SYNTHESIS, SOLUTION DYNAMICS AND X-RAY CRYSTAL-STRUCTURES OF NEODYMIUM-YLIDE COMPLEXES, [(C(5)H(4)R)(3)NDCH2P(ME)PH(2)] (R=H, BU(T))

The interaction of [(C(5)H(4)R)(2)NdCl.2LiCl] (R = H, Bu(t)) with one equivalent of Li[(CH2)(CH2)PPh(2)] in refluxing tetrahydrofuran gave the purplish-blue complex [(C(5)H(4)R)(3)NdCH2P(Me)Ph(2)] in 50% yield. The compounds have been fully characterized by analytical, spectroscopic and X-ray diffraction methods. Variable temperature P-31{H-1} NMR spectroscopy indicated the existence of the following equilibrium: [(C(5)H(4)R)(3)NdCH2P(Me)Ph(2)] + THF reversible arrow (C(5)H(4)R)(3)Nd(THF) + CH2=P(Me)Ph(2). At room temperature, the exchange between the coordinated and free ylide ligand is slow on the NMR time scale.

Electrophoretic migration behavior of DNA fragments in polymer solution

A newly developed polymer coil shrinking theory is described and compared with the existing entangled solution theory to explain electrophoretic migration behaviour of DNA in hydroxypropylmethylcellulose (HPMC) polymer solution in buffer containing 100 mM tris(hydroxymethyl)aminomethane 100 mM boric acid, 2 mm ethylenediaminetetraacetic acid at pH 8.3. The polymer coil shrinking theory gave a better model to explain the results obtained. The polymer coil shrinking concentration, C-s, was found to be 0.305% and the uniform entangled concentration, C+, 0.806%. The existence of three regions (the dilute, semidilute, and concentrated solution) at different polymer concentrations enables a better understanding of the system to guide the selection of the best conditions to separate DNA fragments. For separating large fragments (700/800 bp), dilute solutions (HPMC < 0.3%) should be used to achieve a short migration time (10 min). For small fragments (200/300 bp), concentrated solutions are preferred to obtain constant resolution and uniform separation. The best resolution is 0.6% HPMC due to a combined interaction of the polymer coils and the entangled structure. The possibility of DNA separation in semidilute solution is often neglected and the present results indicate that this region has a promising potential for analytical separation of DNA fragments.

PHOTOPERTURBATION OF THE (1)A-][-(5)T SPIN EQUILIBRIUM IN AN IRON(II) COMPLEX IN SOLUTION VIA LIGAND-FIELD EXCITATION

Variable-temperature magnetic susceptibility measurements in the solid state of the bis complex of tris(1-pyrazolyl)-methane with Fe(II), [Fe(tpm)2](ClO4)2, suggest the existence of singlet-quintet spin crossover with the singlet isomer largely favored at room temperature. In acetonitrile solution, measurement of the absorption spectrum as a function of temperature reveals a spin equilibrium with the quintet population varying from ca. 6% at 233 K to ca. 30% at 295 K. When the complex in solution is irradiated with a laser pulse at wavelengths within the ligand field absorption band of the singlet isomer, ground-state depletion occurs within the pulse duration followed by fast recovery to the original absorbance level with a time constant of 25 +/- 5ns. The recovery time is virtually independent of temperature over the range +23 to -43-degrees-C, but the signal:noise ratio of the transient signals increases with decreasing temperature. The effect was observable at several monitoring wavelengths spanning the LF and MLCT absorption regions of the complex but only when the irradiation wavelength fell within the LF absorption region. Irradiation within the MLCT band produced no effect other than that of laser pulse scatter. The observations are interpreted in terms of photoperturbation of the singlet-quintet spin state equilibrium, which in this case occurs solely through excitation in the ligand field absorption region of the complex and is the first reported instance of this type for a spin-crossover complex in solution.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

Aqueous solution behavior of thermosensitive (N-isopropylacrylamide-acrylic acid-ethyl methacrylate) terpolymers

A series of N-isopropylacrylamide (NIPAM)-acrylic acid-ethyl methacrylate terpolymers with varied monomer compositions was prepared by radical polymerization. The solution behavior of these polymers was studied in dilute aqueous solution using spectrophotometry, fluorescence spectroscopy and high-sensitivity differential scanning calorimetry. The results obtained revealed that the lower critical solution temperatures depend strongly on the copolymer composition, solution pH and ionic strength. At a high pH, the ionization of acrylic acid (AA) units leads to an increase in solution cloud points (T-c). Solutions of polymers containing 10% or less of AA display a constant T-c for pH above 5.5, with 15% there is a continuous increase in T-c with pH and, for higher AA contents, no clouding was observed within the studied temperature range. Fluorescence probe studies were conducted by following the I (1)/I (3) ratio of pyrene vibronic bands and the emission of anilinonaphtalene sulfonic acid, sodium salt (ANS), both approaches revealing the existence of hydrophobic domains for polymers with higher ethyl methacrylate content at temperatures lower than T-c, suggesting some extent of aggregation and/or a coil-to-globule transition. Scanning calorimetry measurements showed an endothermic transition at temperatures agreeing with the previously detected cloud points. Moreover, the transition curves became broader and with a smaller transition enthalpy, as both the AA content and the solution pH were increased. These broader transitions were interpreted to be the result of a wider molecular distribution upon polymer ionization, hence, displaying varied solution properties. The decrease in transition enthalpy was rationalized as a consequence of reminiscent hydration of NIPAM units, even after phase separation, owing to the presence of electric charges along the polymer chain.

