Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Influence of the sample orientation in Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals on the hydrostatic piezoelectric coefficients

The influence of the sample orientation on the effective value of the hydrostatic piezoelectric coefficients d _h ⁽ⁱ⁾ of Sn₂P₂S₆ crystals has been studied. The hydrostatic piezoelectric coefficients d _h ⁽¹⁾ and d′ _h ⁽³⁾ , were measured, d _h ⁽¹⁾ =(244±3) pC/N and d′ _h ⁽³⁾ =(92±1) pC/N. The hydrostatic piezoelectric coefficient d _h ⁽³⁾ for orthogonal axis system was calculated to be d _h ⁽³⁾ =(87±2) pC/N. The, optimal orientation of the sample has been found as (Xy l)−20°-cut. Maximal value of the effective hydrostatic piezoelectric coefficient d _h ⁽¹⁾ equals 260 pC/N. Double rotated samples were also studied. The orientation of the samples insensitive to the pressure has been found. The theoretical mean value of hydrostatic piezoelectric coefficient (d _h ) _mean corresponding to randomly oriented Sn₂P₂S₆ grains in a poled composite has been calculated to be (d _h ) _mean =136 pC/N.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity

We study the solvability and Galerkin approximation of an exterior hyperelastic interface problem arising in plane elasticity. The weak formulation is obtained from an appropriate combination of a mixed finite element approach with a Dirichlet-to-Neumann method. The derivation of our results is based on some tools from nonlinear functional analysis and the Babuska-Brezzi theory for variational problems with constraints.     

Quality assurance for the analytical data of micro elements in food

The micro element content of food is an important quality index due to the action of these elements on human health. In this article, we discuss how to ensure the reliability of analytical data on micro elements in order to truly represent the condition of food. Sampling, treatment of the analytical sample, selection of the analytical method, standard solution, and certified reference material, blank test, calibration of the instrument and equipment, application of the quality control chart, assessment of the final analytical result, and quality assurance system are briefly described. Received: 5 July 2001 Accepted: 19 November 2001     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

Crystal structure and magnetic properties of two new cobalt selenite halides: Co5(SeO3)4X2 (X=Cl, Br)

Two new isostructural cobalt selenite halides Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂ have been synthesized. They crystallize in the triclinic system space group P−1 with the following lattice parameters for Co₅(SeO₃)₄Cl₂: a=6.4935(8) Å, b=7.7288(8) Å, c=7.7443(10) Å, α=66.051(11)°, β=73.610(11)°, γ=81.268(9)°, and Z=1. The crystal structures were solved from single-crystal X-ray data, R1=3.73 and 4.03 for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively. The new compounds are isostructural to Ni₅(SeO₃)₄Br₂.Magnetic susceptibility measurements on oriented single-crystalline samples show anisotropic response in a broad temperature range. The anisotropic susceptibility is quantitatively interpreted within the zero-field splitting schemes for Co²⁺ and Ni²⁺ ions. Sharp low-temperature susceptibility features, at T_N=18 and 20 K for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively, are ascribed to antiferromagnetic ordering in a minority magnetic subsystem. In isostructural Ni₅(SeO₃)₄Br₂ magnetically ordered subsystem represents a majority fraction (T_N=46 K). Nevertheless, anisotropic susceptibility of Ni₅(SeO₃)₄Br₂ is dominated at low temperatures by a minority fraction, subject to single-ion anisotropy effects and increasing population of S_z=0 (singlet) ground state of octahedrally coordinated Ni²⁺.     

Quantification of trace elements in human serum fractions by liquid chromatography and inductively coupled plasma mass spectrometry

On‐line coupling of LC and ICP‐MS has been used for fractionation and detection of species of Cu, Fe, I, Se and Zn in human serum. It has been shown that anion exchange chromatography provided better separation capability (both intra‐ and inter‐element) than size‐exclusion chromatography. The mobile phases for ion exchange chromatography consisted of Tris–HNO₃ buffer and ammonium salt (nitrate, acetate or formate). Formate was found to be the best mobile phase counter ion, enabling good chromatographic separation, and is acceptable for mass spectrometry too. The quantitative evaluation of element concentrations adhering to individual fractions was performed by the peak area normalization method. The repeatability of results ranged from 3 to 15% (depending on the element concentration level) and represented the main part of the result uncertainty. The accuracy of Cu and Zn fraction determinations was confirmed by comparison with the isotope dilution technique. Copyright © 2006 John Wiley & Sons, Ltd.     

新疆野生黑加仑与马林果实的营养成分分析

通过对新疆野生黑加仑和野生马林的脂肪油，8种微量元素，17种氨基酸以及维生素C的含量进行测定得出：黑加仑脂肪油含量为17．9％，马林的脂肪油含量为22．3％，其中，黑加仑脂肪油中，r－亚麻酸的含量为19．02％，而马林中，其含量为9．40％，黑加仑中K，Na,Ca,Cu,Zn,Fe的含量比马林中的含量高，而Mn,Mg元素的含量却比马林含量低；马林的维生素C含量为16．22mg/g，黑加仑的含量为108mg/g，黑加仑的氨基酸的总量为1．63％，马林为1．14％。