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.

Preparation of long alumina fibers by sol-gel method using malic acid

The precursor sol of alumina was prepared by sol-gel method with aluminum nitrate and malic acid as raw materials.The effects of content of malic acid and polyvinylpyrrolidone （PVP） on sol spinnability were explored.The gel fibers with above 80 cm in length were obtained by mixing aluminum nitrate,malic acid and PVP on mass ratio of 10 3 1.5.Thermogravimetry-differential scanning calorimetry （TG-DSC）,Fourier transform infrared （FTIR） spectrum,X-ray diffractometry （XRD）,and scanning electron microscopy （SEM） were used to characterize the properties of the gel and ceramic fibers.The alumina fibers with a smooth surface and about 20μm in diameter were obtained by sintering at 1 200℃,and their main phase was indentified to be α-Al2O3.

A Novel Approach to Synthesizing Porous ZnO Films: Inorganic Chelating Sol-Gel Method

Porous ZnO films are synthesized by inorganic chelating sol-gel method,which is a novel sol-gel technique using zinc nitrate as starting materials and citric acid as the chelating reagent.The crystal structure,surface morphology,porous and optical properties of the deposited films are investigated.X-ray diffraction pattern analysis shows that crystal structure of the ZnO films is hexagonal wurtzite.Scanning electron microscopy (SEM) shows that the ZnO film is porous.The curve of pore size distribution has two peak values at about 2.02nm and 4.97nm and BET surface area of the ZnO film is 27.57m2/g.In addition,the transmittance spectrum gives a high transmittance of 85% in the visible region and optical bandgap of the ZnO film (fired at 500℃) is 3.25eV.

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.

Synthesis of LiMnPO_4/C composite material for lithium ion batteries by sol-gel method

The LiMnPO4/C composite material was synthesized via a sol-gel method based on the citric acid. The X-ray diffraction （XRD）, scanning electron microscopy （SEM） and electrochemical performance tests were adopted to characterize the properties of LiMnPO4/C. The XRD studies show that the pure olivine phase LiMnPO4 can be obtained at a low temperature of 500 °C. The SEM analyses illustrate that the citric acid used as the chelating reagent and carbon source can restrain the particle size of LiMnPO4/C well. The LiMnPO4/C sample synthesized at 500 °C for 10 h performs the highest initial discharge capacity of 122.6 mA-h/g, retaining 112.4 mA-h/g over 30 cycles at 0.05C rate. The citric acid based sol-gel method is favor to obtain the high electrochemical performance of LiMnPO4/C.

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.

Photocatalytic Activity of Nanosized ZnWO_4 Prepared by the Sol-gel Method

Nanosized ZnWO4 photocatalysts were successfully synthesized via the sol-gel process in a temperature range of 450-800℃. The grain size, crystal size, and crystallinity of ZnWO4 particles increased with the increase of calcina- tion temperature and prolonging calcination time. The photocatalytic activity was measured for the degradation of an aqueous Rhodamine-B（RhB） solution and gaseous formaldehyde（FAD）. With the increase of calcination temperature and time, the activities increased to a maximum and then decreased. ZnWO4 photocatalyst prepared at 550℃ for I0 h showed the highest activity, which is similar to the photocatalytic activity of P25TiO2 for the degradation of gase-ous FAD. High crystallinity, large surface area, and good dispersion are responsible for the high photocatalytic per- formance of the prepared ZnWO4.

Direct Synthesis of Diphenyl Carbonate with Heterogeneous Catalyst and Optimal Synthesis Conditions of the Support Prepared by Sol-gel Method

The support of catalyst for the direct synthesis of diphenyl carbonate （DPC） by heterogeneous catalytic reaction was prepared by the sol-gel method. Compared with activated charcoal, molecular sieve, porous ceramics, hopcalite, the support prepared by the sol-gel method has higher activity. The characterization of the support by X-ray diffraction （XRD） and transmission electron microscope （TEM） show that the mare crystal phase is Co2MnO4 and the average particle diameter is about 40 nm. The optimum conditions for synthesis of the support were determined by orthogonal experiments, which indicate that the proportion of Cu, Mn, and Co is the first important factor influencing the yield and selectivity of DPC. Temperature of calcination is the second one. The optimum conditions are： molar proportion of Cu, Mn, and Co being 1 ： 1 ： 1, temperature of calcination 700℃, drying at 100~C, temperature of water bath 85~C. The yield and selectivity of DPC in the process can reach 38% and 99% in the batch operation, respectively. The copper cobalt manganese mixed oxides chosen as the support contribute more to the high catalytic activity than the sol-gel method.

Preparation and properties of nanocrystal SmBO_3 by nitrate-citrate sol-gel combustion method

Nanocrystal SmBO3 powders were synthesized by nitrate-citrate sol-gel combustion method. The phase evolution, morphologies and absorbency of the synthesized powders were characterized by X-ray diffraction （XRD）, Field emission scanning electronic microscope （FESEM）, Fourier transform infrared spectroscopy （FFIR） and UV-3101PC spectrophotometer （UVPC）, respectively. XRD and FESEM results showed that pure SmBO3 phase was obtained at 750 ℃, with an average original particle size of about 100 nm. FTIR showed that there were apparently concentrated absorbent peaks between 500 and 1400 cm^-1. Moreover, the reflectivity of the powders apparently decreased at the wavelength between 1.05 and 1.15 μm. Therefore, SmBO3 might be a kind of absorbent material for infrared laser.