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The subdomain structure of human serum albumin in solution under different pH conditions studied by small angle X-ray scattering

Small-angle X-ray scattering (SAXS) was used to study structural characteristics of human serum albumin (HSA) in solution under different pH conditions. Guinier analysis of SAXS results yielded values of the molecular radius of gyration ranging from 26.7 Å to 34.5 Å for pH varying from 2.5 to 7.0. This suggests the existence of significant differences in the overall shape of the molecule at different pH. Molecular models based on subdomains with different spatial configurations were proposed. The distance distribution functions associated with these models were calculated and compared with those determined from the experimental SAXS intensity functions. The conclusion of this SAXS study is that the arrangement of molecular subdomains is clearly pH dependent; the molecule adopting more or less compact configuration for different pH conditions. The conclusions of this systematic study on the modification in molecular shape of HSA as a response to pH changes is consistent with those of previous investigations performed for particular pH conditions.

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

The Effect of the Cu:Fe''' Ratio Upon the Current Efficiency in the Electrolysis of a Copper Sulfate Solution Containing Iron Sulfate

It is a well-known fact that, in the electrolysis of a CuSO4 solution containing iron sulfate, using insoluble anodes, with the depletion of copper, the point is finally reached where the current efficiency becomes zero. This decrease in current efficiency is due to the oxidation of the ferrous sulfate to the ferric condition at the anode, by the oxygen liberated. The resulting ferric sulfate diffuses over to the cathode and there dissolves copper from the cathode according to the chemical equation Cu + Fe2 (SO4)3 = CuSO4 + 2FeSO4. This copper, which has been deposited at the cathode by the electric current, is thus redissolved by the Fe2(SO4)3. The solution of the copper causes at the same time a formation of FeSO4 which in turn diffuses over to the anode and is there oxidized to Fe2(SO4)3; and so the cycle continues, using electric current without rendering useful work. E. H. Larison has noted that a definite amount of ferric salts must be reduced to the ferrous condition before all the copper will remain on the cathode; he does not state, however, just what this point is. L. Addicks has plotted the relation between current efficiency and ferric sulphate content. The existence of the results scattered the points more or less, although the decrease in current efficiency with increased ferric sulphate content is clearly indicated. E. T.Kern has likewise noted that the smaller the amount of copper in the solution, the greater is the reduction of current efficiency. In this work, therefore, it was desired to determine what amount of ferric iron was permissible in a copper sulfate solution of definite concentration before the current efficiency would drop to zero, and what, if any, was the effect of definite Cu:Fe’’’ratio upon the current efficiency of the electrolysis.

Characterization of the hairpin vortex solution in plane Couette flow

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

Exploration of a simple, low cost, micro gas turbine recuperator solution for a domestic combined heat and power unit

For micro gas turbines (MGT) of around 1 kW or less, a commercially suitable recuperator must be used to produce a thermal efficiency suitable for use in UK Domestic Combined Heat and Power (DCHP). This paper uses computational fluid dynamics (CFD) to investigate a recuperator design based on a helically coiled pipe-in-pipe heat exchanger which utilises industry standard stock materials and manufacturing techniques. A suitable mesh strategy was established by geometrically modelling separate boundary layer volumes to satisfy y + near wall conditions. A higher mesh density was then used to resolve the core flow. A coiled pipe-in-pipe recuperator solution for a 1 kW MGT DCHP unit was established within the volume envelope suitable for a domestic wall-hung boiler. Using a low MGT pressure ratio (necessitated by using a turbocharger oil cooled journal bearing platform) meant unit size was larger than anticipated. Raising MGT pressure ratio from 2.15 to 2.5 could significantly reduce recuperator volume. Dimensional reasoning confirmed the existence of optimum pipe diameter combinations for minimum pressure drop. Maximum heat exchanger effectiveness was achieved using an optimum or minimum pressure drop pipe combination with large pipe length as opposed to a large pressure drop pipe combination with shorter pipe length. © 2011 Elsevier Ltd. All rights reserved.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

A Raman spectroscopic study of the uranyl mineral rutherfordine – revisited

The molecular structure of the uranyl mineral rutherfordine has been investigated by the measurement of the NIR and Raman spectra and complemented with infrared spectra including their interpretation. The spectra of the rutherfordine show the presence of both water and hydroxyl units in the structure as evidenced by IR bands at 3562 and 3465 cm-1 (OH) and 3343, 3185 and 2980 cm-1 (H2O). Raman spectra show the presence of four sharp bands at 3511, 3460, 3329 and 3151 cm-1. Corresponding molecular water bending vibrations were only observed in both Raman and infrared spectra of one of two studied rutherfordine samples. The second rutherfordine sample studied contained only hydroxyl ions in the equatorial uranyl plane and did not contain any molecular water. The infrared spectra of the (CO3)2- units in the antisymmetric stretching region show complexity with three sets of carbonate bands observed. This combined with the observation of multiple bands in the (CO3)2- bending region in both the Raman and IR spectra suggests that both monodentate and bidentate (CO3)2- units may be present in the structure. This cannot be exactly proved and inferred from the spectra; however, it is in accordance with the X-ray crystallographic studies. Complexity is also observed in the IR spectra of (UO2)2+ antisymmetric stretching region and is attributed to non-identical UO bonds. U-O bond lengths were calculated using wavenumbers of the 3 and 1 (UO2)2+ and compared with data from X-ray single crystal structure analysis of rutherfordine. Existence of solid solution having a general formula (UO2)(CO3)1-x(OH)2x.yH2O ( x, y  0) is supported in the crystal structure of rutherfordine samples studied.

A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.