A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network i...A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network is established. The solution of the stiff ordinary differential equations in the n-pentane pyrolysis model is completed by semi implicit Eular algorithm. Then the pyrolysis mechanism based on free radical reaction model is built,and the computational efficiency increases 10 times by algorithm optimization. The validity of this model and its solution method is confirmed by the experimental results of n-pentane pyrolysis.展开更多
The adsorption of pentachlorophenol （PCP） onto quartz, kaolinite, illite, montmorillonite and iron oxides has been investigated by batch equilibrium techniques. The pH-dependent isotherms are curves with peak values...The adsorption of pentachlorophenol （PCP） onto quartz, kaolinite, illite, montmorillonite and iron oxides has been investigated by batch equilibrium techniques. The pH-dependent isotherms are curves with peak values, the position of which is at about pH = 5-6 depending on the mineral species. Based on distribution of both speciation of surface hydroxyls on minerals and PCP in solution a surface reaction model involving surface complexation and surface electrostatic attraction is presented to fit the pH-dependent isotherms, and both reaction constants are calculated. The results show that on quartz and phyllosilicate minerals the predominant adsorption reaction is surface complexation, meanwhile both of surface electrostatic attraction and surface complexation are involved on the iron oxide minerals. The reaction constants of surface electrostatic adsorption are usually one to three orders in magnitude, larger than that of surface complexation. The concentration-dependent isotherms can be well fitted by Langmnir equation with the correlation coefficient R〉0.93 for kaolinite and iron oxides. The maximum adsorption is found in the order： hematite 〉 lepidocrocite 〉 goethite 〉 kaolinite 〉 quartz 〉 montmorillonite ≈ illite, which can be interpreted by consideration of both reaction mechanism and surface hydroxyl density. The significant adsorption of PCP onto mineral surfaces suggests that clay and iron oxide minerals will play an important role as HIOCs are adsorbed in laterite or latertoid soil, which is widespread in South China.展开更多
Through a survey of the literature on geology, hydrogeology and hydrogeochemistry, this paper presents a hydrogeochemical model for the groundwater system in a dross-dumping area of the Shandong Aluminium Plant. It is...Through a survey of the literature on geology, hydrogeology and hydrogeochemistry, this paper presents a hydrogeochemical model for the groundwater system in a dross-dumping area of the Shandong Aluminium Plant. It is considered that the groundwater-bearing medium is a mineral aggregate and that the interactions between groundwater and the groundwater-bearing medium can be described as a series of geochemical reactions. On that basis, the principle of minimum energy and the equations of mass balance, electron balance and electric neutrality are applied to construct a linear programming mathematical model for the calculation of mass transfer between water and rock with the simplex method.展开更多
To better characterize the properties of surface-initiated polymers, simultaneous bulk-and surface-initiated polymerizations are usually carried out by assuming that the properties of the surface-initiated polymers re...To better characterize the properties of surface-initiated polymers, simultaneous bulk-and surface-initiated polymerizations are usually carried out by assuming that the properties of the surface-initiated polymers resemble those of the bulk-initiated polymers. Through a Monte Carlo simulation using a heterogeneous stochastic reaction model, it was discovered that the bulk-initiated polymers exhibit a higher molecular weight and a lower dispersity than the corresponding surface-initiated polymers, which indicates that the equivalent assumption is invalid. Furthermore, the molecular weight distributions of the two types of polymers are also different, suggesting different polymerization mechanisms. The results can be simply explained by the heterogeneous distributions of reactants in the system. This study is helpful to better understand surface-initiated polymerization.展开更多
The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solut...The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.展开更多
A photonuclear reaction transport model based on an isospin-dependent quantum molecular dynamics model （IQMD） is presented in the intermediate energy region, which is named as GiQMD in this study. Methodology to sim...A photonuclear reaction transport model based on an isospin-dependent quantum molecular dynamics model （IQMD） is presented in the intermediate energy region, which is named as GiQMD in this study. Methodology to simulate the course of the photonuclear reaction within the IQMD frame is described to study the photo- absorption cross section and π meson production, and the simulation results are compared with some available experimental data as well as the Giessen Boltzmann-Uehling-Uhlenbeck model.展开更多
Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,...Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.展开更多