Preparation and Characterization of Sodium Sulfate/Silica Composite as a Shape-stabilized Phase Change Material by Sol-gel Method

A sodium sulfate （NaeSO4）/silica （SiO2） composite was prepared as a shape-stabilized solid-liquid phase change material by a sol-gel procedure using Na2SiO3 as the silica source. Na2SO4 in the composite acts as a latent heat storage substance for solid-liquid phase change, while SiO2 acts as a support material to provide structural strength and prevent leakage of melted NazSO4. The microstructure and composition of the prepared composite were characterized by the N2 adsorption, transmission electron microscope （TEM）, scanning electron microscope （SEM）, Fourier transform infrared spectroscopy （FTIR） and X-ray diffraction. The results show that the prepared Na2SOJSiO2 composite is a nanostructured hybrid of NazSO4 and SiO2 without new substances produced during the phase change. The macroscopic shape of the NazSO4/SiO2 composite after the melting and freezing cycles does not change and there is no leakage of Na2SO4. Determined by differential scanning calorimeter （DSC） analysis, the values of phase change latent heat of melting and freezing of the prepared NazSO4/SiO2 （50%, by mass） composite are 82.3 kJ.kg i and 83.7 kJ.kg-1, and temperatures of melting and freezing are 886.0 ℃ and 880.6 ℃, respectively. Furthermore, the Na2SOJSiO2 composite maintains good thermal energy storage and release ability even after 100 cycles of melting and freezing. The satisfactory thermal storage performance renders this composite a versatile tool for high-temperature thermal energy storage.

Grain Size and Photocatalytic Activity of Nanometer TiO_2 Thin Films Prepared by the Sol-gel Method

Transparent anatase TiO2 nanometer thin films with photocatalytic activity were prepared via the sol-gel method on soda-lime glass. The thickness , crystalline phase, grain size, surface hydroxyl amount and so on were characterized by scanning electron microscopy (SEM) , X-ray diffraction (XRD), transmission electron microscopy ( TEM), X-ray photoelectron spectroscopy (XPS) and UV-visible spectrophotometer ( UV-VIS). The photocatalytic activity of TiO2 thin films was evaluated for the photocatalytic decolorization of aqueous methyl orange . The effects of film thickness on the crystalline phase, grain size, transmittance and photocatalytic activity of nanometer Ti02 thin films were discussed.

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.

Luminescence properties of red-emitting Ca_2Al_2SiO_7:Eu^(3+) nanoparticles prepared by sol-gel method

A series of red-emitting Ca2_xA12SiOT：xEu^3＋ （x = 1 mol.%-10 tool.%） phosphors were synthesized by the sol-gel method. The effects of annealing temperature and doping concentration on the crystal structure and luminescence properties of Ca2A12SiO7：Eu^3＋ phosphors were investigated. X-ray diffraction （XRD） profiles showed that all peaks could be attributed to the tetragonal Ca2A12SiO7 phase when the sample was annealed at 1000℃. Scanning electron microscopy （SEM） micrographs indicate that the phosphors have an irregularly rounded mor- phology with particles of about 200 nm. Excitation spectra showed that the strong broad band at around 258 nm and weak sharp lines in 350-490 nm were attributed to the charge transfer band of Eu^3＋-O^2- and f-f transitions within the 4f^6 configuration of Eu^3＋ ions, respectively. Emission spectra implied that the red luminescence could be attributed to the transitions from the ^5D0 excited level to the 7Fj （J = 0, 1, 2, 3, 4） levels of Eu3＋ions with the main electric dipole transition ^5D0→^7F2 （618 and 620 nm）, and Eu^3＋ ions prefer to occupy a lower symmetry site in the crystal lattice. Moreover, the photoluminescence （PL） intensity was strongly dependent on both the sintering temperature and doping concentration, and the highest PL intensity was observed at an Eu^3＋ concentration x = 7 mol.% after annealing at ll00℃. The obtained Ca2A12SiO7：Eu^＋3＋ phosphor may have potential application for the red lamp phosphor.

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.

Effects of sol-gel method and lanthanum addition on catalytic performances of nickel-based catalysts for methane reforming with carbon dioxide

The nickel-based catalysts were prepared by the sol-gel method and used for the CH4 reforming with CO2. The effects of the sol-gel method on the specific surface area, catalytic activity, desorption, and reduction performances of catalysts were investigated with BET, TPR, and TPD. Compared with the catalyst prepared by the impregnation method, the results indicated that the catalysts prepared by the sol-gel method had larger specific surface area, showing higher catalytic activities and exhibiting perfect desorption and reduction performances. In addition, the modification effects of adding La were studied, and it was found that the 0.75NLBT catalyst constituted of 5wt.%Ni-0.75wt.%La was optimal.

Influence of dopant content on morphology and optical constants of ZnO:Na films by sol-gel method

Undoped and Na-doped ZnO films were deposited by sol-gel method.The effects of sodium incorporation on structure,surface morphology and optical constants of the films were investigated.X-ray diffraction patterns show the hexagonal wurtzite polycrystalline structure and that the sodium incorporation leads to the change in the structural characteristics of ZnO films.The SEM observations show that the surface morphology of the films is affected by the sodium incorporation.The transmission spectra show that the average transmittance of the films is above 85% in the visible range.The absorption edge initially blue-shifts and then red-shifts with the increase of Na doping content.The optical constants of these films were calculated using transmission spectra.Refractive indices of the films in the visible range decrease at first and then increase with increasing Na doping content.

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.