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     

Reflection absorption infrared spectroscopy and temperature programmed desorption investigations of the interaction of methanol with a graphite surface

Reflection absorption infrared spectroscopy (RAIRS) and temperature programmed desorption (TPD) have been used to investigate the adsorption of methanol (CH(3)OH) on the highly oriented pyrolytic graphite (HOPG) surface. RAIRS shows that CH(3)OH is physisorbed at all exposures and that crystalline CH(3)OH can be formed, provided that the surface temperature and coverage are high enough. It is not possible to distinguish CH(3)OH that is closely associated with the HOPG surface from CH(3)OH adsorbed in multilayers using RAIRS. In contrast, TPD data show three peaks for the desorption of CH(3)OH. Initial adsorption leads to the observation of a peak assigned to the desorption of a monolayer. Subsequent adsorption leads to the formation of multilayers on the surface and two TPD peaks are observed which can be assigned to the desorption of multilayer CH(3)OH. The first of these shows a fractional order desorption, assigned to the presence of hydrogen bonding in the overlayer. The higher temperature multilayer desorption peak is only observed following very high exposures of CH(3)OH to the surface and can be assigned to the desorption of crystalline CH(3)OH.     

Reflection absorption infrared spectroscopy and temperature-programmed desorption studies of the adsorption and desorption of amorphous and crystalline water on a graphite surface

Reflection absorption infrared spectroscopy (RAIRS) and temperature-programmed desorption (TPD) have been used to perform a detailed investigation of the adsorption of water on highly oriented pyrolytic graphite (HOPG) at 90 K. RAIRS shows that water is physisorbed on HOPG at all coverages, as expected. Experiments at higher surface temperatures show marked changes in the O-H stretching region of the spectrum which can be assigned to the observation of the amorphous to crystalline ice phase transition. The infrared signature of both phases of solid water has been determined on HOPG and can be used to identify the phase of the ice. TPD spectra show the desorption of multilayers of crystalline ice. At high exposures a small bump appears in the TPD spectrum, on the low temperature side of the main peak, which is attributed to the amorphous to crystalline phase transition. At very low exposures of water, it is possible to distinguish the desorption of water from two- and three-dimensional islands and hence to determine the growth mode of water on the HOPG surface. Isothermal TPD studies have also been performed and show that the desorption of water does not obey perfect zero-order kinetics. Desorption orders, derived directly from the TPD spectra, confirm this observation. Desorption energies and preexponential factors have also been determined for this adsorption system.     

Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model

We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R²). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed magnetization yield the same expectation values for gauge invariant local observables as a suitable grand canonical state with fluctuating magnetization. Here, gauge invariant means commuting with the total third component of the spin, which is a conserved quantity of the Hamiltonian. As a corollary of equivalence of ensembles we also prove the convergence of the thermodynamic limit of sequences of canonical states (i.e., with fixed magnetization).     

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.     

A Self-Averaging “Order Parameter” for the Sherrington-Kirkpatrick Spin Glass Model

Following an idea of van Enter and Griffiths, we define a self-averaging parameter for the Sherrington-Kirkpatrick (SK) spin glass which is a self-averaging version of the order parameter introduced by Aizenman, Lebowitz and Ruelle. It is strictly positive at low temperature and zero at sufficiently high temperature. The proof is based on the recent construction of the thermodynamic limit of the free energy by Guerra and Toninelli. We also discuss how our definition compares with various existing definitions of order-parameter like quantities.     

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.