By partial and general dissection of large prebaked alumina electrolysis cells, the macro appearance, chemical composition and phase variations were studied employing actual observations and measurements on the cells ...By partial and general dissection of large prebaked alumina electrolysis cells, the macro appearance, chemical composition and phase variations were studied employing actual observations and measurements on the cells together with X ray diffraction phase analysis and scanning electron microscopy of samples from different locations. According to the practical production, a chemical reaction model of aluminum reduction cell failure was set up in order to reduce the incidence of cell failure and extend pot service life.展开更多
The Global Reaction Model describes a set of chemical reactions that can potentially occur during the process of obtaining silicon rich oxide (SRO) films, regardless of the technique used to grow such films which are ...The Global Reaction Model describes a set of chemical reactions that can potentially occur during the process of obtaining silicon rich oxide (SRO) films, regardless of the technique used to grow such films which are an outside stoichiometry material. Particularly, chemical reactions that occur during the process of growing of SRO films by LPCVD technique are highlighted in this model. We suggest and evaluate either some types of molecules or resulting nanostructures and we predict theoretically, by applying the density functional theory, the contribution that they may have to the phenomenon of luminescence which is measured in SRO films. Also, we have calculated the opto-electronic properties of SRO films. The suggested model provides enough information required to identify the molecular structures resulting from the presence of defects in SRO films and also those corresponding to charged structures. It is also possible to detect the molecular structures which are modified due to the effect of heat treatment, and identify the presence of different oxidation states inclusive the formation of siloxanes.展开更多
The Glauber/eikonal model is a widely used tool for studying intermediate-and high-energy nuclear reactions.When calculating the Glauber/eikonal model phase shift functions,the optical limit approximation(OLA)is often...The Glauber/eikonal model is a widely used tool for studying intermediate-and high-energy nuclear reactions.When calculating the Glauber/eikonal model phase shift functions,the optical limit approximation(OLA)is often used.The OLA neglects the multiple scattering of the constituent nucleons in the projectile and target nuclei.However,the nucleon-target version of the Glauber model(the NTG model)proposed by Abu-Ibrahim and Suzuki includes multiple scattering effects between the projectile nucleons and target nuclei.The NTG model was found to improve the description of the elastic scattering angular distributions and total reaction cross sections of some light heavy-ion systems with respect to the OLA.In this work,we study the single-nucleon removal reactions(SNRRs)induced by carbon isotopes on ^(12)C and ^(9)Be targets using both the NTG model and the OLA.Reduction factors(RFs)of the single-nucleon spectroscopic factors were obtained by comparing the experimental and theoretical SNRR cross sections.On average,the RFs obtained with the NTG model were smaller than those obtained using the OLA by 7.8%,in which the average difference in one-neutron removal was 10.6% and that in one-proton removal was 4.2%.However,the RFs were still strongly dependent on the neutron-proton asymmetryΔS of the projectile nuclei,even when the NTG model was used.展开更多
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ...Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.展开更多
A zero-dimensional model to simulate a nano-pulse-discharged bubble in water was developed. The model consists of gas and liquid phases corresponding to the inside and outside of the bubble, respectively. The diffusio...A zero-dimensional model to simulate a nano-pulse-discharged bubble in water was developed. The model consists of gas and liquid phases corresponding to the inside and outside of the bubble, respectively. The diffusions of chemical species from the gas to the liquid phase through the bubble interface was also investigated. The initial gas is Ar, but includes a little H20 and 02 in the bubble. The time evolution of the OH concentration in the liquid phase was mainly investigated as an important species for water treatment. It was shown that OH was generated in the bubble and then diffused into the liquid. With the application of a continuous nano-pulse discharge, more OH radicals were generated as the frequency increased at a low voltage for a given power consumption.展开更多
The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （...The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.展开更多
IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1<...IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1</sub>, M<sub>2</sub> and M<sub>3</sub> which can react with each other to produce two new kinds of other chemical compounds: （M<sub>2</sub>）<sub>n</sub> （M<sub>1</sub>）<sub>m</sub> and （M<sub>3</sub>）<sub>r</sub> （M<sub>1</sub>）<sub>κ</sub> at the same time. Usually, these reactions are irreversible and they have the following forms:展开更多
Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignitio...Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignition-Growth reaction rate model,which can describe the shock initiation processes of explosives with different initial densities,particle sizes and loading pressures by only one set of model parameters.Compared with the Lee-Tarver reaction rate model,the new Ignition-Growth reaction rate model describes better the shock initiation process of explosives and requires fewer model parameters.Moreover,the shock initiation of a 2,4-Dinitroanisole(DNAN)-based melt-cast explosive RDA-2(DNAN/HMX(octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine)/aluminum)are investigated both experimentally and numerically.A series of shock initiation experiments is performed with manganin piezoresistive pressure gauges and corresponding numerical simulations are carried out with the new Ignition-Growth reaction rate model.The RDA-2 explosive is found to have higher critical initiation pressure and lower shock sensitivity than traditional explosives(such as the Comp.B explosive).The calibrated reaction rate model parameters of RDA-2 could provide numerical basis for its further application.展开更多
A melt-cast Duan-Zhang-Kim(DZK)mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism.A series of shock initiation experimen...A melt-cast Duan-Zhang-Kim(DZK)mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism.A series of shock initiation experiments was performed for the Comp B melt-cast explosive to estimate effects of the loading pressure and the particle size of granular explosive component,and the mesoscopic model is validated against the experimental data.Further numerical simulations indicate that the initial density and formula proportion greatly affect the hot-spot ignition of melt-cast explosives.展开更多
The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated t...The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N^-1.5 （N is the length of chains）, which is in consistent with de Gennes＇s result.展开更多
In this paper the time-space correlation of density fluctuation of the 3He reaction-diffusion model is investigated where the equilibrium distribution is described by the generalized Maxwell Boltzmann distribution in ...In this paper the time-space correlation of density fluctuation of the 3He reaction-diffusion model is investigated where the equilibrium distribution is described by the generalized Maxwell Boltzmann distribution in the framework of Tsallis statistics. By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the nonextensive system. This paper uses the ^3He reaction diffusion model to analyse the effect of nonextensive pressure on the fluctuation and finds that the nonextensive parameter q plays a very important role in determining the characteristics of the fluctuation waves.展开更多
In this study a mathematical model of a small scale single pellet for the oxidative coupling of methane（OCM）over titanite pervoskite is developed.The method is based on a computational fluid dynamics（CFD）code whic...In this study a mathematical model of a small scale single pellet for the oxidative coupling of methane（OCM）over titanite pervoskite is developed.The method is based on a computational fluid dynamics（CFD）code which known as Fluent may be adopted to model the reactions that take place inside the porous catalyst pellet.The steady state single pellet model is coupled with a kinetic model and the intra-pellet concentration profiles of species are provided.Subsequent to achieving this goal,a nonlinear reaction network consisting of nine catalytic reactions and one gas phase reaction as an external program is successfully implemented to CFD-code as a reaction term in solving the equations.This study is based on the experimental design which is conducted in a differential reactor with a Sn/BaTiO3 catalyst（7-8 mesh） at atmospheric pressure,GHSV of 12000 h-1,ratio of methane to oxygen of 2,and three different temperatures of 1023,1048 and 1073 K.The modeling results such as selectivity and conversion at the pellet exit are in good agreement with the experimental data.Therefore,it is suggested that to achieve high yield in OCM process the modeling of the single pellet should be considered as the heart of catalytic fixed bed reactor.展开更多
The treatment of a multicomponent reversible reaction network is extremely complicated because largenumber of rate constants must be precisely determined and because the calculation based on these rateconstants is ted...The treatment of a multicomponent reversible reaction network is extremely complicated because largenumber of rate constants must be precisely determined and because the calculation based on these rateconstants is tedious.In order to reduce the degrees of freedom of the process,the authors propose a methodin which the reactor and the separator are regarded as a whole.Based on this approach,an N-componentreversible reaction system can be dealt with as a two—component system.Consequently,a simple and ac-cessible way of the apparent rate determination is suggested.For fiist-order reactions,an explicit,simplifiedexpression has been derived for both lumped and distributed parameter reaction systems.展开更多
文摘A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network is established. The solution of the stiff ordinary differential equations in the n-pentane pyrolysis model is completed by semi implicit Eular algorithm. Then the pyrolysis mechanism based on free radical reaction model is built,and the computational efficiency increases 10 times by algorithm optimization. The validity of this model and its solution method is confirmed by the experimental results of n-pentane pyrolysis.
