Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

The multigrid method is one of the most efficient techniques for convergence acceleration of iterative methods. In this method, a grid coarsening algorithm is required. Here, an agglomeration scheme is introduced, which is applicable in both cell‐center and cell‐vertex 2 and 3D discretizations. A new implicit formulation is presented, which results in better computation efficiency, when added to the multigrid scheme. A few simple procedures are also proposed and applied to provide even higher convergence acceleration. The Euler equations are solved on an unstructured grid around standard transonic configurations to validate the algorithm and to assess its superiority to conventional explicit agglomeration schemes. The scheme is applied to 2 and 3D test cases using both cell‐center and cell‐vertex discretizations. Copyright © 2009 John Wiley & Sons, Ltd.     

Totally positive extensions and weakly isotropic forms

The aim of this article is to analyse a new field invariant, relevant to (formally) real fields, defined as the supremum of the dimensions of all anisotropic, weakly isotropic quadratic forms over the field. This invariant is compared with the classical u-invariant and with the Hasse number. Furthermore, in order to be able to obtain examples of fields where these invariants take certain prescribed values, totally positive field extensions are studied.     

Effects of anionic additives on the rheological behavior of aqueous calcium montmorillonite suspensions

Three different experimental measurements, namely, rheology, particle sizing, and x-ray diffraction (XRD), were used to study the effect of anionic additives on the properties of bentonite suspensions. The three additives were sodium carboxymethylcellulose, xanthan gum, and sodium dodecyl sulfate. Flow curves were obtained from shear stress–shear rate measurements, and the viscoelastic properties were determined from oscillatory and transient measurements. Mineralogical data were evaluated by XRD and the particle size analysis performed by light scattering technique. The presence of the surfactant modifies the face-to-face interactions and yields changes of the mixtures rheological behavior at low deformation rates. Polymers act by coating each clay particle and prevent their agglomeration. Therefore, the additives are responsible for the mechanisms of destructuration and structure reorganization as well as the mixtures viscous and viscoelastic behavior.     

S-Storage Operators

In 1990, J. L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In the present paper we define for every λ-term S which realizes the successor function on Church integers the notion of S-storage operator. We prove that every storage operator is an S-storage operator. But the converse is not always true.     

Anisotropic Lithium Ion Conductivity in Single‐Ion Diblock Copolymer Electrolyte Thin Films

Well‐defined single‐ion diblock copolymers consisting of a Li‐ion conductive poly(styrenesulfonyllithium(trifluoromethylsulfonyl)imide) (PSLiTFSI) block associated with a glassy polystyrene (PS) block have been synthesized via reversible addition fragmentation chain transfer polymerization. Conductivity anisotropy ratio up to 1000 has been achieved from PS‐b‐PSLiTFSI thin films by comparing Li‐ion conductivities of out‐of‐plane (aligned) and in‐plane (antialigned) cylinder morphologies at 40 °C. Blending of PS‐b‐PSLiTFSI thin films with poly(ethylene oxide) homopolymer (hPEO) enables a substantial improvement of Li‐ion transport within aligned cylindrical domains, since hPEO, preferentially located in PSLiTFSI domains, is an excellent lithium‐solvating material. Results are also compared with unblended and blended PSLiTFSI homopolymer (hPSLiTFSI) homologues, which reveals that ionic conductivity is improved when thin films are nanostructured.

     

Acoustics and dynamics of coaxial interacting vortex rings

Using a contour dynamics method for inviscid axisymmetric flow we examine the effects of core deformation on the dynamics and acoustic signatures of coaxial interacting vortex rings. Both “passage” and “collision” (head-on) interactions are studied for initially identical vortices. Good correspondence with experiments is obtained. A simple model which retains only the elliptic degree of freedom in the core shape is used to explain some of the calculated features.     

Determination of Imidacloprid in Tomato Grown in Greenhouse Based on Copper(II) Phthalocyanine Modified Carbon Ceramic Electrode by Differential Pulse Voltammetry

A new sol‐gel derived electrocatalytic carbon ceramic electrode was prepared by incorporating copper(II) phthalocyanine (CuPc) in a carbon ceramic network. This electrode was used as a sensitive electrochemical sensor for determination of the insecticide Imidacloprid (1‐(6‐chloro‐3‐pyridylmethyl)‐N‐nitro‐imidazolidin‐2‐ylideneamine) by differential pulse voltammetry (DPV). The resulting modified electrode exhibits a cathodic peak potential shifted positively and an increasing in cathodic peak current in comparison with unmodified electrode. The redox properties of this modified electrode at various pH values and CuPc percentage were investigated. The catalytic current obtained from differential pulse voltammetry is linearly dependent on Imidacloprid concentration over the two linear ranges of 0.67‐17 μM and 17‐93 μM with correlation coefficient of R² = 0.9999 and R² = 0.990, respectively. The detection limit for Imidacloprid was found to be 0.28 μM according to lower linear range. Possible interferences from several common pesticides were also evaluated. The inherent stability, high sensitivity, low detection limit and low cost for each preparation are advantages of this sensor. Determination of Imidacloprid in commercial formulation and residual Imidacloprid in tomato grown in greenhouse (protected cultivation) was also conducted. The results obtained from commercial formulation were completely consistent with those obtained through the standard high‐performance liquid chromatography (HPLC) method.