Spline methods for the solution of hyperbolic equation with variable coefficients

In this study, we developed the methods based on nonpolynomial cubic spline for numerical solution of second‐order nonhomogeneous hyperbolic partial differential equation. Using nonpolynomial cubic spline in space and finite difference in time directions, we obtained the implicit three level methods of O(k² + h²) and O(k² + h⁴). The proposed methods are applicable to the problems having singularity at x = 0, too. Stability analysis of the presented methods have been carried out. The presented methods are applied to the nonhomogeneous examples of different types. Numerical comparison with Mohanty's method (Mohanty, Appl Math Comput, 165 (2005), 229–236) shows the superiority of our presented schemes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A finite termination Mehrotra-type predictor–corrector algorithm

Mehrotra-type predictor–corrector algorithms are the backbone of most Interior Point Methods based software packages. Salahi et al. [M. Salahi, J. Peng, T. Terlaky, On Mehrotra-type predictor–corrector algorithms, Technical Report 2005/4, Advanced Optimization Lab., McMaster University, Hamilton, ON, Canada. http://www.cas.mcmaster.ca/~oplab/publication] in their recent works have shown some ill behaviors of Mehrotra’s original algorithm which motivated them to modify it in order to achieve the polynomial iteration complexity while preserving its practical efficiency. In this paper we analyze the same algorithm from a different perspective and give a condition on the maximum feasible step size in the predictor step, violation of which might lead to a very small or even zero step size in the corrector step. If the maximum step size in the predictor step is above a certain threshold, then we cut it to satisfy the derived condition. This enables us to prove that the algorithm terminates finitely.     

Postponing the choice of the barrier parameter in Mehrotra-type predictor–corrector algorithms

Recently Salahi et al. have considered a variant of Mehrotra’s celebrated predictor–corrector algorithm. By a numerical example they showed that this variant might make very small steps in order to keep the iterate in a certain neighborhood of the central path, that itself implies the inefficiency of the algorithm. This observation motivated them to incorporate a safeguard in their algorithmic scheme that gives a lower bound for the step size at each iteration and thus imply polynomial iteration complexity. In this paper we propose a different approach that enables us to have control on the iterates.     

Energy-consuming micromechanisms in the fracture of glassy polymers. I. Chain scission in polystyrene

The number of chain scissions per unit area that occur during the fracture of partially annealed latex films from M_n ? 180,000 g/mol polystyrene particles of about 275 Å radius were measured and correlated to annealing times. A curve with four regimes was found. At short annealing times the curve is nearly flat, in what is called the chain pull-out regime. In the second regime, the number of chains broken per unit area increases with a 0.8 power of annealing time as entanglement of the diffusing polymer chains increases in neighboring host particles. This is in good agreement with Wool's theory which predicts a 0.75 power dependence. Then, after reaching a peak, the number of scissions decreases in the third regime, indicating a change in fracture mechanism. The number of chain scissions increases again in the fourth regime, as final healing of the film interface takes place. Fracture surface analysis reveals a rough surface for short annealing times and a smooth surface for longer annealing times. The number of polymer chain scissions per unit area of fracture surface showed no dependence on initial molecular weights for t ? τ_r where t and τ_r are annealing and relaxation times, respectively. The number of chain bridges crossing a unit area of interface was suggested as the basic molecular property. © 1992 John Wiley & Sons, Inc.     

Application of response surface methodology for optimization of the stability of asphaltene particles in crude oil by TiO2/SiO2 nanofluids under static and dynamic conditions

In this work, the onset of asphaltene flocculation for an Iranian crude oil by titration of samples with heptane in the presence and absence of the TiO₂/SiO₂ nanofluids was obtained by Near-IR spectroscopy. Nanoparticles and nanocomposites were characterized by BET, FESEM, EDX, XRD, and XRF analysis. Modeling and optimization of inhibition of asphaltene flocculation process by TiO₂/SiO₂ nanofluids were conducted by response surface methodology (RSM). Under optimum conditions (nanocomposite composition = 0.04 wt% (80%TiO₂:20%SiO₂), salinity = 4.01 wt%, and pH = 3.42), the onset point increased. For nanofluids stability analysis, the optimum nanofluid was compared with the two other nanofluids (SiO₂ and TiO₂) by visual observation method. The results indicated that high stability and surface area of the 80%TiO₂ nanocomposites increase asphaltene adsorption on the particles surface that subsequently increases the onset point. In addition, the optimum nanofluid performance on the carbonate rocks was evaluated by contact angle and core flooding experiments. The 80% TiO₂ nanofluid changed the wettability of carbonate rocks from strongly oil-wet to strongly water-wet condition and also decreased the residual oil saturation and enhanced the oil recovery with an increase in the recovery factor of about 15%.     

