Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Determination of total phosphorus and nitrogen in turbid waters by oxidation with alkaline potassium peroxodisulfate and low pressure microwave digestion, autoclave heating or the use of closed vessels in a hot water bath: comparison with Kjeldahl digestion

The evaluation of the use of alkaline peroxodisulfate digestion with low pressure microwave, autoclave or hot water bath heating for the determination of total phosphorus and nitrogen in turbid lake and river waters is described. The efficiency of these digestion procedures were compared to a Kjeldahl digestion procedure with sulphuric acid-potassium sulfate and copper sulfate. The final solution before digestion was 0.045 M in potassium peroxodisulfate and 0.04 M in sodium hydroxide. Procedures were evaluated by the analysis of suspensions of two reference materials, National Institute of Environmental Science, Japan, no. 3 Chlorella and no. 2 pond sediment and natural turbid waters. Best recoveries of phosphorus and nitrogen by microwave heating were obtained when solutions were digested at 95 °C for 40 min. Quantitative recoveries of phosphorus from Chlorella suspensions up to 1000 mg/l were obtained by all three heating procedures, but incomplete recoveries of nitrogen occurred above 20 mg N/l in the digested sample. Good recoveries of phosphorus and nitrogen from suspended sediment suspensions were obtained only from solutions containing <150 mg/l of suspended sediments. Recoveries of phosphorus from phosphorus compounds containing COP and CP bonds added to distilled water were quantitative (94-113%) except for polyphosphates (microwave, 34±8; autoclave, 114±6; water bath, 96±4) and aluminium phosphate (8-23%). Recoveries of nitrogen compounds containing CN bonds added to distilled water were quantitative (94-96%). The analysis of a range of natural turbid water samples by alkaline peroxodisulfate and microwave, autoclave and water bath heating gave similar total phosphorus and nitrogen results. All procedures using alkaline peroxodisulfate underestimate phosphorus concentrations at high suspended sediment concentrations (>150 mg/l) and are only suitable for the analysis of very turbid samples when the turbidity is due to organic matter (algal cells, plant detritus). Underestimation of nitrogen occurs when samples contain more than 20 mg N/l.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an X-ray diffraction study

The effective thickness of ferroelastic twin-walls (W-walls) in Pb₃(PO₄)₂ at room temperature (≈ 0.7 T _c ) was determined by X-ray diffraction. The diffraction profiles were analysed using a wall profile e=eotanh x/w where W is the effective wall thickness including the effects of wall bending and surface relaxations. The experimental value W is around 10 unit cells which is larger than expected from standard renormalization arguments. The limitations of such experimental studies are discussed.     

High precision delta(17)O isotope measurements of oxygen from silicates and other oxides: method and applications

The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd.     

The effect of the diphosphine basicity on the excited-state properties of trans-(N2)2W(R2PCH2CH2PR2)2: identification of near-degenerate, luminescent 3MLCT and 3LF terms

Absorption spectra (77 and 298 K), luminescence spectra (5-80 K), and luminescence lifetimes (5-80 K) for the title complexes have been correlated to increasing diphosphine basicity (R = 4-CF(3)-Ph < 4-H-Ph < 4-CH(3)O-Ph < Et). As a consequence, spectral peaks have been assigned to (1,3)MLCT (B(1u), W --> phosphorus) and (1,3)LF (B(2g)) terms. As the ligand basicity increases, the (3)MLCT bands observed in absorption blue-shift nearly 8000 cm(-1) and the vibrationally structured (3)LF bands observed in emission red-shift approximately 1300 cm(-1). (3)LF terms lie lowest in energy in the 4-H-Ph, 4-CH(3)O-Ph, and Et compounds, and temperature-dependent lifetime data suggest emission from each be assigned to the equilibrated, spin-orbit split levels of the (3)LF term. The (3)LF and (3)MLCT excited-state terms lie close in energy in the 4-CF(3)-Ph compound, resulting in an emission band shape that is temperature-dependent. At 77 K, the emission band is broad and structureless and is assigned to arise primarily from the (3)MLCT term. As the temperature is lowered toward 5 K, the (3)MLCT emission diminishes in intensity accompanied by the development of a vibrational structure that is characteristic of emission from the (3)LF term. These excited-state terms satisfy the requirements (different orbital origins, near-degeneracy) for separation by a Franck-Condon energy barrier, resulting in simultaneous emission from both terms between 5 and 77 K.     

Test of bell’s inequality using the one-atom micromaser

We examine a local realist bound in the case of a one-atom micromaser. It is shown that such a bound is violated using a simplified treatment of the micromaser. We consider the effect of dissipation in a proposed experiment with the real micromaser. It is seen that the magnitude of violation of a Bell-type inequality depends significantly on the cavity parameters.     

Order-parameter saturation and low-temperature extension of Landau theory

The temperature evolution of the structural order parameter in displacive phase transitions with high transition temperatures (e.g. quartz, As₂O₅, LaAlO₃, CaCO₃, NaNO₃, Pb₃(PO₄)₂ etc.) follows a Landau-type behaviour over large temperature intevals. Below a saturation temperatureT _s , however, the order parameter tends to become temperature independent. A quantitative analysis shows the correlationk _B T _s =/4, where is the frequency of the relevant local excitation atT _s . A general Landau-type expression for the Gibbs energy is given which includes the effects of order-parameter saturation.