different solvents with the treated times and concentrations as variables. The degradation rate was sorted in different solvents as water, methanol, acetone and then acetoacetate. The tendencies of the degradation rates with treated time in water and methanol were optimally fitted with first-order kinetics equations while those in acetone and acetoacetate were fitted with zeroth-order kinetics equations. The difference was attributed to the stronger polarity of water and methanol. The weak correlation of the degradation rates with time was mainly because the high-temperature of the arc discharge tube and the chemically-active species generated by the discharge. The degradation half-life was extended with increase of chlorpyrifos concentration. A degradation half-life less than 3 min was achieved for chlorpyrifos in water and methanol when the initial concentration was less than 300 μg/ml.
文摘This paper gives the kinetic formation of multi-dimensional conservation laws and proves the compactness of velocity averages by employing the compactness theorem in L(loc)(1)(R(n) x R(t)). As a by product, the existence and uniqueness of the generalized solution is obtained.