基金the National Natural Science Foundation of China （grant No. 40373045） the Natural Science Foundation of Guangdong Province, China （grant No. 030461） the Chinese Academy of Sciences Innovation Project （GIGCX-04-02）.
文摘The adsorption of pentachlorophenol （PCP） onto quartz, kaolinite, illite, montmorillonite and iron oxides has been investigated by batch equilibrium techniques. The pH-dependent isotherms are curves with peak values, the position of which is at about pH = 5-6 depending on the mineral species. Based on distribution of both speciation of surface hydroxyls on minerals and PCP in solution a surface reaction model involving surface complexation and surface electrostatic attraction is presented to fit the pH-dependent isotherms, and both reaction constants are calculated. The results show that on quartz and phyllosilicate minerals the predominant adsorption reaction is surface complexation, meanwhile both of surface electrostatic attraction and surface complexation are involved on the iron oxide minerals. The reaction constants of surface electrostatic adsorption are usually one to three orders in magnitude, larger than that of surface complexation. The concentration-dependent isotherms can be well fitted by Langmnir equation with the correlation coefficient R〉0.93 for kaolinite and iron oxides. The maximum adsorption is found in the order： hematite 〉 lepidocrocite 〉 goethite 〉 kaolinite 〉 quartz 〉 montmorillonite ≈ illite, which can be interpreted by consideration of both reaction mechanism and surface hydroxyl density. The significant adsorption of PCP onto mineral surfaces suggests that clay and iron oxide minerals will play an important role as HIOCs are adsorbed in laterite or latertoid soil, which is widespread in South China.
文摘Through a survey of the literature on geology, hydrogeology and hydrogeochemistry, this paper presents a hydrogeochemical model for the groundwater system in a dross-dumping area of the Shandong Aluminium Plant. It is considered that the groundwater-bearing medium is a mineral aggregate and that the interactions between groundwater and the groundwater-bearing medium can be described as a series of geochemical reactions. On that basis, the principle of minimum energy and the equations of mass balance, electron balance and electric neutrality are applied to construct a linear programming mathematical model for the calculation of mass transfer between water and rock with the simplex method.
基金financially supported by the National Natural Science Foundation of China (No.22263002)the “Overseas 100 Talents Program” of Guangxi Higher Education。
文摘To better characterize the properties of surface-initiated polymers, simultaneous bulk-and surface-initiated polymerizations are usually carried out by assuming that the properties of the surface-initiated polymers resemble those of the bulk-initiated polymers. Through a Monte Carlo simulation using a heterogeneous stochastic reaction model, it was discovered that the bulk-initiated polymers exhibit a higher molecular weight and a lower dispersity than the corresponding surface-initiated polymers, which indicates that the equivalent assumption is invalid. Furthermore, the molecular weight distributions of the two types of polymers are also different, suggesting different polymerization mechanisms. The results can be simply explained by the heterogeneous distributions of reactants in the system. This study is helpful to better understand surface-initiated polymerization.
