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     

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.     

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.     

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.     

Cobalt-containing silicotungstate sandwich dimer [{Co3(B-beta-SiW9O33(OH))(B-beta-SiW8O29(OH)2)}2]22-

The 6-cobalt-substituted [{Co3(B-beta-SiW9O33(OH))(B-beta-SiW8O29(OH)2)}2]22- has been characterized by IR and UV-vis spectroscopy, elemental analysis, magnetic studies, electrochemistry, and gel filtration chromatography. A single-crystal X-ray analysis was carried out on K10Na12[{Co3(B-beta-SiW9O33(OH))(B-beta-SiW8O29(OH)2)}2].49H2O (KNa-1), which crystallizes in the monoclinic system, space group P2(1)/n, with a=19.9466(8) A, b=24.6607(10) A, c=34.0978(13) A, beta=102.175(1) degrees, and Z=2. Polyanion 1 represents a novel class of asymmetric sandwich-type polyanions. It contains three cobalt ions, which are encapsulated between an unprecedented (B-beta-SiW9O34) fragment and a (B-beta-SiW8O31) unit. Polyanion 1 is composed of two sandwich species via two Co-O-W bridges in the solid state and almost certainly in solution as well based on gel filtration chromatography. UV-visible spectroscopy and cyclic voltammetry also confirmed its stability. Two well-separated groups of waves appeared in the voltammetric pattern: the wave observed in the negative potential range versus a saturated calomel electrode features the redox processes of WVI centers; the two reversible redox couples observed in the positive potential domain are attributed to the redox processes of Co2+ centers and indicated that the two types of Co2+ centers in the structure are oxidized in separate waves. Such reversibility of Co2+ centers within multi-Co-substituted polyoxometalates is uncommon. The magnetic properties of KNa-1 are also discussed. The ferromagnetic ground state has been studied by magnetic susceptibility and magnetization measurements and fitted according to an anisotropic exchange model.     

Analysis of a two-dimensional nonsmooth Poincaré-like map

A two-dimensional nonsmooth Poincaré-like map is investigated in the present work. The map generalizes in some sense the so-called Nordmark map, which is related to one-dimensional impacting oscillators near grazing points, and constitutes an intuitive basis for dynamics related to degenerate grazing in such oscillators.     

Analysis of a 3D chaotic system

A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connection between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results.     

On the beam propagation through active media

An analytical iterative procedure has been established to determine the amplitude of a laser beam propagating through an active medium. The treatment is valid for both homogeneous and inhomogeneous broadening, and for arbitrary inhomogeneities of the parameters characterizing the active medium, namely, the refractive index, the small-signal gain and the saturation intensity. After a supplementary approximation, a thin-sheet gain approach is derived from the first iteration. The formalism enables us to provide analytical criteria for evaluating both the accuracy of each iteration and the propagation distances for which the thin-sheet solution can be used. This revised version was published online in November 2006 with corrections to the Cover Date.     

Analysis of a map-based neuronal model

ABSTRACT

Subthreshold oscillations in neurons are those oscillations which do not attain the critical value of the membrane's voltage needed for triggering an action potential (a spike). Their contribution to the forming of action potentials in neurons is a current field of research in biology. The present work approaches this subject using tools from mathematical modelling, more exactly, a neuronal non-smooth map-based model is proposed and studied. The behaviour of the model in a noisy medium is also studied.