Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.     

Fast photoluminescence decay processes of doped ZnO phosphors

Lifetime measurements have been carried out for ZnO doped with killer impurities (Fe, Co or Ni) having doping concentrations 0.05 to 1.00% by weight using a pulsed UV laser (nitrogen laser) as the excitation source having a short pulse width and a high photon flux density. The high photon flux density of the laser is very useful to excite the short-lived shallow trapping states which otherwise would be impossible to excite. Fast photoluminescence emission in the microsecond time domain has been obtained due to killer impurities at room temperature. The effect of killer dopants as well as the effect of their concentrations on lifetime values has been observed. Other optical parameters such as trap depth and decay constant are also reported in the present context. Lifetime values are found to be in the microsecond time domain and a reverse trend is obtained with increase in concentration of killer impurities. PACS 78.55.-m; 78.55.Ap; 78.66.Db; 78.66.Hf     

Solutions of differential equations in a Bernstein polynomial basis

An algorithm for approximating solutions to differential equations in a modified new Bernstein polynomial basis is introduced. The algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval and then makes use of the Galerkin method to determine the expansion coefficients to construct a solution. Matrix formulation is used throughout the entire procedure. However, accuracy and efficiency are dependent on the size of the set of Bernstein polynomials and the procedure is much simpler compared to the piecewise B spline method for solving differential equations. A recursive definition of the Bernstein polynomials and their derivatives are also presented. The current procedure is implemented to solve three linear equations and one nonlinear equation, and excellent agreement is found between the exact and approximate solutions. In addition, the algorithm improves the accuracy and efficiency of the traditional methods for solving differential equations that rely on much more complicated numerical techniques. This procedure has great potential to be implemented in more complex systems where there are no exact solutions available except approximations.     

On series solution for generalized Falkner–Skan flow of a FENE‐P model

This paper deals with the viscoelastic boundary layer flow past a plate. Constitutive assumptions of the FENE‐P model are taken into account. The pressure gradient is taken as non‐zero. The series solution of the non‐linear problem modelled in (Appl. Math. Lett. 2007; 20 :1211–1215) is developed by a homotopy analysis method (HAM). Numerical solution of the skin friction coefficient is also computed. Further a comparison between the numerical and HAM solutions is provided. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of outliers on QTL mapping for complex traits

A method was proposed for the detection of outliers and influential observations in the framework of a mixed linear model, prior to the quantitative trait locus （QTL） mapping analysis. We investigated the impact of outliers on QTL mapping for complex traits in a mouse BXD population, and observed that the dropping of outliers could provide the evidence of additional QTL and epistatic loci affecting the 1 stBrain-OB and the 2ndBrain-OB in a cross of the abovementioned population. The results could also reveal a remarkable increase in estimating heritabilities of QTL in the absence of outliers. In addition, simulations were conducted to investigate the detection powers and false discovery rates （FDRs） of QTLs in the presence and absence of outliers. The results suggested that the presence of a small proportion of outliers could increase the FDR and hence decrease the detection power of QTLs. A drastic increase could be obtained in the estimates of standard errors for position, additive and additive× environment interaction effects of QTLs in the presence of outliers.     

Cryoelectrochemical reduction of a phenyl sulfide in tetrahydrofuran: mediated reduction gives different products compared to direct reduction

An electrocatalytic reduction of [(3‐{[trans‐4‐(methoxymethoxy)cyclohexyl]oxy}propyl)thio]benzene (RSPh) in the presence of naphthalene as a mediator is investigated, using steady‐state voltammetry at various sized platinum microelectrodes and at low temperature (201 K) in tetrahydrofuran (THF). This mediated process has been found to involve the transfer of one electron, in contrast to the direct electrochemical reduction which involves two electrons. In addition, the mediated reduction proceeds at a potential, some 500 mV less negative than the direct electrochemical reduction. The evidence for the proposed mechanism has been obtained from theoretical simulations, using DIGISIM which shows satisfactory fitting to experimental results and allowed the determination of the rate constant for the homogeneous step. In contrast to direct reduction of RSPh where only one product, trans‐1‐ (methoxymethoxy)‐4‐propoxycyclohexane (RH), has been obtained, the isolation of two products, RH and the dimer, diphenyl disulfide, PhSSPh, following mediated preparative electrolysis of RSPh, in presence of naphthalene shows that this one‐electron process may be carried out at the reduction potential of naphthalene at low temperature and has also validated deductions made from voltammetric results. Copyright © 2007 John Wiley & Sons, Ltd.     

Real‐time FTIR monitoring of the mechanism of initiation of isobutylene polymerizations by epoxide/Lewis acid systems

Real‐time Fourier Transformation Infrared (FTIR) spectroscopy with a fiber optic transmission probe (TR) was used to monitor the polymerization of isobutylene (IB) initiated by α‐methylstyrene epoxide (MSE) and 1,2‐epoxi‐2,4,4‐trimethylpentane (TMPO‐1) in conjunction with TiCl₄ and BCl_3. In the presence of an equimolar amount of BCl₃, MSE and TMPO‐1 underwent ring opening via S_N1 mechanism. In contrast to TiCl₄‐coinitiated reactions, no oligoether formation via S_N2 mechanism was observed. TMPO‐1 with excess BCl₃ initiated IB polymerization, yielding a telechelic PIB carrying α‐primary OH and ω‐tertiary Cl functionalities with 70% initiator efficiency. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3611–3618, 2008     

A note on series solution for generalized Couette flow

The problem of generalized Couette flow is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed. Finally, the results are presented graphically and the effects of emerging parameters are analyzed.     

Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space

This work is aimed at describing the heat transfer on the peristaltic motion in a porous space. An incompressible and magnetohydrodynamic (MHD) viscous fluid is taken in an asymmetrical channel. Expressions of dimensionless stream function and temperature are obtained analytically by employing long wavelength and low Reynolds number assumptions. The influence of various parameters of interest is seen through graphs on pumping and trapping phenomena and temperature profile.     

On accelerated flows of an Oldroyd-B fluid in a porous medium

In this work, the problems dealing with unsteady unidirectional flows of an Oldroyd-B fluid in a porous medium are investigated. By using modified Darcy's law of an Oldroyd-B fluid, the equations governing the flow are modelled. Employing Fourier sine transform, the analytic solutions of the modelled equations are developed for the following two problems: (i) constant accelerated flow, (ii) variable accelerated flow. Explicit expressions for the velocity field and adequate tangential stress are obtained in each case. The solutions for Newtonian, second grade and Maxwell fluids in a porous medium appear as the limiting cases of the present analysis.