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.

Effects of reaction parameters on preparation of Cu nanoparticles via aqueous solution reduction method with NaBH_4

The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.

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.

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

Al-Al3Ti composites were prepared by a direct reaction method, in which Al3Ti was formed by the reaction of Ti and Al in aluminum alloy melt. The morphology of Al3Ti changes apparently from the fine particle, needle-like to large block with the increase of Al3Ti content. The addition of magnesium can markedly change the morphology of Al3Ti and reduce their size. Short rod-like Al3Ti was formed and homogeneous distribution was obtained with the addition of 3 wt.% Mg. The effect of Al3Ti and Mg on the microstructure of Al-Al3Ti composites and the mechanism were also discussed.

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.

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 （Δ0） was estimated by extrapolation with given lag time of steady-state reaction. With Km fixed at 12.5μmol/L, background absorbance （Δb） 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 Δ0 and Δb. Results .Ab usually showed deviation 〈3% from direct assay with residual substrate done 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.

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.

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 calculated from AA, 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.

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.

Kinetics of synthesis of Li_4Ti_5O_(12) through solid-solid reaction

Sohd-solid reaction under low heat or low temperature is an approach to synthesize various kinds of materials that were widely used in electrochemistry field. In this paper a theoretical treatment has been presented for analyzing the mechanism of sohd-solid reaction and deriving a series of formulae to describe the variation and rate of reactions. This new model has been used in the manufacturing of spinel Li4Ti5O12. The results show that this new model works very well and will play a useful role for guiding the manufacturing of electrochemical materials.

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.

Single Step Solid-Solid Reaction Scheme for the Synthesis of Cobalt Sulphide-Oxide Nanoparticles in Polymer Matrix

At present, there is considerable interest in polymer-metal chalcogenides/oxides based nano-composites on account of their tunable optical, magnetic, electronic and catalytic properties. Here in, we report a simple single step approach for the in-situ synthesis of combined cobalt sulphide/cobalt oxide in polyphenylenesulphide (PPS) polymer matrix. We have illustrated the suitability of this methodology by reacting commonly available cobalt precursors with engineering thermoplastic, PPS. The cobalt precursor was homogeneously mixed with PPS in the molar ratios of 1:1, 1:5, 1:10, 1:15, respectively, followed by heating the mixtures obtained at the melting temperature of the polymer (285?C) for six hours. The resultant products were characterized by X-ray Diffractometry (XRD), Field-Emission Scanning Electron Microscopy (FESEM), High Resolution Transmission Electron Microscope (HRTEM), Diffuse Reflectance Spectroscopy (DRS) technique and Fourier Transformation Infra red Spectroscopy (FTIR). Formation of mixed phases viz., sulphide and oxide of cobalt within modified PPS matrix was confirmed by XRD. The resultant nanoparticles of cobalt sulphide and cobalt oxide embedded in the PPS matrix showed crooked and chunk morphology. The optical properties of the resultant nanocomposites indicate the shift in the absorption hump due to nanoscale size effect.

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.

Thermal kinetic analysis of a complex process from a solid-state reaction by deconvolution procedure from a new calculation method and related thermodynamic functions of Mn_(0.90)Co_(0.05)Mg_(0.05)HPO_4?3H_2O

Three individual peaks of thermal solid-state reaction processes of the synthesized Mn0.90Co0.05Mg0.05HPO4?3H2O were observed corresponding to dehydration I,dehydration II and polycondensation processes.An alternative method for the calculation of the extent of conversion was proposed from the peak area of the individual DTG peak after applying the best fitting deconvolution function(Frazer–Suzuki function).An iterative integral isoconversional equation was used to compute the values of the apparent activation energy Eαand they were found to be 65.87,78.16 and 119.32 kJ/mol for three peaks,respectively.Each individual peak was guaranteed to be a single-step kinetic system with its unique kinetic parameters.The reaction mechanism functions were selected by the comparison between experimental and model plots.The results show that the first,second and final individual peaks were two-dimensional diffusion of spherical symmetry(D2),three-dimensional diffusion of spherical symmetry(D3)and contracting cylinder(cylindrical symmetry,R2)mechanisms.Pre-exponential factor values of 3.91×106,1.35×107 and 2.15×107 s?1 were calculated from the Eαvalues and reaction mechanisms.The corresponded standard thermodynamic functions of the transition-state(activated)complexes were determined and found to agree well with the experimental data.

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.

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).

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.

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.

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.