A finite element formulation for laminar flow of a fluid with microstructure

A finite element formulation for the steady laminar flow of an incompressible fluid with microstructure has been developed. The particular fluids considered are commonly known as micropolar fluids, in which case suspended particulate microstructures are modelled by an ‘extended’ continuum formulation. The particle microspin is a new kinematic variable which is independent of the classical vorticity vector and thereby allows relative rotation between particles and the surrounding fluid. This formulation also gives rise to couple stresses in addition to classical force or traction stresses. The finite element formulation utilizes a variational approach and imposes conservation of mass through a penalty function. A general boundary condition for microspin has been incorporated whereby microspin at a solid boundary is constrained to be proportional to the fluid vorticity. The proportionality constant in this case can vary from zero to unity. Sample solutions are presented for fully developed flow through a straight tube and compared with an analytical solution. Results are also generated for flow through a constricted tube and compared with a Newtonian fluid solution.     

Effects of recombinant human erythropoietin on the haemopoietic bone marrow monitored by magnetic resonance spectroscopy in patients with end-stage renal disease

Volume selective magnetic resonance (MR) proton spectroscopy was used to investigate changes in the haemopoietic bone marrow in patients with end-stage renal disease undergoing treatment with recombinant human erythropoietin (rHuEPO). Significant changes could be detected in the spectra 14 days after the beginning of treatment, before any response was seen in the haemoglobin concentration of peripheral blood. The spectral changes indicate an alteration in cellular composition of haemopoietic bone marrow with an increase in the amount of haemopoietic active tissue. One patient showed a major change in the spectrum four days after treatment began, indicating that MR spectroscopy may detect early changes in the cellular composition of the bone marrow. This noninvasive method may be useful in evaluating treatment effects of recombinant human haemopoietic growth factors in the bone marrow, as well as investigating bone marrow response from different modes of rHuEPO administration.     

A versatile spectrometer for secondary x-ray fluorescence excitation

Inexpensive research equipment for secondary x-ray fluorescence excitation is described. The primary beam from a high-powered x-ray tube is collimated onto the targets, six of which may be easily and safely interchanged. A collimator system ensures that the detector receives radiation from well defined areas of the sample. The geometry minimizes radiation from Compton scattering, the twice-scattered continuum radiation from the x-ray tube, and the characteristic lines from the secondary target. The unit is designed for use with standard x-ray tubes and generators, and is part of an energy-dispersive spectrometer used for multielement analysis. The performance of the system with a variety of samples is described.     

Pyridinethiones—V : Spectroscopic investigation and electronic structure of 3-formyl-2(1H)-pyridones, -thiones and -selones

The 3-formyl-2(1$\text{H}$)-pyridone, -thione and -selone systems have been investigated by UV photoelectron, UV-visible, ¹H and ¹³C NMR spectroscopy. It is demonstrated that the electronic build-up of these systems as derived from the spectroscopic data may be correlated with their chemical behaviour through application of the perturbation model for chemical reactivity.     

Kinetics and mechanism of the reaction between dibenzyl triselenocarbonate and oxygen-bases

The base-induced solvolysis of dibenzyl triselenocarbonate in DMSO/water (4:1) has been studied by UV spectrophotometric measurements under pseudo-first order conditions, using KOH, Me₄NOH, Bu₄ⁿNOH and Bu₄ⁿNHCO₃ as bases. The reaction is first order with respect to the substrate as well as to the base. Rate constants and activation parameters for the four bases indicate that the rate determining step is the nucleophilic attack by the base, as an ionic couple, on the substrate. Fast reactions, due to strong nucleophilic selenolate species, may follow this slow step; a tentative mechanism is proposed on the basis of experimental evidence.     

In vivo estimation of relaxation processes in benign hyperplasia and carcinoma of the prostate gland by magnetic resonance imaging

Tissue characterization for separating malignant from benign tissue is a clinically very important potential of magnetic resonance imaging (MRI). In this study quantitative determination of T1- and T2-relaxation processes was accomplished in five healthy volunteers, 10 patients with benign hyperplasia of the prostate gland and eight patients with prostatic carcinoma. Histological verification was obtained in all the patients. The measurements were performed on a wholebody MR-scanner operating at 1.5 T using six inversion recovery sequences (TR = 4000 msec) for T1-determination and a 32 spin-echo sequence (TR = 3000 or 2000 msec) for T2-estimation. The T1-relaxation curves all appeared monoexponential, whereas the T2-curves in most cases showed a multiexponential behaviour. A considerable overlap of the relaxation curves was seen. Consequently, we found no statistically significant differences between the T1- or the T2-relaxation times of the three groups investigated. It is concluded that tissue characterization based on relaxation time measurements with MRI does not seem to have a clinically useful role in prostatic disease.     

