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
Possibilities of synchronized oscillations in glycolysis mediated by various extracellular metabolites are investigated theoretically using two-dimensional reaction-diffusion systems, which originate from the existing...Possibilities of synchronized oscillations in glycolysis mediated by various extracellular metabolites are investigated theoretically using two-dimensional reaction-diffusion systems, which originate from the existing seven-variable model. Our simulation results indicate the existence of alternative mediators such as ATP and 1,3-bisphosphoglycerate, in addition to already known acetaldehyde or pyruvate. Further, it is also suggested that the alternative intercellular communicator plays a more important role in the respect that these can synchronize oscillations instantaneously not only with difference phases but also with different periods. Relations between intercellular coupling and synchronization mechanisms are also analyzed and discussed by changing the values of parameters such as the diffusion coefficient and the cell density that can reflect in tercellular coupling strength.展开更多
In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous...Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.展开更多
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for...This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.展开更多
Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated ...Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.展开更多
This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by ...This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.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
Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Men...Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.展开更多
A new visualization method for studying the damage to gel structure caused by high salinity ions is explored by using the characteristics of suppression image signal of Mn^(2+) and nuclear magnetic resonance(NMR) imag...A new visualization method for studying the damage to gel structure caused by high salinity ions is explored by using the characteristics of suppression image signal of Mn^(2+) and nuclear magnetic resonance(NMR) imaging technique. The diffusion and distribution characteristics of Mn^(2+) in porous media-gel system were studied based on manganese chloride static diffusion and gel flooding experiments, and the gel's nuclear magnetic image and displacement pressure were tested. The results show that the diffusion of Mn^(2+)conforms to the Fick diffusion law in porous media-gel system, and the diffusion speed of Mn^(2+) increases and the area of gel image decreases gradually with the increase of concentration, and the image of gel decreases faster and the pressure drop of water drive is larger in flooding experiment of manganese chloride with higher concentration. Reaction-diffusion model with the reaction of Mn^(2+) with gel was established to study the concentration distribution characteristics of Mn^(2+). The model is validated by comparing the results with magnetic resonance imaging(MRI) experiments and the diffusion coefficient of Mn^(2+) equals 1.6 mm^2/h, and the minimum concentration of Mn^(2+) to impact gel NMR image signals is 2.5 g/L. The above results show that the diffusion of Mn^(2+) into the gel in the rock core inhibits the imaging signal of the gel and damages its strength, and the greater the concentration is, the greater the influence. Increase of adsorption amount of gel and reaction rate, reduction of diffusion time, and addition of ion adsorption isolator all can reduce the impact of Mn^(2+) on the gel.展开更多
In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we estab...In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we establish the threshold dynamic behavior of the model based on the basic reproduction number R0, specifically, we prove the globally asymptotic stability of the disease-free equilibrium and the uniform persistence of the model. Thirdly, we show the existence and stability of the endemic equilibrium of the homogeneous system and obtain different cases of positive solution. Fourthly, we investigate the effects of vaccination rate and saturated incidence rate on the basic reproduction number. The results indicate that increasing vaccination rate and saturation rate can effectively control the transmission of the disease. Finally, we conduct numerical simulations to verify the aforementioned conclusions.展开更多
Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations cont...Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations contains a non-linear term related to Monod kinetics, Andrews kinetics, interactive model from Monod kinetics and Andrews kinetics. Analytical expression of concentration of VOC (Volatile organic compounds) and oxygen are derived by solving the system of non-linear equations using Adomian decomposition method (ADM) method. Our analytical results are also compared with the simulation results. Satisfactory agreement is noted.展开更多
In the development of Li-ion batteries(LIBs)with high energy/power density,long cycle-life,fast charging,and high safety,an insight into charge transfer reactions is required.Although electrochemical impedance spectro...In the development of Li-ion batteries(LIBs)with high energy/power density,long cycle-life,fast charging,and high safety,an insight into charge transfer reactions is required.Although electrochemical impedance spectroscopy(EIS)is regarded as a powerful diagnosis tool,it is not a direct but an indirect measurement.With respect to this,some critical questions need to be answered:(i)why EIS can reflect the kinetics of charge transfer reactions;(ii)what the inherent logical relationship between impedance models under different physical scenes is;(iii)how charge transfer reactions compete with each other at multiple scales.This work aims at answering these questions via developing a theory framework so as to mitigate the blindness and uncertainty in unveiling charge transfer reactions in LIBs.To systematically answer the above questions,this article is organized into a three-in-one(review,tutorial,and research)type and the following contributions are made:(i)a brief review is given for impedance model development of the LIBs over the past half century;(ii)an open source code toolbox is developed based on the unified impedance model;(iii)the competive mechanisms of charge transfer reactions are unveiled based on the developed EIS-Toolbox@LIB.This work not only clarifies theoretical fundamentals,but also provides an easy-to-use open source code for EIS-Toolbox@LIB to optimize fast charge/discharge,mitigate cycle aging,and improve energy/power density.展开更多
A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten ki...A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation.展开更多
The detailed mechanism of CuI-catalyzed C-O intramolecular coupling reaction of 2-（2-bromo-4-fluoro-phenyl）-l- cyclohexen-1-yl trifluoromethane-sulfonate was studied with the density functional theory （DFT）. The g...The detailed mechanism of CuI-catalyzed C-O intramolecular coupling reaction of 2-（2-bromo-4-fluoro-phenyl）-l- cyclohexen-1-yl trifluoromethane-sulfonate was studied with the density functional theory （DFT）. The geometries of the reactants, transition states, intermediates and products were optimized at the B3LYP/6-31 ＋G＊ level. Meanwhile, the single point energy of species involved in gas and solvent at B3LYP/6-31 I＋G＊ level was individually investigated. Polarizable continuum models （PCM） were applied to the dioxane and water solutions at the same level, respectively. Results show that the rate-limiting step, M3→TS3, does not change in different solutions. However, the activation energy in a dioxane solution is lower than that in water, which explains the previous experimental results. Compared with the non-catalyzed reaction process, the activation energy of the rate- limiting step is reduced by 56.53 kJ mo1-1 in gas and 44.84 kJ mol-l in solvent, demonstrating a high catalytic efficiency of CuI.展开更多
A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reactio...A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.展开更多
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Possibilities of synchronized oscillations in glycolysis mediated by various extracellular metabolites are investigated theoretically using two-dimensional reaction-diffusion systems, which originate from the existing seven-variable model. Our simulation results indicate the existence of alternative mediators such as ATP and 1,3-bisphosphoglycerate, in addition to already known acetaldehyde or pyruvate. Further, it is also suggested that the alternative intercellular communicator plays a more important role in the respect that these can synchronize oscillations instantaneously not only with difference phases but also with different periods. Relations between intercellular coupling and synchronization mechanisms are also analyzed and discussed by changing the values of parameters such as the diffusion coefficient and the cell density that can reflect in tercellular coupling strength.
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
文摘Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.
文摘This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
文摘Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.
基金supported by the NSFC Grant(No.11171158)Project of Graduate Education Innovation of Jiangsu Province(No.KYLX 0719)Project of Natural Science Research of Higher Education Institutions of Jiangsu Province(No.15KJB110008)
文摘This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.
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Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.
基金Supported by the National Natural Science Foundation of China(51274136 51704190)
文摘A new visualization method for studying the damage to gel structure caused by high salinity ions is explored by using the characteristics of suppression image signal of Mn^(2+) and nuclear magnetic resonance(NMR) imaging technique. The diffusion and distribution characteristics of Mn^(2+) in porous media-gel system were studied based on manganese chloride static diffusion and gel flooding experiments, and the gel's nuclear magnetic image and displacement pressure were tested. The results show that the diffusion of Mn^(2+)conforms to the Fick diffusion law in porous media-gel system, and the diffusion speed of Mn^(2+) increases and the area of gel image decreases gradually with the increase of concentration, and the image of gel decreases faster and the pressure drop of water drive is larger in flooding experiment of manganese chloride with higher concentration. Reaction-diffusion model with the reaction of Mn^(2+) with gel was established to study the concentration distribution characteristics of Mn^(2+). The model is validated by comparing the results with magnetic resonance imaging(MRI) experiments and the diffusion coefficient of Mn^(2+) equals 1.6 mm^2/h, and the minimum concentration of Mn^(2+) to impact gel NMR image signals is 2.5 g/L. The above results show that the diffusion of Mn^(2+) into the gel in the rock core inhibits the imaging signal of the gel and damages its strength, and the greater the concentration is, the greater the influence. Increase of adsorption amount of gel and reaction rate, reduction of diffusion time, and addition of ion adsorption isolator all can reduce the impact of Mn^(2+) on the gel.
