Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow

Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996     

Equilibrium distributions of stochastic networks without detailed balance

We present results for the determination of the equilibrium microstate probability distribution of a class of strongly interacting systems obeying stochastic dynamics but without the necessity of detailed balance. The specific case of Ising systems is highlighted, with applications to non-symmetric synaptic neural networks and more general recurrent Boolean networks.     

Substitution of calcium by strontium within selected calcium phosphates

Sr incorporation in the molecules of amorphous calcium phosphate, apatitic tricalcium phosphate, hydroxyapatite, octacalcium phosphate and dicalcium phosphate dihydrate was investigated. The concentration of Sr ranged from 225 to 1010 μ g / g, i.e. it overlapped with the physiological range of Sr concentrations in human bone. The leading experimental technique was extended X-ray absorption fine structure (EXAFS) at the Sr K edge. Results of these studies demonstrated the following: (1) Sr incorporation in the calcium phosphates is compound-dependent, (2) the coordination of incorporated Sr atoms in the Ca-P molecules is similar to that of Ca atoms, but interatomic distances are ≈0.015 nm larger, (3) in apatitic tricalcium phosphate, hydroxyapatite and octacalcium phosphate lattices Sr atoms may occupy selected Ca sites, which was not the case for dicalcium phosphate dihydrate, (4) in the apatite lattice Sr atoms are coordinated by 6 PO₄ tetrahedrals and (5) EXAFS spectra at the K edge of the incorporated Sr may be used to distinguish the structures of amorphous calcium phosphate, dicalcium phosphate dihydrate as well as apatite and its derivatives (apatitic tricalcium phosphate, octacalcium phosphate).     

Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

Investigation of the stability of metal species with respect to liquid chromatographic separations

Summary For accurate speciation analyses it is important to know the stability of the respective species, especially in the case of metal complexes. Factors affecting the chromatographic stability of such metal species are investigated. By using thermodynamic models for complex formation and chromatographic retention equilibria the influence of species concentration, stoichiometry and excess of ligand is calculated and compared with experimental results for iron complexes (lactate, gluconate and citrate species). Iron citrate is the only species, that is chromatographed as 1:2 complex (metal: ligand), while iron lactate and gluconate are transformed to 1:1 species. Problems resulting from the coelution of different species are discussed.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Matrix effects in the determination of butyltin compounds in environmental samples by GC AA after hydride generation

Experiments for the determination of mono-, di and tri-butyltin (MBT, DBT and TBT) by hydride generation/gas chromatography/atomic absorption spectrometry in various matrices (sediment, suspended matter, mussel, algae and water) have revealed that poor butyltin recoveries are obtained in sediments displaying high sulphur and hydrocarbon contents; very poor recoveries were also observed for TBT in sediments with high chlorophyll pigment contents as well as in algal samples. It was however not clear whether the hydride generatin was inhibited by these infering compounds, as was previously assumed in the case of hydrocarbons, or whether interferences affected the atomization rate. Further studies were performed to solve this problem in order to validate this method in the case of analyses of, for example, oil-contaminated sediment and algae. This paper presents the results obtained. It is concluded here that the poor recoveries were due to an inhibition of hydride generation rather than to interference at the atomization stage.     

TLC-screening of important pharmaceutical substances using fluorescence detection

Summary Observation of fluorescence reactions on TLC plates is a valuable additional tool within the scope of screening procedures for many toxicologically relevant substances commonly encountered in clinical- and forensic-toxicological analysis. The reactions are based on native fluorescence without any treatment and on reactions obtained with an approved derivatization procedure. Due to the enormous sensitivity of the fluorescence detection, the method is also applicable to very low concentrations and small amounts of biological materials. The procedures described in this article have proven their high pragmatic usefulness in many practical cases.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday