STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

Solid Solution Characteristics of Pb(B_(1/3)Nb_(2/3))O_(3)-based Composite Ceramics

The solid solution characteristics of Pb（B1/3Nb2/3）O3-based （B=Zn^2＋, Mg^2＋, Ni^2＋） composite ceramics prepared by two-phase mixed-sintering method were developed based on dielectric measurements. Results show that there are double dielectric peaks for PZN-based composite ceramic, implying two phases coexist. However single dielectric peak was presented in PMN- and PNN-based composite ceramics, respectively. It is indicated that obvious solid solution reaction exists during the sintering process of these two systems. The effects of B-site ion difference on the solid solution characteristics were discussed by crystal chemistry. SEM was employed to investigated the microstructures of composite ceramics. The influences of solid solution reaction on grain growth were discussed.

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

Asymptotic behavior of solutions for some chemical reaction models

IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M1, M2 and M3 which can react with each other to produce two new kinds of other chemical compounds: （M2）n （M1）m and （M3）r （M1）κ at the same time. Usually, these reactions are irreversible and they have the following forms:

Microstructure evolution of coke under CO2 and H2O atmospheres

The microstructure of coke has an important influence on its thermal properties.The solution loss reactions of coke in CO2 and H2O atmospheres were investigated by in situ observation.The results showed that the isotropic components had a more vigorous reaction than the anisotropic components,and the solution loss reaction of the fine-grained mosaic structure was faster than that of the coarse-grained mosaic structure under the CO2 and H2O atmospheres.The coarse-grained mosaic structure and the flowing structure had a relatively higher anti-erosion ability in the CO2 atmosphere than in the H2O atmosphere,and there was no distinct difference in the solution loss of the isotropic structure under the CO2 and H2O atmospheres.The electron probe microanalysis showed that the Al-Si-Fe compounds in the carbon matrix had positive influence on the solution loss reaction of the anisotropic structure.The iron compounds were able to destroy the pore walls of coke and accelerate the solution loss rate of coke.

Thermochemical Study on the Chiral Sodium Zincophosphate Nanocrystalline

Chirai sodium zincophosphate nanocrystalline has been prepared and characterized. The standard molar enthaipy of the following reaction 12Na3PO4·12H2O（s）＋ 12ZnSO4·7H2O（s）= Na12（Zn12P12O48）·12H2O（s）＋ 12Na2SO4（s）＋216H2O（1） was determined by solution reaction calorimetric at 298.15 K, and calculated to be 33.666±0.195 kl/mol. From the results and other auxiliary quantities, the standard enthalpy of formation for sodium zincophosphate nanocrystalline was derived to be △fHm^⊙ [Na12（Zn12P12O48）·12H2O（s）, 298.15 K] =- 24268.494 ± 0.815 kJ/mol.

A Polyanionic,Quasi-zero-strain and Open-framework K_(0.76)V_(0.55)Nb_(0.45)OPO_(4) for Sodium-ion Batteries

A carbon-coated K_(0.76)V_(0.55)Nb_(0.45)OPO_(4)(KVNP@C)polyanion material was successfully synthesized by a simple sol-gel method.The KVNP@C possesses a highly stable inorganic open-framework structure,which is hard to be affected by the Na^(+) intercalation/deintercalation when used as an anode material for sodium-ion batteries(NIBs).The assembled KVNP@C/Na half-cell shows a capacity retention of 81.2%and an average Coulombic efficiency of 99.8%at a current density of 300 mA/g after 1500 cycles.In-situ XRD analysis reveals a single-phase solid solution reaction mechanism with a lattice expansion of 4.76%.This work sheds insights into the quest for developing novel polyanion-based anode materials for sodium-ion batteries.