A tau approach for solution of the space fractional diffusion equation

Fractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre-tau idea are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.     

The finite volume spectral element method to solve Turing models in the biological pattern formation

It is well known that reaction-diffusion systems describing Turing models can display very rich pattern formation behavior. Turing systems have been proposed for pattern formation in various biological systems, e.g. patterns in fish, butterflies, lady bugs and etc. A Turing model expresses temporal behavior of the concentrations of two reacting and diffusing chemicals which is represented by coupled reaction-diffusion equations. Since the base of these reaction-diffusion equations arises from the conservation laws, we develop a hybrid finite volume spectral element method for the numerical solution of them and apply the proposed method to Turing system generated by the Schnakenberg model. Also, as numerical simulations, we study the variety of spatio-temporal patterns for various values of diffusion rates in the problem.     

Sintering Behavior and Machinability of Phlogopite Glass Ceramics Containing Fe2O3

Mica-based glasses in the SiO₂-Al₂O₃-MgO-K₂O-F system were prepared by a sintering method to investigate the effects of different amounts of hematite (Fe₂O₃) on thermal and sintering behaviors besides machinability of the glasses by means of differential thermal analysis (DTA), X-ray diffraction, and scanning electron microscope techniques. DTA analysis on fine and coarse glass powders indicated that the main crystallization mechanism in this system occurred in the bulk rather than the surface. Increasing Fe₂O₃ content to 5 wt.% improved machinability of the glass ceramic. Fe₂O₃ led to the disruption of the glass matrix and facilitated the nucleation of the crystalline phase. Precipitation of sellite (MgF₂) crystals as heterogeneous nucleating sites for potassium phlogopite crystals acted as a second contribution to the machinability of the 5 wt.% Fe₂O₃-containing sample. However, introducing more than 5 wt.% Fe₂O₃ to the base glass prohibited the nucleation of MgF₂, and as a result, large micas formed within the glass. This together with precipitation of cordierite aggregates in highly doped glass with Fe₂O₃ led to lower machinability in these samples.     

Improvement of Structural and Mechanical Properties of Al-1100 Alloy via Friction Stir Processing

In the present study, the relationship between structural and mechanical properties of friction stir processed Al-1100 alloy and process parameters (tool rotation rate: ω and traverse speed: ν) was studied to get an better understanding and optimizing the friction stir processing (FSP) condition of this alloy. Microstructural studies revealed that increasing of ω up to 720 rpm resulted in grain refinement in the stirred zone (SZ), but higher increasing of ω caused grain growth in this zone. These variations of SZ grain size illustrated that the prevailing factor that determined the SZ grain size was plastic deformation at first and thereafter, peak temperature in the SZ. Mechanical properties investigations were in accordance with microstructural findings and illustrated that optimized FSP condition for Al-1100 alloy was 720 rpm and 20 mm/min. Optimized FSP condition resulted in a significant improvement of tensile strength and elongation up to 22 and 8% of those of base metal, respectively.     

Growth,corrosion and wear resistance of SiC nanoparticles embedded MAO coatings on AZ31B magnesium alloy

In this research, nanocomposite coating was deposited on magnesium matrix AZ31B alloy using the micro arc oxidation (MAO) method. MAO was carried out in SiC-nanoparticles containing suspension using the sodium silicate and sodium aluminate bases at constant current density. The effect of nanopowder addition and MAO periods were also investigated in the present work. Using the Scanning electron microscopy (SEM), the thickness and surface morphology of the coatings were studied. The coefficient of friction and abrasion rate curves were used to analyze nanopowder addition on resistance to abrasion, while the potentiodynamic curves were used for assessing the resistance to corrosion in the ceramic nanocomposite coating deposited on surface of alloy AZ31B. The morphological studies on surface of coatings revealed that the cavitation level and size increases with the increasing coating duration. Besides, Energy Dispersive X-Ray Diffraction (EDS) analyses from cross section and surface of the prepared coatings revealed that nanopowder distribution on interface of coating with matrix and boundaries of the cavities is almost uniform. The cross section studies of the coatings revealed that their thickness increases, as coating duration prolongs. Furthermore, the corrosion behavior of the samples indicated that presence of nanopowder does not significantly affect the resistance to corrosion of the coatings; however, coefficient of friction and abrasion rate of coatings indicates a respective rise and drop in presence of these nanopowders.     