Ab initio ground state phenylacetylene-argon intermolecular potential energy surface and rovibrational spectrum

We evaluate the phenylacetylene-argon intermolecular potential energy surface by fitting a representative number of ab initio interaction energies to an analytic function. These energies are calculated at a grid of intermolecular geometries, using the CCSD(T) method and the aug-cc-pVDZ basis set extended with a series of 3s3p2d1f1g midbond functions. The potential is characterized by two equivalent global minima where the Ar atom is located above and below the phenylacetylene plane at a distance of 3.5781 A? from the molecular center of mass and at an angle of 9.08° with respect to the axis perpendicular to the phenylacetylene plane and containing the center of mass. The calculated interaction energy is -418.9 cm(-1). To check further the potential, we obtain the rovibrational spectrum of the complex and the results are compared to the available experimental data.     

Some properties of algebras of real-valued measurable functions

Measures and measurable functions are used primarily as tools for carrying out various calculations to increase our knowledge. We learn how to combine them in various ways by studying real analysis; a very useful subject on which very much has been written. In this paper, we regard measurable functions as algebras of real-valued functions (or equivalence classes of them) on a set or topological space under point-wise addition, multiplication, or lattice operations and our techniques resemble closely those used to study algebras of continuous functions. This is done by examining a number of explicit examples including Borel and Lebesgue measures and measurable functions.     

Computer extended series solution for unsteady flow in a contracting or expanding pipe

Unsteady flow in a semi-infinite contracting or expanding pipeis reinvestigated using long series analysis. The proposed seriesmethod is useful in analysing the problem for a moderately largeconstant ( = aa/, where a = a(t), the radius of the pipe isa function of time, a(t) is the velocity of the wall, and iskinematic viscosity). For positive values of (expansion ofthe pipe) accuracy of the series representing shear stress andpressure gradient is increased from = 2.89 to = 6.0 by extractingthe singularity followed by completion of the series. For negativevalues of (contraction of the pipe), we revert the series whichresults into the increase of the region of validity of the transposedseries from = -25.0 to = -2.89. Later we use Padé approximantsfor summing them. Also, the asymptotic solution for large valuesof is obtained and it agrees closely with pure numerical valuesof shear stress at the wall and pressure gradient.     

Preparation, properties, and reactivities of unprecedented oxo-sulfido Nb(IV) aqua ions and crystal structure of (Me2NH2)6[Nb5(mu3-S)2(mu3-O)2(mu2-O)2(NCS)14].3.5H2O

By treatment of Zn-reduced ethanolic solutions of NbCl5 with HCl in the presence of sulfide followed by cation-exchange chromatography, two oxo-sulfido niobium aqua ions, the red [Nb4(mu4-S)(mu2-O)5(H2O)10]4+ and the yellow-brown [Nb5(mu3-S)2(mu3-O)2(mu2-O)2(H2O)14]8+, were isolated. Both readily form their respective thiocyanate complexes, for which the structure for the former has been previously reported. Brown crystals of (Me2NH2)6[Nb5S2O4(NCS)14].3.5H2O (1) were isolated in the case of the latter, and the structure was determined by X-ray crystallography (space group: a = 15.4018(5) A, b = 21.1932(8) A, c = 22.0487(8) A, alpha=gamma = 90 degrees , beta = 103.4590(10) degrees , and R(1) = 0.0659). An unprecedented pentanuclear Nb5S2O48+ core is revealed in which short Nb-Nb distances (2.7995(8)-2.9111(8) A) are consistent with metal-metal bonding. A stopped-flow kinetic study of the 1:1 equilibration of NCS- with [Nb4(mu4-S)(mu2-O)5(H2O)10]4+ has been carried out. Equilibration rate constants are independent of [H(+)] in the range investigated (0.5-2.0 M) and at 25 degrees C; kf= 9.5 M(-1) s(-1), kaq = 2.6 x 10(-2) s(-1), and K = 365 M1). Conditions with first NCS- and then [Nb4(mu4-S)(mu2-O)5(H2O)10]4+ in excess revealed a statistical factor of 4, suggesting the presence of four kinetically equivalent Nb atoms. Attempts to study the 1:1 substitution of NCS- with [Nb5(mu3-S)2(mu3-O)2(mu2-O)2(H2O)14]8+ showed signs of saturation kinetics. Quantum chemical calculations using the density functional theory (DFT) approach were performed on both the Nb4O5S4+ and Nb5O4S28+ naked clusters. The highest occupied and lowest unoccupied molecular orbitals have dominant Nb(4d) character. The HOMO for Nb4O5S4+ is a nondegenerate fully filled MO, whereas for Nb5O4S28+, it is a nondegenerate partially filled MO with one unpaired electron. EPR spectroscopy on [Nb5(mu3-S)2(mu3-O)2(mu2-O)2(H2O)14]8+ shows that the molecule has total anisotropy (C2v), with all three tensors, gx= 2.399, gy= 1.975, and gz= 1.531, resolved. No hyperfine interaction expected from the nuclear moment of I = 9/2 for 93Nb was observed.