Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.     

Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) method is an efficient mesh free technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. In a meshless method, a set of scattered nodes are used instead of meshing the domain of the problem. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes.     

Zein film as a novel natural biopolymer membrane in electrochemical detections

Permselective modifier films are very important in preparing highly sensitive electrochemical sensors. In this work, for the first time, the behavior of gold and glassy carbon electrodes coated with biocompatible zein film as a permselective membrane for the electrochemical detection of various compounds has been investigated. For this purpose, several electroactive cationic (methylene blue, brilliant green, and thionine) and anionic (potassium ferricyanide, alizarin red S, and riboflavin-5’-phosphate) compounds have been used as model. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) showed that zein membranes prepared from casting solution containing 1% zein in ethanol/water have porous structures with high nanometric roughness. The capacitance values of electrical double layers of electrodes modified with zein film were very high for hydrophilic ions in comparison with hydrophobic ions. Point of zero charge pH (pH_pzc) of zein membrane was 4.8. The results of cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) as well as pH_pzc study indicated that zein permselective membrane acts as ion exchanger film for selected cationic compounds with fast electrochemical kinetics responses in aqueous solution (pH=7). This behavior was confirmed by circulating solutions containing model compounds from homemade continuous cell equipped with polyamide membranes modified with zein film.

Graphical Abstract

     

Fabrication of Ti2SnC-MAX Phase Blended PES Membranes with Improved Hydrophilicity and Antifouling Properties for Oil/Water Separation

In this research work, the Ti₂SnC MAX phase (MP) was synthesized via the reactive sintering procedure. The layered and crystalline structure of this MP was verified by SEM, HRTEM, and XRD analyses. This nano-additive was used for improvement of different features of the polyethersulfone (PES) polymeric membranes. The blended membranes containing diverse quantities of the MP (0–1 wt%) were fabricated by a non-solvent-induced phase inversion method. The asymmetric structure of the membranes with small holes in the top layer and coarse finger-like holes and macro-voids in the sublayer was observed by applying SEM analysis. The improvement of the membrane’s hydrophilicity was verified via reducing the contact angle of the membranes from 63.38° to 49.77° (for bare and optimum membranes, respectively). Additionally, in the presence of 0.5 wt% MP, the pure water flux increased from 286 h to 355 L/m² h. The average roughness of this membrane increased in comparison with the bare membrane, which shows the increase in the filtration-available area. The high separation efficiency of the oil/water emulsion (80%) with an improved flux recovery ratio of 65% was illustrated by the optimum blended membrane.     

Preparation and characterization of Cu (II) supported on poly(8‐hydroxyquinoline‐p‐styrene sulphonate) and its application as catalyst for the synthesis of hexahydroquinolines

Cu ( II ) supported on poly(8‐hydroxyquinoline‐p‐styrenesulfonate) (Cu ( II )@PHQSS) was prepared and fully characterized by the different techniques including fourier transform infrared spectroscopy (FT‐IR), ¹H NMR, ¹³C NMR, thermal gravimetric analysis (TGA), differential thermal gravimetric (DTG), differential thermal analysis (DTA), scanning electron microscope (SEM) and energy dispersive X‐ray analysis (EDS). Afterward, the Cu ( II )@PHQSS as nanostructured catalyst was used as catalyst for the synthesis of hexahydroquinolines.     

The use of Sinc‐collocation method for solving Falkner–Skan boundary‐layer equation

The MHD Falkner–Skan equation arises in the study of laminar boundary layers exhibiting similarity on the semi‐infinite domain. The proposed approach is equipped by the orthogonal Sinc functions that have perfect properties. This method solves the problem on the semi‐infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, the governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by the Sinc‐collocation method. It is shown that the Sinc‐collocation method converges to the solution at an exponential rate. Copyright © 2010 John Wiley & Sons, Ltd.     

Cavity detection in a heat conductor using linear sampling method

In this paper, solution of inverse problems in heat conduction transient fields is investigated. For this purpose, a new time-domain version of linear sampling method (TDLSM) is developed for cavity detection in a heat conductor. The linear sampling method (LSM) is an effective approach to image the geometrical features of unknown targets. Although this method has been used in the context of inverse scattering problems such as solid, acoustics, and electromagnetism, there is no specific attempt to apply this method to identification of cavities in heat conductors. This study emphasizes the implementation of the LSM in the time-domain fields using finite element method. A set of numerical simulations on two-dimensional transient heat conduction problems is presented to highlight many effective features of the proposed TDLSM fast qualitative identification method.