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
This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to cons...This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.展开更多
This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled ope...This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.展开更多
A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for b...A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface(downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.展开更多
A stable and homogeneous well-aligned air microplasma device for application at atmospheric pressure is designed and its electrical and optical characteristics are investigated. Current-voltage measurements and intens...A stable and homogeneous well-aligned air microplasma device for application at atmospheric pressure is designed and its electrical and optical characteristics are investigated. Current-voltage measurements and intensified charge coupled device （ICCD） images show that the well-aligned air microplasma device is able to generate a large-area and homogeneous discharge at the applied voltages ranging from 12 kV to 14 kV, with a repetition frequency of 5 kHz, which is attributed to the diffusion effect of plasma on dielectric surface. Moreover, this well-aligned microplasma device may result in the uniform and large-area surface modification of heat-sensitive PET polymers without damage, such as optimization in hydrophobicity and biocompatibility. In the biomedical field, the utility of this well-aligned microplasma device is further testified. It proves to be very efficient for the large-area and uniform inactivation of E. coli cells with a density of 103/cm2 on LB agar plate culture medium, and inactivation efficiency can reach up to 99% for 2-min treatment.展开更多
To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been ...To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.展开更多
We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative...We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.展开更多
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transforma...We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.展开更多
When people try to decide to buy or not to, they are often influenced by both their inherentopinions and the social marketing activities e.g. advertising, social news with strong point of view.Then people will make th...When people try to decide to buy or not to, they are often influenced by both their inherentopinions and the social marketing activities e.g. advertising, social news with strong point of view.Then people will make their final choice, or even convince other people to buy. After all, this is thebrand acceptance formation process. Factually, the dynamics of brand acceptance is essentially aninterwoven dynamics of endogenous opinion dynamics disturbed by an information diffusion process.To have a better understanding of the dynamics of brand acceptance, we propose and analyze a coupledagent-based dynamic model that combines the Majority-Rule-based Voter model in opinion dynamicswith the SI Model for information spreading to analyze the dynamics of brand acceptance in socialmedia. We focus on two important parameters in diffusion dynamics： the decayed transmission rate （fl）and the diffusion frequency （f）. When the system is stable, the order parameter of the system is theduration time （r）. In the absence of opinion interaction, the simulation results indicate that, when abrand tries to occupy a larger market share through social marketing approaches, it is always effectiveto let the opponent to be the propaganda target. While with the Majority-Rule-based Voter Modelincluded, we observe that the opinion interaction could have a dual function, which shows that a brandholding a small market share in the first place needs to adopt diverse marketing approaches accordingto different marketing environment types.展开更多
On September 10, 2015, unprecedented flood was occurred in Kinugawa River basin located on eastern Japan. It inundated 40 km2 of flood plain in Joso city, Ibaraki Prefecture, and more than 4000 people there called for...On September 10, 2015, unprecedented flood was occurred in Kinugawa River basin located on eastern Japan. It inundated 40 km2 of flood plain in Joso city, Ibaraki Prefecture, and more than 4000 people there called for help despite supposedly having sufficient time to evacuate. Some said that small initial flood before main severe flood arrived made them make a mistake in deciding whether to evacuate or stay there, despite having to actually evacuate in reality. This study focused on flood behaviour in this area, in particular, the effect of a small drainage channel lying on the flood plain which caused fast flood diffusion in case of occurring huge overflowing. Field investigations starting on time of the disaster with high-resolution positioning system were conducted to obtain spatial maps of flood depth and height. For appropriate modelling of the effect of small channel, we applied simulation model coupling 1-dimensional (1D) and 2-dimensional (2D) hydraulic scheme on the field and compared results from the 1D/2D coupled model and model without 1D scheme. The models provided information that the flood could reach 4 hours earlier to the city central of Joso city comparing in case of model without 1D scheme. The water depth rose irregularly and it was more confusing and difficult for the victims to make appropriate evacuation act.展开更多
The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to...The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.展开更多
In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantit...In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.展开更多
In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
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 the National Natural Science Foundation of China under Grant Nos.61473097,11301090the State Key Program of Natural Science Foundation of China under Grant No.U1533202+2 种基金Shandong Independent Innovation and Achievements Transformation Fund under Grant No.2014CGZH1101Civil Aviation Administration of China under Grant No.MHRD20150104Guangxi Natural Science Foundation under Grant No.2016JJA110005
文摘This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.
基金Supported by the NNSF of China(Grant Nos.11961052,11761029)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2317)the NSF of Inner Mongolia(Grant Nos.2021MS01006,2020ZD01)。
文摘This paper is concerned with the representation problem of a coupled operator in a product space.A necessary and sufficient condition is given for a class of operators with closed range to have a one-sided coupled operator matrix representation.The applications of this result in a delay equation and in a diffusion-transport system with dynamical boundary conditions are further presented.
基金Project supported by the National Natural Science Foundation of China(No.11332005)
文摘A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface(downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.