Combined methane reforming over nano LaNiO<Subscript>3</Subscript> catalyst with modified active surface

In this study, nano catalyst LaNiO₃ with perovskite structure was synthesized using the citrate sol–gel method in the combined methane reforming with CO₂ and O₂ (CRM). The effects of increasing the surface area of the LaNiO₃ perovskite on the catalytic activity were investigated by changing the method of preparing and creating holes in the surface of the samples. Physical and chemical properties of the samples, before and after the reactor test, were determined through ICP, AA, XRD, TGA, TPR, BET, SEM, EDX and TEM techniques. The results of XRD, ICP, AA, SEM, EDX and TEM tests indicated that the citrate sol–gel method is a good way to prepare a homogeneous perovskite LaNiO₃ sample on a scale of nanometers. The results of the TPR test showed using etching in the citrate sol–gel method can produce samples with high stability. The BET results indicated that the surface area of the LaNiO₃ sample tripled with the method suggested in this paper. Changes in preparation method lead to induction time decreasing and temperature increasing. Use of etching in the citrate sol gel method had no significant effect in the results of activity tests versus time reaction at a temperature of 800 °C. TGA curves revealed no production of coke over the process for the produced samples.     

Carbon Paste Electrode Modified with ZrO<Subscript>2</Subscript> Nanoparticles and Ionic Liquid for Sensing of Dopamine in the Presence of Uric Acid

A novel carbon paste electrode modified with ZrO₂ nanoparticles and an ionic liquid (n-hexyl-3- methylimidazolium hexafluorophosphate) was fabricated. The electrochemical study of the modified electrode, as well as its efficiency for simultaneous voltammetric oxidation of dopamine and uric acid is described. The electrode was also employed to study the electrochemical oxidation of dopamine and uric acid, using cyclic voltammetry, chronoamperometry and square wave voltammetry as diagnostic techniques. Square wave voltammetry exhibits linear dynamic range from 1.0 × 10^?6 to 9.0 × 10^?4 M for dopamine. Also, square wave voltammetry exhibits linear dynamic range from 9.0 × 10^?6–1.0 × 10^?3 M for uric acid. The modified electrode displayed strong function for resolving the overlapping voltammetric responses of dopamine and uric acid into two well-defined voltammetric peaks. In the mixture containing dopamine and uric acid, the two compounds can be well separated from each other with potential difference of 155 mV, which is large enough to determine dopamine and uric acid individually and simultaneously. Finally, the modified electrode was used for determination of dopamine and uric acid in real samples.     

Magnetic iron oxide nanoparticles/K<Subscript>2</Subscript>S: a simple and scale-up method for the direct synthesis of symmetrical disulfides from aryl halides

A simple, one-pot, efficient and novel protocol has been developed for direct synthesis of symmetrical organic disulfides by domino reaction of aryl halides and K₂S in the presence of magnetic Fe₃O₄ nanoparticles as a readily available, highly efficient and recyclable catalyst. A variety of diaryl disulfides can be obtained in good-to-excellent yields up to 98%.     

Efficient synthesis of pyrazolopyranopyrimidines using DBU-based nanomagnetic catalyst

A simple and efficient method for the synthesis of pyrazolopyranopyrimidines under solvent-free has been developed. The one-pot multicomponent condensation of arylaldehydes with hydrazine hydrate, ethyl acetoacetate and barbituric acid in the vicinity of a mesoporous basic nanomagnetic catalyst, namely DBU immobilized on Fe₃O₄@nSiO₂@mSiO₂ was synthesized in remarkably high yields and in short reaction times. Significantly, this catalyst can be easily separated from the reaction media by applying an external magnet, and can be reused for several cycles.

Graphical abstract