A comparison of preconditioners for incompressible Navier–Stokes solvers

We consider solution methods for large systems of linear equations that arise from the finite element discretization of the incompressible Navier–Stokes equations. These systems are of the so‐called saddle point type, which means that there is a large block of zeros on the main diagonal. To solve these types of systems efficiently, several block preconditioners have been published. These types of preconditioners require adaptation of standard finite element packages. The alternative is to apply a standard ILU preconditioner in combination with a suitable renumbering of unknowns. We introduce a reordering technique for the degrees of freedom that makes the application of ILU relatively fast. We compare the performance of this technique with some block preconditioners. The performance appears to depend on grid size, Reynolds number and quality of the mesh. For medium‐sized problems, which are of practical interest, we show that the reordering technique is competitive with the block preconditioners. Its simple implementation makes it worthwhile to implement it in the standard finite element method software. Copyright © 2007 John Wiley & Sons, Ltd.     

Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations

In this work, we investigate existence and uniqueness of solutions for a class of nonlinear multi-point boundary value problems for fractional differential equations. Our analysis relies on the Schauder fixed point theorem and the Banach contraction principle.     

Lie ideals and (\alpha ,\beta )-derivations of *-prime rings

Let \((R,*)\) be a \(2\)-torsion free \(*\)-prime ring with involution \(*\), \(L\ne \{0\}\) be a \(*\)-Lie ideal of \(R\). An additive mapping \(d:R\rightarrow R\) is called an \((\alpha ,\beta )\)-derivation of \(R\) such that \(d(xy)=d(x)\alpha (y)+\beta (x)d(y)\). In the present paper, we shall show that when \(L\) satisfies any of several identities involving \(d\), then \(L\) is central.     

Copolyesteramides: synthesis and kinetic analysis

The synthesis of copolyesteramides using para-acetamido benzoic acid (PABA) and polyethylene terephthalate (PET) by melt polymerization has been studied in detail. The performance of three transesterification catalysts are assessed for three different initial compositions, PABA 60 mol%/PET 40%, PABA 50 mol%/PET 50% and PABA 40 mol%/PET 60%. The polycondensations are found to obey second order kinetics, irrespective of whether the reaction was catalysed or not. The mechanism of initial stage polymerization kinetics of the copolymers has been fully explained.It is suggested that acetic acid is evolved only by the homopolymerization of PABA and that the insertion of a monomer of homopolymer of PABA into PET does not yield any acetic acid. A set of differential equations containing three different rate constants, k₁ for homopolymerization of PABA, k₂ for PET reaction with dimer of PABA and k₃ for PABA reaction with copolymer of PABA and PET has been developed and numerically solved, to study the initial stage kinetics. The computed values of acetic acid are compared with the experimentally collected amount and the three rate constants are optimized using a differential algebraic optimization technique. The present model represents the data with an acceptable accuracy with an average % error of less than 5% between experimental and computed values for the entire experimental range. The correlation coefficient values range between 0.988 and 0.999.Differential scanning analysis of the copolyestermides indicates that 40 mol% PABA and 60% PET had the highest enthalpy values of the order of 18 kJ/mol. It is found that within the copolyesteramide series the degree of crystallinity increased with the increase of PET contents in the feed mixture to the batch reactor.     

Experimental Study of Effect of Temperature Variations on the Impedance Signature of PZT Sensors for Fatigue Crack Detection

Structural health monitoring (SHM) is recognized as an efficient tool to interpret the reliability of a wide variety of infrastructures. To identify the structural abnormality by utilizing the electromechanical coupling property of piezoelectric transducers, the electromechanical impedance (EMI) approach is preferred. However, in real-time SHM applications, the monitored structure is exposed to several varying environmental and operating conditions (EOCs). The previous study has recognized the temperature variations as one of the serious EOCs that affect the optimal performance of the damage inspection process. In this framework, an experimental setup is developed in current research to identify the presence of fatigue crack in stainless steel (304) beam using EMI approach and estimate the effect of temperature variations on the electrical impedance of the piezoelectric sensors. A regular series of experiments are executed in a controlled temperature environment (25°C–160°C) using 202 V1 Constant Temperature Drying Oven Chamber (Q/TBXR20-2005). It has been observed that the dielectric constant ε₃₃^T which is recognized as the temperature-dependent constant of PZT sensor has sufficiently influenced the electrical impedance signature. Moreover, the effective frequency shift (EFS) approach is optimized in term of significant temperature compensation for the current impedance signature of PZT sensor relative to the reference signature at the extended frequency bandwidth of the developed measurement system with better outcomes as compared to the previous literature work. Hence, the current study also deals efficiently with the critical issue of the width of the frequency band for temperature compensation based on the frequency shift in SHM. The results of the experimental study demonstrate that the proposed methodology is qualified for the damage inspection in real-time monitoring applications under the temperature variations. It is capable to exclude one of the major reasons of false fault diagnosis by compensating the consequence of elevated temperature at extended frequency bandwidth in SHM.     

Living fungal hyphae-templated porous gold microwires using nanoparticles as building blocks

Abstract  

A simple and environmentally benign green method is reported to decorate growing fungal hyphae with high loading of gold nanoparticles, which were initially produced using aqueous tea extract as a sole reducing/stabilizing agent. Inoculation of fungal spores in aqueous suspension of nanoparticles led to the growth of intensely red-coloured fungal hyphae due to the accumulation of gold nanoparticles. Heat treatment of these hybrid materials led to the formation of porous gold microwires. This report is thus an interesting example of using green and sustainable approach to produce nanostructured materials which have potential applications in catalysis, sensing and electronics.     

A sunlight-induced method for rapid biosynthesis of silver nanoparticles using an <Emphasis Type="Italic">Andrachnea chordifolia</Emphasis> ethanol extract

In this study a sunlight-induced method for rapid synthesis of silver nanoparticles using an ethanol extract of Andrachnea chordifolia is described. The silver nitrate solutions (1 mM) containing the ethanol extract of Andrachnea chordifolia were irradiated by both sunlight radiation and by sunlight radiation passed through different colored filters (red, yellow or green). The smallest size of silver nanoparticles was obtained when a silver ion solution was irradiated for 5 minutes by direct sunlight radiation. Further examination of the shape and size and of the surface chemistry of these biogenic silver nanoparticles, which were prepared under sunlight radiation, was carried out using transmission electron microscopy and infrared spectroscopy, respectively. Transmission electron microscopy images show spherical particles with an average size of 3.4 nm. Hydroxyl residues were also detected on the surface of these biogenic silver nanoparticles fabricated using plant extract of Andrachnea chordifolia under sunlight radiation. Our study on the reduction of silver ions by this plant extract in darkness shows that the synthesis process can take place under dark conditions at much longer incubations (48 hours). Larger silver polydispersed nanoparticles ranging in size from 3 to 30 nm were obtained when the silver ions were treated with the ethanol extract of Andrachnea chordifolia under dark conditions for 48 hours.