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
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 paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-d...This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.展开更多
Enhancing the kinetic stability of glasses typically requires deepening their thermodynamic stability,which increases structural rigidity and degrades ductility;decoupling these properties remains a major challenge.He...Enhancing the kinetic stability of glasses typically requires deepening their thermodynamic stability,which increases structural rigidity and degrades ductility;decoupling these properties remains a major challenge.Here,we demonstrate that spatial patterning in metallic glasses produces exceptional kinetic ultrastability that coexists with a thermodynamically metastable,high-energy state and excellent plasticity.Guided by atomistic simulations using replica exchange molecular dynamics and machine learning interatomic potentials,we reveal that oxygen,through reaction-diffusion-coupled pattern dynamics,self-organizes into oxygen-centered pinned structures(OPSs)that serve as localized kinetic constraints.These motifs drastically slow structural relaxation,delivering kinetic stability comparable to ultrastable glasses even as the system retains the high inherent energy of rapidly quenched states.The OPSs’topology yields a spatially uniform activation of plastic events,promoting strain delocalization under mechanical load.By geometrically tailoring oxygen patterns,we increase the glass transition onset temperature(Tonset)by about 200 K with negligible loss of deformability.Our findings establish a practicable paradigm for decoupling kinetic and thermodynamic stability and point to a scalable,additive route for designing amorphous materials that combine hyperstability with plasticity.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
In this work,a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil hydrodesulfu...In this work,a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil hydrodesulfurization(HDS).The non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat.The reaction rate along the reactor is mainly dominated by the temperature,and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor,leading to the increased internal effectiveness factor.For the fixed catalyst bed volume,there exists a compromise between the catalyst reaction rate and effectiveness factor.Under commonly studied catalyst pellet size of 0.8-3 mm and porosity of 0.4-0.8,an optimization of the temperature and catalyst pellet structures is carried out,and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of the catalyst pellet size and 0.40 of the catalyst porosity.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
This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly suppo...This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.展开更多
The main objective of this article is to obtain the new analytical and numerical solutions of fractional Fitzhugh-Nagumo equation which arises as a model of reaction-ifusion systems,transmission of nerve impulses,circ...The main objective of this article is to obtain the new analytical and numerical solutions of fractional Fitzhugh-Nagumo equation which arises as a model of reaction-ifusion systems,transmission of nerve impulses,circuit theory,biology and the area of population genetics.For this aim conformable derivative with fractional order which is a well behaved,understandable and applicable definition is used as a tool.The analytical solutions were got by utilizing the fact that the conformable fractional derivative provided the chain rule.By the help of this feature which is not provided by other popular fractional derivatives,nonlinear fractional partial differential equation is turned into an integer order differential equation.The numerical solutions which is obtained with the aid of residual power series method are compared with the analytical results that obtained by performing sub equation method.This comparison is made both with the help of three-dimensional graphical representations and tables for different values of theγ.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
Microbiological experiments show that the colonies of the bacterium bacillus subtilis placed on a dish filled with an agar medium and nutrient form varied spatial patterns while the individual cells grow, reproduce an...Microbiological experiments show that the colonies of the bacterium bacillus subtilis placed on a dish filled with an agar medium and nutrient form varied spatial patterns while the individual cells grow, reproduce and migrate on the dish in clumps. In this paper, we discuss a system of reaction-diffusion equations that can be used with a view to modelling this phenomenon and we solve it numerically by means of the method of lines. For the spatial discretization, we use the finite difference method and Galerkin finite element method. We present how the spatial patterns obtained depend on the spatial discretization employed and we measure the experimental order of convergence of the numerical schemes used. Further, we present the numerical results obtained by solving the model in a cubic domain.展开更多
The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present invest...The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.展开更多
Accurately predicting the mechanical behavior of pure metals at different radiation doses and prescribing the microstructure evolutions,such as the dislocation structures,remain challenging.This work introduces a 3D h...Accurately predicting the mechanical behavior of pure metals at different radiation doses and prescribing the microstructure evolutions,such as the dislocation structures,remain challenging.This work introduces a 3D hybrid numerical simulation scheme that integrates finite element(FE)and finite difference(FD)modules.The FE module is used to implement the crystal plasticity model,while the FD module is used to solve the reaction-diffusion model regarding dislocation nucleation and transportation.Our hybrid model successfully replicates the mechanical behavior of pristine Cu single crystals and provides details of dislocation cell structures that agree with the experimental observation.Furthermore,the model effectively reflects the irradiation hardening effects for Cu single crystals and demonstrates the formation of dislocation channels and shear band type of strain localization.Our work offers an effective approach for predicting the mechanical responses and the safety evaluation of pure metals in extreme working conditions.展开更多
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.
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 National Natural Science Foundation of China(Grant Nos.125610811246108612271147)。
文摘This paper aims to study the optimal control and algorithm implementation of a generalized epidemic model governed by reaction-diffusion equations.Considering individual mobility,this paper first proposes a reaction-diffusion epidemic model with two strains.Furthermore,applying vaccines as a control strategy in the model,an optimal control problem is proposed to increase the number of healthy individuals while reducing control costs.By applying the truncation function technique and the operator semigroup methods,we prove the existence and uniqueness of a globally positive strong solution for the control model.The existence of the optimal control strategy is proven by using functional analysis theory and minimum sequence methods.The first-order necessary condition satisfied by the optimal control is established by employing the dual techniques.Finally,a specific example and its algorithm are provided.
