Wick-stochastic finite element solution of reaction–diffusion problems

Real life reaction–diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a finite element solution of reaction–diffusion equations of Wick type. Using the Wick-product properties and the Wiener–Itô chaos expansion, the stochastic variational problem is reformulated to a set of deterministic variational problems. To obtain the chaos coefficients in the corresponding deterministic reaction–diffusion, we implement the usual Galerkin finite element method using standard techniques. Once this representation is computed, the statistics of the numerical solution can be easily evaluated. Computational results are shown for one- and two-dimensional test examples.     

Synthesis of oxime phosphoranes from reaction between triphenylphosphine and acetylenic esters in the presence of oxime derivatives

A new one-pot, simple and effective procedure is presented for the preparation of O-containing phosphorus ylides by the Michael addition reaction of N-methylpyrrole-2-carbaldehydoxime, pyridin-2-carbaldehydoxime or acetophenonoxime with acetylenic esters.     

Prediction of the particle-laden jet with a two-equation turbulence model

A two-equation turbulence model for two-phase flows has recently been proposed by Elghobashi & Abou-Arab (1983). They derived the exact equations of the kinetic energy of turbulence and the rate of dissipation of that energy, and modeled the turbulent correlations, resulting from time-averaging, up to third order. In order to validate the proposed model, a turbulent axisymmetric gaseous jet laden with spherical uniform-size solid particles is studied here. The predictions of the mean flow properties of the two-phases and the turbulence kinetic energy and shear stress of the carrier phase show good agreement with the experimental data.     

On van der Pol's equation

Summary The family of trajectories (in the phase plane) of van der Pol's equation is a one parameter family of curves; no explicit analytical expression for it is known. The same is true for the orthogonal trajectories of this family. The differential equation of the orthogonal curves is solved here exactly in terms of modified Bessel functions. Two curves of the orthogonal family are found to be especially simple, and a graph is given which would permit plotting the solutions of van der Pol's equation with an accuracy higher than that attainable with the usual methods.     

Optimization using response surface methodology for fast removal of hazardous azo dye by γ-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>@CuO nanohybrid synthesized by sol–gel combustion

An efficient adsorption system was developed for removal of hazardous Direct Blue 71 as a sample azo dye. The γ-Fe₂O₃@CuO adsorption system was synthesized based on a sol–gel combustion route and characterized by energy-dispersive X-ray (EDX) analysis, X-ray diffraction (XRD) analysis, vibrating-sample magnetometry (VSM), and field-emission scanning electron microscopy (FESEM) techniques. The response surface methodology with Box–Behnken design was used to evaluate the effects of pH, shaking time, and adsorbent dose on dye adsorption. The results showed that solution pH was the parameter with greatest effect on dye adsorption. Adsorption equilibrium was reached quickly, within 8 min. Study of isotherms revealed adsorption capacity of 45.7 mg g^?1 according to the Freundlich model. Sorbent regeneration could be performed using methanol–NaOH (0.1 mol L^?1) solution.     

Polyhydroxyquinoline-carbon nanotube chelating resin for selective adsorption of lead ions: multivariate optimization,isothermic, and thermodynamic study

In this work a facile hydrothermal route has been employed to prepare a multiwall carbon nanotube wrapped in a chelating resin. 8-Hydroxyquinoline and p-formaldehyde were used as monomer and linker for polymer synthesis. The prepared composite was employed as an efficient adsorbent for lead adsorption and preconcentration from various matrices. Effective parameters on lead adsorption have been optimized by central composite design. Results showed that equilibrium adsorption was obtained at pH = 4, with a shacking time of 15 min and adsorbent dosage of 15 mg. Isotherm study showed that the sorbent has adsorbent capacity of 250 mg g^?1; moreover, the process followed a Langmuir isotherm model. Thermodynamic investigation confirmed that lead adsorption is spontaneous, as well as follows endothermic path.     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

Rapid,green, and catalyst-free one-pot three-component syntheses of 5-substituted 1<Emphasis Type="Italic">H</Emphasis>-tetrazoles in magnetized water

The catalyst-free multi-component reactions of aldehydes, malononitrile, and sodium azide at a relatively low temperature in magnetized water provided 5-substituted 1H-tetrazoles in high-to-excellent yields. This method offers the advantages of short reaction times, low costs, quantitative reaction yields, simple work-up, green, and no need for any organic solvent.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.