A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems ...A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems of reaction diffusion equations is studied usingthe theory of differential inequalities.展开更多
The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior ...The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.展开更多
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the re...In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.展开更多
For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geomet...For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.展开更多
A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh tra...A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.展开更多
In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers r...In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.展开更多
Electrochemical N_(2) reduction reaction(eNRR) over Cu-based catalysts suffers from an intrinsically low activity of Cu for activation of stable N_(2) molecules and the limited supply of N_(2) to the catalyst due to i...Electrochemical N_(2) reduction reaction(eNRR) over Cu-based catalysts suffers from an intrinsically low activity of Cu for activation of stable N_(2) molecules and the limited supply of N_(2) to the catalyst due to its low solubility in aqueous electrolytes.Herein,we propose phosphorus-activated Cu electrocatalysts to generate electron-deficient Cu sites on the catalyst surface to promote the adsorption of N_(2) molecules.The eNRR system is further modified using a gas diffusion electrode(GDE) coated with polytetrafluoroethylene(PTFE) to form an effective three-phase boundary of liquid water-gas N_(2)-solid catalyst to facilitate easy access of N_(2) to the catalytic sites.As a result,the new catalyst in the flow-type cell records a Faradaic efficiency of 13.15% and an NH_(3) production rate of 7.69 μg h^(-1) cm^(-2) at-0.2 V_(RHE),which represent 3.56 and 59.2 times increases from those obtained with a pristine Cu electrode in a typical electrolytic cell.This work represents a successful demonstration of dual modification strategies;catalyst modification and N_(2) supplying system engineering,and the results would provide a useful platform for further developments of electrocatalysts and reaction systems.展开更多
The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and a...The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.展开更多
A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptoti...A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.展开更多
The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifyi...The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.展开更多
We consider, from the point of view of a coaccelerated frame, a uniformly accelerated multi-level atom in interaction with vacuum quantum electromagnetic fields in the multi-polar coupling scheme, and calculate the ra...We consider, from the point of view of a coaccelerated frame, a uniformly accelerated multi-level atom in interaction with vacuum quantum electromagnetic fields in the multi-polar coupling scheme, and calculate the rate of change of the atom＇s energy assuming a thermal bath at a finite temperature T in the Rindler wedge. Comparison with the spontaneous excitation rate of the atom calculated in the instantaneous inertial frame of the atom shows that both the inertial and coaccelerated observer would agree with each other only when the temperature of the thermal bath equals the FDU value TFDU = α/2π.展开更多
A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michael...A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.展开更多
In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the...In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave （AOMSW）, we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of ε.展开更多
A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalitie...A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.展开更多
基金Supported by the National Natural Science Foundation of China(No.90211004 No. 10471039)the Natural Science Foundation of Zhejiang Province (No.102009).
文摘A nonlinear singularly perturbed problems for reaction diffusion equationwith boundary perturbation is considered. Under suitable conditions, the asymptotic behavior ofsolution for the initial boundary value problems of reaction diffusion equations is studied usingthe theory of differential inequalities.
基金Supported by the National Natural Science Foundation of China (No 90111011 and 10471039)by the Natural Science Foundation of Zhejiang (No.102009).
文摘The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.
基金Project supported by the National Natural Science Foundation of China （Nos. 40676016, 10471039）, the National Key Basic Research Special Foundation of China （No. 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （No. KZCX3-SW-221） and in part by EInstitutes of Shanghai Municipal Education Commission （No. E03004）
文摘In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
文摘For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.
基金Acknowledgments. The support from the National Natural Science Foundation of China under Grants No.10671146 and No.50678122 is acknowledged. The authors are grateful to the referee and the editor for helpful comments and suggestions.
文摘A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.
基金supported by National Natural Science Foundation of China(Grant No.11071209)Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(Grant No.2010-0025700)Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(Grant No.12KJD110008)
文摘In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.
基金supported by the Climate Change Response Project (NRF-2019M1A2A2065612)the Brainlink Project (NRF2022H1D3A3A01081140)+3 种基金the NRF-2021R1A4A3027878 and the No. RS-2023-00212273 funded by the Ministry of Science and ICT of Korea via National Research Foundationresearch funds from Hanhwa Solutions Chemicals (1.220029.01)UNIST (1.190013.01)supported by the Institute for Basic Science (IBS-R019-D1)。
文摘Electrochemical N_(2) reduction reaction(eNRR) over Cu-based catalysts suffers from an intrinsically low activity of Cu for activation of stable N_(2) molecules and the limited supply of N_(2) to the catalyst due to its low solubility in aqueous electrolytes.Herein,we propose phosphorus-activated Cu electrocatalysts to generate electron-deficient Cu sites on the catalyst surface to promote the adsorption of N_(2) molecules.The eNRR system is further modified using a gas diffusion electrode(GDE) coated with polytetrafluoroethylene(PTFE) to form an effective three-phase boundary of liquid water-gas N_(2)-solid catalyst to facilitate easy access of N_(2) to the catalytic sites.As a result,the new catalyst in the flow-type cell records a Faradaic efficiency of 13.15% and an NH_(3) production rate of 7.69 μg h^(-1) cm^(-2) at-0.2 V_(RHE),which represent 3.56 and 59.2 times increases from those obtained with a pristine Cu electrode in a typical electrolytic cell.This work represents a successful demonstration of dual modification strategies;catalyst modification and N_(2) supplying system engineering,and the results would provide a useful platform for further developments of electrocatalysts and reaction systems.
基金supported by the State Key Program of National Natural Science Foundation of China(Grants No.11731008)the National Natural Science Foundation of China(Grants No.10771087)。
文摘The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.
基金Supported by the National Natural Science Foundation of China (40676016 and 10471039)the National Key Basic Research Special Foundation of China (2004CB418304)+1 种基金the Key Basic Research Foundation of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission (N.E03004).
文摘A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
文摘The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.
基金Supported in part by the National Natural Science Foundation of China under Grants Nos 10575035 and 10775050, the Programme for NCET under Grant No 04-0784, the SRFDP under Grant No 20070542002, and the Programme for the Key Discipline in Hunan Province.
文摘We consider, from the point of view of a coaccelerated frame, a uniformly accelerated multi-level atom in interaction with vacuum quantum electromagnetic fields in the multi-polar coupling scheme, and calculate the rate of change of the atom＇s energy assuming a thermal bath at a finite temperature T in the Rindler wedge. Comparison with the spontaneous excitation rate of the atom calculated in the instantaneous inertial frame of the atom shows that both the inertial and coaccelerated observer would agree with each other only when the temperature of the thermal bath equals the FDU value TFDU = α/2π.
文摘A mathematical model of the oscillatory regimes of CO oxidation over plantinum-group metal catalysts are discussed. The model is based on nonstationary diffusion equation containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents the analytical and numerical solution of the system of non-linear differential equations. Here the Homotopy perturbation method (HPM) is used to find out the analytical expressions of the concentration of CO molecules, O atom and oxide oxygen respectively. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical and numerical results is observed.
基金Project supported by the Major Program of the National Natural Science Foundation for （Grant No 10335010） and the National Natural Science Foundation-the Science Foundation of China Academy of Engineering Physics （NSAF） （Grant No 10576005）. We are grateful to Professor Li Jing-Hui and Dr Yuan Guo-Yong for valuable discussion.
文摘In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter ε is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave （AOMSW）, we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of ε.
基金supported by the National Natural Science Foundation of China (Nos.40676016,40876010)the Key Innovation Project of the Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)the E-Institute of Shanghai Municipal Education Commission (No. E03004)
文摘A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.