基金supported by the National Natural Science Foundation of China(Grants Nos.T2325004)the Advanced Materials-National Science and Technology Major Project(Grant No.2024ZD0606900)+3 种基金the Talent Hub for‘AI+New Materials’Basic Researchsupported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant Nos.XDB0620103 and XDB0510301)the National Natural Science Foundation of China(Grant No.12472112)R.S.acknowledges the Young Scientists Fund of the National Natural Science Foundation of China(51801046).
文摘Enhancing the kinetic stability of glasses typically requires deepening their thermodynamic stability,which increases structural rigidity and degrades ductility;decoupling these properties remains a major challenge.Here,we demonstrate that spatial patterning in metallic glasses produces exceptional kinetic ultrastability that coexists with a thermodynamically metastable,high-energy state and excellent plasticity.Guided by atomistic simulations using replica exchange molecular dynamics and machine learning interatomic potentials,we reveal that oxygen,through reaction-diffusion-coupled pattern dynamics,self-organizes into oxygen-centered pinned structures(OPSs)that serve as localized kinetic constraints.These motifs drastically slow structural relaxation,delivering kinetic stability comparable to ultrastable glasses even as the system retains the high inherent energy of rapidly quenched states.The OPSs’topology yields a spatially uniform activation of plastic events,promoting strain delocalization under mechanical load.By geometrically tailoring oxygen patterns,we increase the glass transition onset temperature(Tonset)by about 200 K with negligible loss of deformability.Our findings establish a practicable paradigm for decoupling kinetic and thermodynamic stability and point to a scalable,additive route for designing amorphous materials that combine hyperstability with plasticity.
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.
基金supported by the National Key R&D Program of China(2018YFB0604500)the National Natural Science Foundation of China(21922803 and 21776077)+4 种基金the Shanghai Natural Science Foundation(17ZR1407300 and 17ZR1407500)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learningthe Shanghai Rising-Star Program(17QA1401200)the Open Project of SKLOCE(SKL-Che-15C03)the 111 Project of the Ministry of Education of China(B08021)。
文摘In this work,a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil hydrodesulfurization(HDS).The non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat.The reaction rate along the reactor is mainly dominated by the temperature,and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor,leading to the increased internal effectiveness factor.For the fixed catalyst bed volume,there exists a compromise between the catalyst reaction rate and effectiveness factor.Under commonly studied catalyst pellet size of 0.8-3 mm and porosity of 0.4-0.8,an optimization of the temperature and catalyst pellet structures is carried out,and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of the catalyst pellet size and 0.40 of the catalyst porosity.
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 by the National Natural Science Foundation of China(11371179)。
文摘This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.
文摘The main objective of this article is to obtain the new analytical and numerical solutions of fractional Fitzhugh-Nagumo equation which arises as a model of reaction-ifusion systems,transmission of nerve impulses,circuit theory,biology and the area of population genetics.For this aim conformable derivative with fractional order which is a well behaved,understandable and applicable definition is used as a tool.The analytical solutions were got by utilizing the fact that the conformable fractional derivative provided the chain rule.By the help of this feature which is not provided by other popular fractional derivatives,nonlinear fractional partial differential equation is turned into an integer order differential equation.The numerical solutions which is obtained with the aid of residual power series method are compared with the analytical results that obtained by performing sub equation method.This comparison is made both with the help of three-dimensional graphical representations and tables for different values of theγ.
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.
基金The projects “Applied Mathematics in Physics and Technical Sciences” number MSM684077 0010 of the Ministry of Education Youth and Sports of the Czech Republic and “Advanced Supercomputing Methods for Implementation of Mathematical Models” number SGS11/161/OHK4/3T/14
文摘Microbiological experiments show that the colonies of the bacterium bacillus subtilis placed on a dish filled with an agar medium and nutrient form varied spatial patterns while the individual cells grow, reproduce and migrate on the dish in clumps. In this paper, we discuss a system of reaction-diffusion equations that can be used with a view to modelling this phenomenon and we solve it numerically by means of the method of lines. For the spatial discretization, we use the finite difference method and Galerkin finite element method. We present how the spatial patterns obtained depend on the spatial discretization employed and we measure the experimental order of convergence of the numerical schemes used. Further, we present the numerical results obtained by solving the model in a cubic domain.
文摘The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.
基金supported by the National Natural Science Foundation of China(Grant Nos.12325202,12172005,and 11988102)。
文摘Accurately predicting the mechanical behavior of pure metals at different radiation doses and prescribing the microstructure evolutions,such as the dislocation structures,remain challenging.This work introduces a 3D hybrid numerical simulation scheme that integrates finite element(FE)and finite difference(FD)modules.The FE module is used to implement the crystal plasticity model,while the FD module is used to solve the reaction-diffusion model regarding dislocation nucleation and transportation.Our hybrid model successfully replicates the mechanical behavior of pristine Cu single crystals and provides details of dislocation cell structures that agree with the experimental observation.Furthermore,the model effectively reflects the irradiation hardening effects for Cu single crystals and demonstrates the formation of dislocation channels and shear band type of strain localization.Our work offers an effective approach for predicting the mechanical responses and the safety evaluation of pure metals in extreme working conditions.
