Exponential Time Differencing Method for a Reaction-Diffusion System with Free Boundary

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.

Comparison of the interface reaction behaviors of CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) solid-state systems based on the diffusion couple method

The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag.In this work,CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms.Then,the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis.Results show that with the extension of the roasting time,the diffusion reaction gradually proceeds among the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples.The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V_(2)O_(5) diffusion couple.Meanwhile,for the MnO_(2)–V_(2)O_(5) diffusion couple,MnO_(2) gradually decomposes to form Mn_(2)O_(3),and vanadium diffuses into the interior of Mn_(2)O_(3).Only a part of vanadium combines with manganese to form the diffusion production layer.CaV_(2)O_(6) and MnV_(2)O_(6) are the interfacial reaction products of the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples,respectively,whose thicknesses are 39.85 and 32.13μm when roasted for 16 h.After 16 h,both diffusion couples reach the reaction equilibrium due to the limitation of diffusion.The diffusion coefficient of the CaO–V_(2)O_(5) diffusion couple is higher than that of the MnO_(2)–V_(2)O_(5) diffusion couple for the same roasting time,and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.

Synthesis strategies of covalent organic frameworks: An overview from nonconventional heating methods and reaction media

Covalent organic frameworks(COFs), as an emerging class of porous crystalline materials constructed by covalent links between the building monomers, have gained tremendous attention. Over the past 15 years, COFs have made rapid progress and substantial development in the chemistry and materials fields. However, the synthesis of COFs has been dominated by solvothermal methods for a long time and it usually involves high temperature, high pressure and toxic organic solvents, which created many challenges for environmental considerations. Recently,the exploration of new approaches for facile fabrication of COFs has aroused extensive interest. Hence, in this review, we comprehensively describe the synthetic strategies of COFs from the aspects of nonconventional heating methods and reaction media. In addition, the advantages,limitations and properties of the preparation methods are compared. Finally, we outline the main challenges and development prospects of the synthesis of COFs in the future and propose some possible solutions.

Highly Defective Dark TiO_(2) Modified with Pt: Effects of Precursor Nature and Preparation Method on Photocatalytic Properties

The study focused on the modification with platinum of dark defective titania obtained via pulsed laser ablation. Both the method of Pt introduction and the nature of the Pt precursor were varied. All samples exhibited similar phase compositions, specific surface areas, and Pt contents. High-resolution transmission electron microscopy coupled with pulsed CO adsorption revealed increased dispersity when photoreduction and the hydroxonitrate complex (Me _(4) N) _(2) [Pt _(2) (OH) _(2) (NO _(3) ) _(8) ] were used. The sample featured a high content of single-atom species and subnano-sized Pt clusters. The X-ray photoelectron spectroscopy results showed that the photoreduction method facilitated the appearance of a larger number of Pt ^(2+) states, which appeared owing to the strong metal-support interaction (SMSI) eff ect of the transfer of electron density from the electron-saturated defects on the TiO _(2) surface to Pt ^(4+) . In the hydrogen evolution reaction, samples with a significant fraction of the Pt ^(2+) ionic component, capable of generating short-lived Pt^(0) single-atom sites under irradiation due to the SMSI eff ect, exhibited the highest photocatalytic activity. The 0.5Pt(C)/TiO_(2) -Ph sample exhibited the highest hydrogen yield with a quantum efficiency of 0.53, retaining its activity even after 8 h of operation.

Extracting reaction mechanism analysis of Zn and Si from zinc oxide ore by NaOH roasting method

The orthogonal test was used to optimize the reaction conditions of roasting zinc oxide ore with NaOH aiming to comprehensively utilize zinc oxide ore.The optimized reaction conditions were molar ratio of NaOH to zinc oxide ore 6:1,roasting temperature 450°C,holding time 150 min.The molar ratio of NaOH to zinc oxide ore was the most predominant factor affecting the extraction ratios of zinc oxide and silica.The mineral phase transformations were investigated by testing the phases of specimens obtained at different temperatures.The process was that silica reacted with molten NaOH to form Na_2SiO_3 at first,then transformed into Na_4SiO_4 with temperature rising.ZnCO_3 and its decomposing product ZnO reacted with NaOH to form Na_2ZnO_2.Na_2ZnSiO_4was also obtained.The reaction rate was investigated using unreacted shrinking core model.Two models used were chemical reaction at the particle surface and diffusion through the product layer.The results indicated that the reaction rate was combine-controlled by two models.The activation energy and frequency factor were obtained as 24.12 k J/mol and 0.0682,respectively.

ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION

In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

Strontium ferrite powders prepared from oily cold rolling mill sludge by solid-state reaction method

Oily cold rolling mill （CRM） sludge is one of the pollutants emitted by iron and steel plants. Recycling oily CRM sludge can not only reduce pollution but also bring social and environmental benefits. In this study, using oily CRM sludge as sources of iron oxide, the strontium ferrite powders were synthesized in multiple steps including vacuum distillation, magnetic separation, oxidizing roasting, and solidstate reaction. The optimal technological conditions of vacuum distillation and oxidizing roasting were studied carefully. To consider the effects of Fe203/ SrCO3 tool ratio, calcination temperature, milling time and calcination time on magnetic properties of prepared strontium ferrite powders, the orthogonal experimental method was adopted. The maximum saturation magneti- zation （62.6 mA-m2.g-1） of the synthesized strontium ferrite powders was achieved at the Fe203/SrCO3 mol ratio of 6, 5 h milling time, 1250 ~C calcination temperature, and 1 h calcination time. Strontium ferrite powders syn- thesis method not only provides a cheap, high quality raw material for the production of strontium ferrite powders, but also effectively prevents the environmental pollution.

Structure and Performance of Fe-N_x-C Catalyst for Oxygen Reduction Reaction Prepared by Vacuum Casting Method and the Second Pyrolysis

Affordable non-precious metal（NPM） catalysts played a vital role in the wide application of polymer electrolyte membrane fuel cells（PEMFC）. In current work, a facile vacuum casting reacting method based on vacuum casting was introduced to prepare Fe-N_x-C oxygen reduction reaction（ORR） catalysts with high efficient in acid medium. The catalysts were prepared with ammonium ferrous sulfate hexahydrate（AFS） and 1,10-phenanthroline monohydrate utilizing homemade mesoporous silica template. The heat treatment and its influence on structure and performance were systematically evaluated to achieve superior ORR performance and some clues were found. And 850 ℃ was found to be the best temperature for the first and second pyrolysis. The linear sweep voltammetry（LSV） results showed that there were only 18 mV slightly negative shifts of half-wave potential（E_（1/2）） of the optimal catalyst（749 mV） compared with the commercial Pt/C（20 μg·Pt·cm^-2）. Besides, I850 R also showed better electrochemical stability and methanol-tolerance than that of Pt/C. All evidences proved that our vacuum casting reacting strategy and heat treatment process were prospective for the future R＆D of high performance Fe-N_x-C ORR catalysts.

Synthesis of Low-cost LiFePO_4 from Li_2CO_3 by a Novel Hydrothermal Method and Investigation on the Reaction Mechanism

Phspho-olivine Li Fe PO4 was synthesized from the relatively insoluble lithium source Li2CO3, proper iron and phosphorus sources（n（Li）：n（Fe）：n（P）=1：1：1） by a novel hydrothermal method. Afterwards, the optimal sample was mixed with glucose and two-step calcinated（500 ℃ and 750 ℃） under high-purity N2 to obtain the Li Fe PO4/C composite. The resultant samples were characterized by X-ray diffraction（XRD）, atomic absorption spectrometry（AAS）, scanning electron microscops（SEM）, transmission electron microscopy（TEM）, energy dispersive spectrometry（EDS）, elementary analysis（EA） and electrochemical tests. The results show that the optimal reaction condition is to set the reactant concentration at 0.5 mol·L^-1, the reaction temperature at 180 ℃ for 16 h duration. During the reaction course, an intermediate product NH4 Fe PO4·H2O was first synthesized, and then it reacted with Li＋ to form Li Fe PO4. The optimized Li Fe PO4 sample with an average particle size（300 to 500 nm） and regular morphology exhibits a relatively high discharge capacity of 84.95 m Ah· g^-1 at the first charge-discharge cycle（0.1C, 1C=170 m A·g^-1）. Moreover, the prepared Li Fe PO4/C composite shows a high discharge capacity of 154.3 m Ah·g^-1 at 0.1C and 128.2 m Ah·g^-1 even at 5C. Besides it has good reversibility and stability in CV test.

Preparation of Al-Al_3Ti in situ composites by direct reaction method

Al-Al_3Ti composites 被一个直接反应方法准备，在 whichAl_3Ti 被 Ti 和艾尔的反应在铝合金形成融化。Al_3Tichanges 的形态学显然从好粒子，对有 Al_3Ticontent 的增加的大块像针。镁罐头的增加显著地改变 Al_3Ti 的形态学并且减少他们的尺寸。短像杆的 Al_3Ti 被形成，同类的分发与 3 wt.% Mg 的增加被获得。Al-Al_3Ti composites 和机制的微观结构上的 Al_3Ti 和 Mg 的效果也被讨论。

Kinetic method for enzymatic analysis by predicting background with uricase reaction as model

Objective:To investigate the reliability for kinetic assay of substance with background predicted by the integrated method using uricase reaction as model. Methods: Absorbance before uricase action （A0） was estimated by extrapolation with given lag time of steady-state reaction. With Km fixed at 12.5 μmol/L, background absorbance （Ab） was predicted by nonlinearly fitting integrated Michaelis-Menten equation to Candida utilis uricase reaction curve. Uric acid in reaction solution was determined by the difference （ΔA） between A0 and Ab. Results:Ab usually showed deviation <3% from direct assay with residual substrate <one-fifth of initial substrate for analysis. ΔA showed CV <5% with resistance to common interferences except xanthine, and it linearly responded to uric acid with slope consistent to the absorptivity of uric acid. The lower limit was 2.0 μmol/L and upper limit reached 30 μmol/L in reaction solution with data monitored within 8 min reaction at 0.015 U/ml uricase. Preliminary application to serum and urine gave better precision than the direct equilibrium method without the removal of proteins before analysis. Conclusion:This kinetic method with background predicted by the integrated method was reliable for enzymatic analysis, and it showed resistance to common interferences and enhanced efficiency at much lower cost.