基金the National Sciences Foundation of China and the Doctorial Program of Higher Edua-tion
文摘The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11421505 and 11220101005the National Basic Research Program of China under Grant No 2014CB845401the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB16
文摘A photonuclear reaction transport model based on an isospin-dependent quantum molecular dynamics model （IQMD） is presented in the intermediate energy region, which is named as GiQMD in this study. Methodology to simulate the course of the photonuclear reaction within the IQMD frame is described to study the photo- absorption cross section and π meson production, and the simulation results are compared with some available experimental data as well as the Giessen Boltzmann-Uehling-Uhlenbeck model.
文摘Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.
文摘By partial and general dissection of large prebaked alumina electrolysis cells, the macro appearance, chemical composition and phase variations were studied employing actual observations and measurements on the cells together with X ray diffraction phase analysis and scanning electron microscopy of samples from different locations. According to the practical production, a chemical reaction model of aluminum reduction cell failure was set up in order to reduce the incidence of cell failure and extend pot service life.
文摘The Global Reaction Model describes a set of chemical reactions that can potentially occur during the process of obtaining silicon rich oxide (SRO) films, regardless of the technique used to grow such films which are an outside stoichiometry material. Particularly, chemical reactions that occur during the process of growing of SRO films by LPCVD technique are highlighted in this model. We suggest and evaluate either some types of molecules or resulting nanostructures and we predict theoretically, by applying the density functional theory, the contribution that they may have to the phenomenon of luminescence which is measured in SRO films. Also, we have calculated the opto-electronic properties of SRO films. The suggested model provides enough information required to identify the molecular structures resulting from the presence of defects in SRO films and also those corresponding to charged structures. It is also possible to detect the molecular structures which are modified due to the effect of heat treatment, and identify the presence of different oxidation states inclusive the formation of siloxanes.
基金financially supported by the National Key R&D Program of China(No.2023YFA1606702)the National Natural Science Foundation of China(Nos.U2067205 and 12205098).
文摘The Glauber/eikonal model is a widely used tool for studying intermediate-and high-energy nuclear reactions.When calculating the Glauber/eikonal model phase shift functions,the optical limit approximation(OLA)is often used.The OLA neglects the multiple scattering of the constituent nucleons in the projectile and target nuclei.However,the nucleon-target version of the Glauber model(the NTG model)proposed by Abu-Ibrahim and Suzuki includes multiple scattering effects between the projectile nucleons and target nuclei.The NTG model was found to improve the description of the elastic scattering angular distributions and total reaction cross sections of some light heavy-ion systems with respect to the OLA.In this work,we study the single-nucleon removal reactions(SNRRs)induced by carbon isotopes on ^(12)C and ^(9)Be targets using both the NTG model and the OLA.Reduction factors(RFs)of the single-nucleon spectroscopic factors were obtained by comparing the experimental and theoretical SNRR cross sections.On average,the RFs obtained with the NTG model were smaller than those obtained using the OLA by 7.8%,in which the average difference in one-neutron removal was 10.6% and that in one-proton removal was 4.2%.However,the RFs were still strongly dependent on the neutron-proton asymmetryΔS of the projectile nuclei,even when the NTG model was used.
基金国家自然科学基金，NKBRD of China，Doctor Foundation of Education Commission of China
文摘Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.
基金supported partially by Japan Society for the Promotion of Science(JSPS)KAKENHI(No.26249015)
文摘A zero-dimensional model to simulate a nano-pulse-discharged bubble in water was developed. The model consists of gas and liquid phases corresponding to the inside and outside of the bubble, respectively. The diffusions of chemical species from the gas to the liquid phase through the bubble interface was also investigated. The initial gas is Ar, but includes a little H20 and 02 in the bubble. The time evolution of the OH concentration in the liquid phase was mainly investigated as an important species for water treatment. It was shown that OH was generated in the bubble and then diffused into the liquid. With the application of a continuous nano-pulse discharge, more OH radicals were generated as the frequency increased at a low voltage for a given power consumption.
文摘The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method （LWPM）. Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge-Kutta method of order four （RK-4）. Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.