基金supported by the Natural Science Foundation of Fujian Province,China(Grant No.2014J01025)the National Natural Science Foundation of China(Grant No.11275261)+1 种基金the Natural Science Foundation of Guangdong Province,China(Grant No.2015A030313005)the Fund from the Fujian Provincia Key Laboratory for Plasma and Magnetic Resonance,China
文摘A stable and homogeneous well-aligned air microplasma device for application at atmospheric pressure is designed and its electrical and optical characteristics are investigated. Current-voltage measurements and intensified charge coupled device （ICCD） images show that the well-aligned air microplasma device is able to generate a large-area and homogeneous discharge at the applied voltages ranging from 12 kV to 14 kV, with a repetition frequency of 5 kHz, which is attributed to the diffusion effect of plasma on dielectric surface. Moreover, this well-aligned microplasma device may result in the uniform and large-area surface modification of heat-sensitive PET polymers without damage, such as optimization in hydrophobicity and biocompatibility. In the biomedical field, the utility of this well-aligned microplasma device is further testified. It proves to be very efficient for the large-area and uniform inactivation of E. coli cells with a density of 103/cm2 on LB agar plate culture medium, and inactivation efficiency can reach up to 99% for 2-min treatment.
基金This work was partially supported by the National Natural Science Foundation of China （11771381） and Project funded by China Postdoctoral Science Foundation.
文摘To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.
文摘We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.
基金Supported by the National Natural Science Foundation of China under Grant No 10671156, and the Programme for New Century Excellent Talents in University （NCET-04-0968）.
文摘We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
文摘When people try to decide to buy or not to, they are often influenced by both their inherentopinions and the social marketing activities e.g. advertising, social news with strong point of view.Then people will make their final choice, or even convince other people to buy. After all, this is thebrand acceptance formation process. Factually, the dynamics of brand acceptance is essentially aninterwoven dynamics of endogenous opinion dynamics disturbed by an information diffusion process.To have a better understanding of the dynamics of brand acceptance, we propose and analyze a coupledagent-based dynamic model that combines the Majority-Rule-based Voter model in opinion dynamicswith the SI Model for information spreading to analyze the dynamics of brand acceptance in socialmedia. We focus on two important parameters in diffusion dynamics： the decayed transmission rate （fl）and the diffusion frequency （f）. When the system is stable, the order parameter of the system is theduration time （r）. In the absence of opinion interaction, the simulation results indicate that, when abrand tries to occupy a larger market share through social marketing approaches, it is always effectiveto let the opponent to be the propaganda target. While with the Majority-Rule-based Voter Modelincluded, we observe that the opinion interaction could have a dual function, which shows that a brandholding a small market share in the first place needs to adopt diverse marketing approaches accordingto different marketing environment types.
文摘On September 10, 2015, unprecedented flood was occurred in Kinugawa River basin located on eastern Japan. It inundated 40 km2 of flood plain in Joso city, Ibaraki Prefecture, and more than 4000 people there called for help despite supposedly having sufficient time to evacuate. Some said that small initial flood before main severe flood arrived made them make a mistake in deciding whether to evacuate or stay there, despite having to actually evacuate in reality. This study focused on flood behaviour in this area, in particular, the effect of a small drainage channel lying on the flood plain which caused fast flood diffusion in case of occurring huge overflowing. Field investigations starting on time of the disaster with high-resolution positioning system were conducted to obtain spatial maps of flood depth and height. For appropriate modelling of the effect of small channel, we applied simulation model coupling 1-dimensional (1D) and 2-dimensional (2D) hydraulic scheme on the field and compared results from the 1D/2D coupled model and model without 1D scheme. The models provided information that the flood could reach 4 hours earlier to the city central of Joso city comparing in case of model without 1D scheme. The water depth rose irregularly and it was more confusing and difficult for the victims to make appropriate evacuation act.
基金Project (50136020) supported by the National Natural Science Foundation of China Project (01056) supported by theKey Project of Education Ministry of China
文摘The coupled three-components liquid diffusion within a porous pellet was investigated. The coupled diffusion model was given according to irreversible thermodynamics, and the rigorous solutions of the model subject to the homogeneous boundary conditions of the first kind are derived by employing Hankel transform technique and the standard technique resolving ordinary differential system. The method can also be used to solve the other coupled diffusion problems within a pellet with different kinds of boundary conditions. Then the case computations were conducted. The calculation results show that the effect of interdiffussion on the concentration of components depends upon the diffusion time strongly, after a long diffusion period, a very small cross diffusion coefficient will induce the observable change of concentration profile, and that, when the cross coefficients are close to 5%7% of the main coefficients, the significant effect of coupled diffusion on the concentration profiles of components is observed. The case computations also show that interdiffussion can induce non-monotonous concentration profiles. So, for the diffusion taking place within ternary system, the concentration profiles obtained by the analysis of interdiffussion can be very different from that obtained by the equivalent binary system analysis method.
文摘In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.
文摘In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