Measurement of ^(232)Th(n,2n)^(231)Th reaction cross-sections at neutron energies of 14.1 MeV and 14.8 MeV using neutron activation method

In this study, the activation cross-sections were measured for ^(232)Th(n,2n)^(231)Th reactions at neutron energies of 14.1 and 14.8 MeV, which were produced by a neutron generator through a T(d,n)~4He reaction. Induced gamma-ray activities were measured using a low background gamma ray spectrometer equipped with a high resolution HPGe detector. In the cross-section calculations, corrections were made regarding the effects of gamma-ray attenuation, dead-time, fluctuation of the neutron flux, and low energy neutrons. The measured cross-sections were compared with the literature data, evaluation data(ENDF-B/VII.1, JENDL-4.0 and CENDL-3.1), and the results of the model calculation(TALYS1.6).

Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes

Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some improvements to the use of the Hyperstatic Reaction Method-HRM for analysing tunnels with horseshoe-shaped cross-sections when these tunnels operate under the influence of earthquakes, particularly in cases when the tunnel lining is a continuous lining. The analysis used parameters of a tunnel from the Hanoi metro system, as well as parameters of the strongest earthquake that may occur in the central Hanoi area in the improved HRM and 2 D numerical methods using the ABAQUS software. On the basis of the results obtained, the paper gives conclusions about the HRM methodology when it is used to calculate tunnels that have horseshoe cross-sections operating under the influence of earthquakes.

The Quantum Scattering Study for Ion-pair Formation Reaction Na+I_2→Na^+I_2^- with the LCAC-SW method

The selected-state probabilities of collinear ion-pair formation process Na+I2→Na++I2-on Aten-Laming-Los two-State potential energy surface have been calculated by using LCAC-SW method. The results show that reaction probabilities are oscillatory with collision energy; the threshold energy of this ioniZation reaction is 2.8 ev, which is in modest agreement with experimental result.

Science Letters:Evaluation of a kinetic uricase method for serum uric acid assay by predicting background absorbance of uricase reaction solution with an integrated method

A patented kinetic uricase method was evaluated for serum uric acid assay. Initial absorbance of the reaction mixture before uricase action (A0) was obtained by correcting the absorbance at 293 nm measured before the addition of uricase solution, and background absorbance (Ab) was predicted by an integrated method. Uric acid concentration in reaction solution was calcu-lated from ?A, the difference between A0 and Ab, using the absorptivity preset for uric acid. This kinetic uricase method exhibited CV<4.3% and recovery of 100%. Lipids, bilirubin, hemoglobin, ascorbic acid, reduced glutathione and xanthine <0.32 mmol/L in serum had no significant effects. ?A linearly responded to 1.2 to 37.5 μmol/L uric acid in reaction solution containing 15 μl serum. The slope of linear response was consistent with the absorptivity preset for uric acid while the intercept was consistent with that for serum alone. Uric acid concentrations in clinic sera by different uricase methods positively correlated to each other. By Bland-Altman analysis, this kinetic uricase method accorded with that by quantifying the total change of UV absorbance on the completion of uricase reaction. These results demonstrated that this kinetic uricase method is reliable for serum uric acid assay with enhanced resistance to both xanthine and other common errors, wider range of linear response and much lower cost.

Studies on Reduced Extent Method for Inhibited Thermokinetics Of Enzyme－Catalyzed Reaction──Inhibition of the laccase－catalyzed oxidation of o－dihydroxybenzene by m－dihydroxybenzene

The thermokinetic reduced extent equations of reversible inhibitions for Michaiels-Menten enzymatic reaction were deduced, and then the criteria for distingushing inhibition type was given and the methods for calculating kinetic parameters, KM,Ki and Urn were suggested. This theory was applied to inverstigate the inhibited thermokinetics of laccase-catalyzed oxidation of o-dihydroxybenzene by m-dihydroxybenzene. The experimental results show the inhibition belongs to reversible competitive type, KM=6.224×10-3 mol L-1, Ki=2. 363 × 10-2 mol. L-1.

Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations

The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.

A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations

A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.

OPERATOR-SPLITTING GALERKIN METHOD FOR ONE KIND OF OIN REACTION MODEL FOR THE POLLUTION IN GROUNDWATER

The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.