文摘IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1</sub>, M<sub>2</sub> and M<sub>3</sub> which can react with each other to produce two new kinds of other chemical compounds: （M<sub>2</sub>）<sub>n</sub> （M<sub>1</sub>）<sub>m</sub> and （M<sub>3</sub>）<sub>r</sub> （M<sub>1</sub>）<sub>κ</sub> at the same time. Usually, these reactions are irreversible and they have the following forms:
基金supported by the Innovative Group of Material and Structure Impact Dynamics(Grant No.11521062)。
文摘Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignition-Growth reaction rate model,which can describe the shock initiation processes of explosives with different initial densities,particle sizes and loading pressures by only one set of model parameters.Compared with the Lee-Tarver reaction rate model,the new Ignition-Growth reaction rate model describes better the shock initiation process of explosives and requires fewer model parameters.Moreover,the shock initiation of a 2,4-Dinitroanisole(DNAN)-based melt-cast explosive RDA-2(DNAN/HMX(octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine)/aluminum)are investigated both experimentally and numerically.A series of shock initiation experiments is performed with manganin piezoresistive pressure gauges and corresponding numerical simulations are carried out with the new Ignition-Growth reaction rate model.The RDA-2 explosive is found to have higher critical initiation pressure and lower shock sensitivity than traditional explosives(such as the Comp.B explosive).The calibrated reaction rate model parameters of RDA-2 could provide numerical basis for its further application.
基金the National Natural Science Foundation of China(Grant No.11772056)the NSAF Joint Fund(Grants No.U1630113)and the Innovative Group of Material and Structure Impact Dynamics(Grant No.11521062)。
文摘A melt-cast Duan-Zhang-Kim(DZK)mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism.A series of shock initiation experiments was performed for the Comp B melt-cast explosive to estimate effects of the loading pressure and the particle size of granular explosive component,and the mesoscopic model is validated against the experimental data.Further numerical simulations indicate that the initial density and formula proportion greatly affect the hot-spot ignition of melt-cast explosives.
基金This work was financially supported by the National Natural Science Foundation of China (No. 50390090).
文摘The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N^-1.5 （N is the length of chains）, which is in consistent with de Gennes＇s result.
文摘In this paper the time-space correlation of density fluctuation of the 3He reaction-diffusion model is investigated where the equilibrium distribution is described by the generalized Maxwell Boltzmann distribution in the framework of Tsallis statistics. By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the nonextensive system. This paper uses the ^3He reaction diffusion model to analyse the effect of nonextensive pressure on the fluctuation and finds that the nonextensive parameter q plays a very important role in determining the characteristics of the fluctuation waves.
文摘In this study a mathematical model of a small scale single pellet for the oxidative coupling of methane（OCM）over titanite pervoskite is developed.The method is based on a computational fluid dynamics（CFD）code which known as Fluent may be adopted to model the reactions that take place inside the porous catalyst pellet.The steady state single pellet model is coupled with a kinetic model and the intra-pellet concentration profiles of species are provided.Subsequent to achieving this goal,a nonlinear reaction network consisting of nine catalytic reactions and one gas phase reaction as an external program is successfully implemented to CFD-code as a reaction term in solving the equations.This study is based on the experimental design which is conducted in a differential reactor with a Sn/BaTiO3 catalyst（7-8 mesh） at atmospheric pressure,GHSV of 12000 h-1,ratio of methane to oxygen of 2,and three different temperatures of 1023,1048 and 1073 K.The modeling results such as selectivity and conversion at the pellet exit are in good agreement with the experimental data.Therefore,it is suggested that to achieve high yield in OCM process the modeling of the single pellet should be considered as the heart of catalytic fixed bed reactor.
文摘The treatment of a multicomponent reversible reaction network is extremely complicated because largenumber of rate constants must be precisely determined and because the calculation based on these rateconstants is tedious.In order to reduce the degrees of freedom of the process,the authors propose a methodin which the reactor and the separator are regarded as a whole.Based on this approach,an N-componentreversible reaction system can be dealt with as a two—component system.Consequently,a simple and ac-cessible way of the apparent rate determination is suggested.For fiist-order reactions,an explicit,simplifiedexpression has been derived for both lumped and distributed parameter reaction systems.
