Compressibility effects on the dynamic characteristics of gas lubricated mechanical components

The present Note deals with the effects of compressibility on the linearized dynamic characteristics of gas lubricated mechanical components (journal and thrust bearings). Although the effect of compressibility on the static characteristics is well known, its influence on the dynamic characteristics is still not clearly understood. The present Note uses Lubrication's simplest model problems (the 1D slider) to qualitatively describe this effect. An analytic solution obtained for the parallel 1D slider depicts the variation of stiffness and damping with the excitation frequency and shows that this nonlinearity must be taken into account for squeeze number larger than 1. A convenient way of handling this nonlinearity in a dynamic system is described for an aerodynamic thrust bearing. To cite this article: M. Arghir, P. Matta, C. R. Mecanique 337 (2009).     

Crystallization study of sol-gel un-doped and Pd-doped TiO2 materials

Sol-gel nanostructured titania materials have been reported to have applications in areas ranging from optics via solar energy to gas sensors. In order to enhance the photocatalytic activity, there are many studies regarding the doping of titanium dioxide (TiO₂) material with either non-metals (S, C, N, P) or metals (Ag, Pt, Nd, Fe). The present work has studied some un-doped and Pd-doped sol-gel TiO₂ materials (films and gels), with various surface morphologies and structures, obtained by simultaneous gelation of both precursors Ti(OEt)₄ and Pd(acac)₂. Their structural evaluation and crystallization behavior with thermal treatment were followed by DTA/TG analysis, infrared (IR) spectroscopy, Fourier transform infrared (FTIR), spectroellipsometry (SE), X-ray diffraction (XRD) and atomic force microscope (AFM). The influence of Pd on TiO₂ crystallization for both supported and un-supported materials was studied (lattice parameters, crystallite sizes, internal microstrains). The changes in the optical properties of the TiO₂-based vitreous materials were correlated with the changes of the structure. The hydrophilic properties of the films were also connected with their structure, composition and surface morphology.     

Induced birefringence of rubbed and stretched polyvinyl alcohol foils as alignment layers for nematic molecules

Some optical properties of poly (vinyl alcohol) (PVA) films are investigated prior and after the rubbing and stretching of the samples. Birefringence of the prepared foils is enhanced as their stretching degree and rubbing become larger. These processing factors are also affecting the values of the ordinary and extraordinary refractive indices. The induced anisotropy in PVA foils is evidenced in the morphological characteristics observed by optical microscopy. The spreading and adhesion behaviors of a nematic liquid crystal on PVA foils are analyzed by means of contact angle measurements. Preliminary testing of the nematic on the PVA films revealed significant variations in transmitted light intensity during sample rotation under crossed polarizers. The high contrast between dark and bright patterns is indicative of uniform and homogenous alignment of nematic on the rubbed and stretched PVA foils.     

On the Stable Morse number of a Closed Manifold

This paper provides examples of closed manifolds having a Morsenumber different from the stable Morse number. 2000 MathematicsSubject Classification 57Q10, 20F05.     

Catalytic determination of Pb(II) in the presence of Cu(II)

A kinetic method is presented to determine micro-molar amounts of Pb(II) from various river and wastewater samples, in the presence of trace copper. The procedure is based on the catalytic effect of both species on the oxidation of mercaptosuccinic acid by chromate in acidic media. The extent of the reaction is followed spectrophotometrically at 420 nm and pseudo-first-order rate coefficients of the rate-determining step are determined as a function of catalyst concentrations. The optimum operating conditions (ionic strength, temperature, and concentration of reagents) regarding sensitivity towards lead were established. Interference by several ionic species has been studied. The effect of Fe(III), the only severe interferent, is suppressed by complexation with 1,10-phenantroline. The bi-component calibration model employs an artificial neural network to compute the Pb(II) concentration from a k(obsd) value and the a priori-known Cu(II) concentration of the sample. Working concentration ranges are 20-2160 micro g L(-1) for Pb(II) and 80-650 micro g L(-1) for Cu(II), respectively. Detection limits are 20 micro g L(-1) Pb(II) and 80 micro g L(-1) Cu(II), respectively. The relative standard deviations (3 measurements) for four different testing points are lower than 2.5%. The method was applied to samples of river and wastewater of the mining region of Baia-Mare, Northern Romania. The results were compared to those obtained by an officially standardized AAS method. Good agreement was achieved. The method is inexpensive, fairly rapid, and sensitive. Its working range covers the exact range of concentrations usually encountered in the mentioned geographic area.     

Kinetic catalytic determination of trace Cu(II) in water samples with the thioglycolic/thiolactic acid–chromate reaction

The use of two novel similar indicator reactions as applied to the kinetic determination of Cu(II) in water is investigated. The methods rely on the catalytic effect of the analyte on the oxidation of thioglycolic (TGA) and thiolactic (TLA) acids by chromate in acidic media. The extent of the reactions was followed spectrophotometrically at 345 nm. Pseudo-first-order rate coefficients, k_obsd, were determined as a function of catalyst concentration. Interference of Fe(III) and Pb(II) was suppressed by complexation with pyrophosphate. For the reaction of TGA, a linear regression for k_obsd versus [Cu(II)] was obtained for the entire concentration range considered. Although the plot corresponding to TLA oxidation exhibits a sharp change of slope at approximately 1.8×10^–5 M Cu(II), it can still be described effectively by two linear regressions with different slopes. The reaction of TGA is more sensitive than that of TLA at low Cu(II) concentration. The opposite is true for higher catalyst contents. The detection limits were 65 gL^–1 for TGA and of 80 gL^–1 for TLA oxidation, respectively. The relative standard deviations, of 0.4% for TGA and 1.1% for TLA oxidation, respectively, were obtained for five replicate runs at 1000 g L^–1. Samples of river and wastewater from the mining region of Baia-Mare, Northern Romania were analyzed using the more sensitive reaction of thioglycolic acid. Results were compared to those obtained by the officially standardized methods. Good agreement was obtained, even for an untreated sample. Measurements did not require prior separation of interfering species.     

Invariant Theory for Non-Associative Real Two-Dimensional Algebras and Its Applications

The set ${\mathcal A}$ of all non-associative algebra structures on a fixed 2-dimensional real vector space $A$ is naturally a ${\mbox{\rm GL}}(2,{\mbox{\bf R}})$-module. We compute the ring of ${\mbox{\rm SL}}(2,{\mbox{\bf R}})$-invariants in the ring of polynomial functions, ${\mathcal P}$, on ${\mathcal A}$. We use invariant theory to compute the exact number of nonzero idempotents of an arbitrary 2-dimensional real division algebra. We show that the absolute invariants (i.e.,the ${\mbox{\rm GL}}(2, {\mbox{\bf R}})$-invariants in the field of fractions of ${\mathcal P}$) distinguish the isomorphism classes of 2-dimensional non-associative real division algebras. We show that the (open) set $\Omega^+\subset{\mathcal A}$ of all division algebra structures on $A$ has four connected components. A similar result is proved for another class of regular 2-dimensional real algebras (the principal isotopes of the algebra ${\mbox{\bf R}}\oplus{\mbox{\bf R}}$).