文摘In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we establish the threshold dynamic behavior of the model based on the basic reproduction number R0, specifically, we prove the globally asymptotic stability of the disease-free equilibrium and the uniform persistence of the model. Thirdly, we show the existence and stability of the endemic equilibrium of the homogeneous system and obtain different cases of positive solution. Fourthly, we investigate the effects of vaccination rate and saturated incidence rate on the basic reproduction number. The results indicate that increasing vaccination rate and saturation rate can effectively control the transmission of the disease. Finally, we conduct numerical simulations to verify the aforementioned conclusions.
文摘Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations contains a non-linear term related to Monod kinetics, Andrews kinetics, interactive model from Monod kinetics and Andrews kinetics. Analytical expression of concentration of VOC (Volatile organic compounds) and oxygen are derived by solving the system of non-linear equations using Adomian decomposition method (ADM) method. Our analytical results are also compared with the simulation results. Satisfactory agreement is noted.
基金the financial support from the National Science Foundation of China(22078190)the National Key R&D Plan of China(2020YFB1505802)。
文摘In the development of Li-ion batteries(LIBs)with high energy/power density,long cycle-life,fast charging,and high safety,an insight into charge transfer reactions is required.Although electrochemical impedance spectroscopy(EIS)is regarded as a powerful diagnosis tool,it is not a direct but an indirect measurement.With respect to this,some critical questions need to be answered:(i)why EIS can reflect the kinetics of charge transfer reactions;(ii)what the inherent logical relationship between impedance models under different physical scenes is;(iii)how charge transfer reactions compete with each other at multiple scales.This work aims at answering these questions via developing a theory framework so as to mitigate the blindness and uncertainty in unveiling charge transfer reactions in LIBs.To systematically answer the above questions,this article is organized into a three-in-one(review,tutorial,and research)type and the following contributions are made:(i)a brief review is given for impedance model development of the LIBs over the past half century;(ii)an open source code toolbox is developed based on the unified impedance model;(iii)the competive mechanisms of charge transfer reactions are unveiled based on the developed EIS-Toolbox@LIB.This work not only clarifies theoretical fundamentals,but also provides an easy-to-use open source code for EIS-Toolbox@LIB to optimize fast charge/discharge,mitigate cycle aging,and improve energy/power density.
文摘A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation.
文摘The detailed mechanism of CuI-catalyzed C-O intramolecular coupling reaction of 2-（2-bromo-4-fluoro-phenyl）-l- cyclohexen-1-yl trifluoromethane-sulfonate was studied with the density functional theory （DFT）. The geometries of the reactants, transition states, intermediates and products were optimized at the B3LYP/6-31 ＋G＊ level. Meanwhile, the single point energy of species involved in gas and solvent at B3LYP/6-31 I＋G＊ level was individually investigated. Polarizable continuum models （PCM） were applied to the dioxane and water solutions at the same level, respectively. Results show that the rate-limiting step, M3→TS3, does not change in different solutions. However, the activation energy in a dioxane solution is lower than that in water, which explains the previous experimental results. Compared with the non-catalyzed reaction process, the activation energy of the rate- limiting step is reduced by 56.53 kJ mo1-1 in gas and 44.84 kJ mol-l in solvent, demonstrating a high catalytic efficiency of CuI.
文摘A theoretical model for the non steady-state response of a pH-based potentiometric biosensor immobilizing organophosphorus hydrolase (OPH) is discussed. The model is based on a system of five coupled nonlinear reaction-diffusion equations under non steady-state conditions for enzyme reactions occurring in potentiometric biosensor that describes the concentration of substrate and hydrolysis products within the membrane. New approximate analytical expressions for the concentration of the substrate (organophosphorus pesticides (OPs)) and products are derived for all values of Thiele modulus and buffer concentration using new approach of homotopy perturbation method. The analytical results are also compared with numerical ones and a good agreement is obtained. The obtained results are valid for the whole solution domain.