Attaining optimal dyeability and tensile properties of polypropylene/poly(ethylene terephthalate) blends with a special cubic mixture experimental design

In this investigation, we attempted to enhance the dyeability of polypropylene (PP) with disperse dyestuffs without adversely affecting its tensile properties. To this end, a special cubic experimental design was used to predict the effect of variations in the properties of a tricomponent mixture composed of PP, poly(ethylene terephthalate) (PET), and maleic anhydride grafted polypropylene (PP‐g‐MA) on the dyeability and tensile properties of the resultant polymer blend. The results illustrate that there seemed to be critical PET content, above which the blend's dye uptake tended to remain constant, but the tensile properties were adversely affected. Further analysis of the results indicated that the PP/PET/PP‐g‐MA blends in which the PET and PP‐g‐MA contents were in the range 10–15 and 4–5 wt %, respectively, gave maximal dye uptake and desirable tensile properties. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Preparation of modified polyethersulfone membranes using variation in coagulation bath temperature and addition of hydrophilic surfactant

In this study, novel asymmetric polyethersulfone membranes were prepared from PES/PEG/Tween-20/NMP system via immersion precipitation. Pure water was used as gelation media. Simultaneous effects of variation in coagulation bath temperature (CBT) and addition of Tween-20 on morphology, wettabiliy, pure water permeation flux (PWF) and bovine serum albumin (BSA) rejection of the prepared membranes were studied by scanning electron microscopy (SEM), atomic force microscopy (AFM), contact angle measuring instrument and experimental set up. The obtained results indicate that the small addition of surfactants in the casting solution along with using the lowest level of CBT increases hydrophilicity of the PES membranes. Also it was found out that addition of Tween-20 in the casting solution along with increasing the CBT incites the formation of the bigger pores on the top surface and results in the formation of membranes with higher porosity in the sublayer.     

Comparison of Preparation Methods of Iron‐Based Catalysts for High‐Temperature Water‐Gas Shift Reaction

The influence of preparation methods on structural and catalytic properties of the Fe₂O₃‐Cr₂O₃‐CuO catalyst during the high‐temperature water‐gas shift reaction was determined. The prepared samples were characterized by X‐ray diffraction (XRD), Brunauer‐Emmett‐Teller method (BET), and temperature‐programmed reduction (TPR). The results revealed that the type of coprecipitation, i.e., simple, inverse, and differential, had a significant effect on both structural and catalytic properties. The catalyst prepared by the simple precipitation method exhibited higher activity than the catalysts generated by inverse and differential coprecipitation and the commercial catalyst. The types of precipitation agent and iron and chromium precursors were found to have a significant impact on the structural and catalytic features.     

Application of response surface methodology for optimization and determination of palladium by in-tube ultrasonic and air-assisted liquid–liquid microextraction coupled with flame atomic absorption spectrometry

A highly sensitive, simple and rapid in-tube ultrasonic and air-assisted liquid–liquid microextraction (IT-UAA-LLME) coupled with flame atomic absorption spectrometry was developed for preconcentration and determination of palladium (Pd) in soil and water samples. The effective parameters were optimized by the Plackett–Burman (P–B) and Box–Behnken design (BBD) methods. Under the optimum conditions, the calibration graph was linear over the range of 5–800 μgL^?1 (R² = 0.998). Detection limit, relative standard deviation (RSD) and the enrichment factor were 0.94 μgL^?1, 2.64% (n = 7, C = 40 μgL^?1) and 156, respectively. The proposed method was successfully applied for the determination of trace amounts of Pd in the soil and water samples.     

Electron Microscopy Study of γ-Al2O3 Supported Cobalt Fischer–Tropsch Synthesis Catalysts

Three supported catalysts containing 20 wt% cobalt and 0.5 wt% rhenium were subjected to electron microscopy studies in their calcined state. The catalysts were prepared by incipient wetness impregnation of γ-Al₂O₃ supports of different pore characteristics with aqueous solutions of cobalt nitrate hexahydrate and perrhenic acid. The influence of the support on the Co₃O₄ crystallite size and distribution was studied by X-ray diffraction and electron microscopy. There was a positive correlation between the pore diameter of the support and the post calcination Co₃O₄ crystallite size. On all three γ-Al₂O₃ supports, Co₃O₄ was present as aggregates of many crystallites (20–270 nm in size). Cobalt oxide did not crystallise as independent crystallites, but as an interconnected network, with a roughly common crystallographic orientation, within the matrix pore structure. The internal variations in crystallite size between the catalysts were maintained after reduction. Fischer–Tropsch synthesis was carried out in a fixed-bed reactor at industrial conditions (T = 483 K, P = 20 bar, H₂/CO = 2.1). Although the cobalt-time yields varied significantly (4.6–6.7 × 10^?3 mol CO/mol Co s), the site-time yields were constant (63–68 × 10^?3 s^?1) for the three samples. The C₅₊ selectivity could not be correlated to the cobalt oxide aggregate size and is more likely related to the cobalt particle size and chemical properties of the γ-Al₂O₃ support.