The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh...The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.展开更多
An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into th...An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper. The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer. A significant change from previous modelling exercises in the study of hydrodynamic dispersion, different molecular diffusivity has been considered for the different region yet to be constant. For all time period, finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation. The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter, yield stress, viscosity ratio, peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers. This kind of study may be useful for understanding the dispersion process in the blood flow analysis.展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
The properties of materials are strongly dependent on their structures. The diffusion effect is a main kinetic factor that can be used to regulate the growth and structure of materials. In this work, we developed a sy...The properties of materials are strongly dependent on their structures. The diffusion effect is a main kinetic factor that can be used to regulate the growth and structure of materials. In this work, we developed a systematic and feasible strategy to synthesize Cu2O solid spheres and hexahedrons by controlling the diffusion coefficients. These Cu2O products can be successively transformed into corresponding Cu hollow spheres and hexahedrons as well as CuO porous spheres and hexahedrons by controlling hydrogen diffusion in hydrazine hydrate solution and controlling oxygen diffusion in air, respectively. The formation of these transformations was also discussed in detail. Tested for Rochow reaction, the as-prepared Cu2O solid and CuO porous spheres exhibit higher dimethyldichlorosilane selectivity and Si conversion than Cu hollow spheres, which is attributed to the active sites for CH3Cl adsorption formed in CuxSi phase after the removal of oxygen atoms in Cn2O and CuO in the formation of dimethylchlorosilane. The present work not only develops a feasible method for preparing well shape-defined Cu2O solid spheres and hexahedrons but also clarifies the respective roles of Cu, Cu2O and CuO in dimethyldichlorosilane synthesis via Rochow reaction.展开更多
By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attrac...By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.展开更多
The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of t...The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.展开更多
This article studies propagating wave fronts in an isothermal chemical reaction A + nB →(n + 1)B involving two chemical species,a reactant A and an auto-catalyst B whose diffusion coefficients,DA and DB,are unequal d...This article studies propagating wave fronts in an isothermal chemical reaction A + nB →(n + 1)B involving two chemical species,a reactant A and an auto-catalyst B whose diffusion coefficients,DA and DB,are unequal due to different molecular weights and/or sizes.More accurate bounds v* and v* that depend on DB/DA,when the ratio is less than 1,are derived such that there is a unique travelling wave of every speed v v* and there does not exist any travelling wave of speed v < v*.The refined bounds for DB/DA < 1 case is compatible to what has been shown in earlier work for DB/DA > 1 when n 3.展开更多
In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggre...In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equi- librium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.展开更多
文摘The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
文摘An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper. The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer. A significant change from previous modelling exercises in the study of hydrodynamic dispersion, different molecular diffusivity has been considered for the different region yet to be constant. For all time period, finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation. The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter, yield stress, viscosity ratio, peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers. This kind of study may be useful for understanding the dispersion process in the blood flow analysis.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
基金supported by the National Natural Science Foundation of China (21506224)the Institute of Chemical and Engineering Sciences (ICES) for the kind support of the collaboration
文摘The properties of materials are strongly dependent on their structures. The diffusion effect is a main kinetic factor that can be used to regulate the growth and structure of materials. In this work, we developed a systematic and feasible strategy to synthesize Cu2O solid spheres and hexahedrons by controlling the diffusion coefficients. These Cu2O products can be successively transformed into corresponding Cu hollow spheres and hexahedrons as well as CuO porous spheres and hexahedrons by controlling hydrogen diffusion in hydrazine hydrate solution and controlling oxygen diffusion in air, respectively. The formation of these transformations was also discussed in detail. Tested for Rochow reaction, the as-prepared Cu2O solid and CuO porous spheres exhibit higher dimethyldichlorosilane selectivity and Si conversion than Cu hollow spheres, which is attributed to the active sites for CH3Cl adsorption formed in CuxSi phase after the removal of oxygen atoms in Cn2O and CuO in the formation of dimethylchlorosilane. The present work not only develops a feasible method for preparing well shape-defined Cu2O solid spheres and hexahedrons but also clarifies the respective roles of Cu, Cu2O and CuO in dimethyldichlorosilane synthesis via Rochow reaction.
基金Project supported by the National Natural Science Foundation of China (No. 19971036)the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education of China.
文摘By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.
基金supported by a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Programme(No. MTKD-CT-2004-013389)
文摘The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.
基金supported by Shanxi Bairen PlanNational Natural Science Foundation of China (Grant No. 11001157)
文摘This article studies propagating wave fronts in an isothermal chemical reaction A + nB →(n + 1)B involving two chemical species,a reactant A and an auto-catalyst B whose diffusion coefficients,DA and DB,are unequal due to different molecular weights and/or sizes.More accurate bounds v* and v* that depend on DB/DA,when the ratio is less than 1,are derived such that there is a unique travelling wave of every speed v v* and there does not exist any travelling wave of speed v < v*.The refined bounds for DB/DA < 1 case is compatible to what has been shown in earlier work for DB/DA > 1 when n 3.
文摘In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equi- librium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.
