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     

Pure iron compressed and heated to extreme conditions

The results of a first-principles study supported by the temperature-quenched laser-heated diamond anvil-cell experiments on the high-pressure high-temperature structural behavior of pure iron are reported. We show that in contrast to the widely accepted picture, the face-centered cubic (fcc) phase becomes as stable as the hexagonal-close-packed (hcp) phase at pressures around 300-360 GPa and temperatures around 5000-6000 K. Our temperature-quenched experiments indicate that the fcc phase of iron can exist in the pressure-temperature region above 160 GPa and 3700 K, respectively. This, in particular, means that the actual structure of the Earth's core may be a complex phase with a large number of stacking faults.     

Interaction of Au nanowires with impurities

We report the results of our first-principles studies of the interaction between an infinite monoatomic gold nanowire and a carbon-monoxide molecule. We show that the gold monoatomic nanowire is capable of absorbing the CO molecule at the distances of about 1.8 ? and forms a bond with the carbon atom. Further, we find that dissociation of the CO molecule as the source of gold nanowire contamination with carbon, which is widely discussed in literature as the possible reason for the striking stability of gold nanowires under stretching, is thermodynamically unfavored.     

Fluctuating lattice constants of indium under high pressure

Recent high-pressure investigations of elemental In have yielded controversial results. We show that the observed high-pressure face-centered orthorhombic (fco) structure can be explained as an intermediate state between two body-centered tetragonal (bct) structures with different c/a ratios (c/a < square root [2] and c/a > square root [2], respectively). In a pressure range from about 50 to 200 GPa these two bct structures correspond to local minima of the total energy with respect to orthorhombic distortion of the ground-state bct In structure. The fco saddle point represents a tiny barrier and even at low temperatures rapid structural fluctuations should occur. Such a situation has not been identified in any other elemental metal.     

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.     

Electronic topological transition in metastable Al-Ge solid solutions

Al-rich Al-Ge solid solutions synthesized under high pressure demonstrate physical properties strikingly different from those of pure Al. In particular, enhanced superconductivity temperature (T_c), anomalies in the phonon spectra and decrease of the Debye temperature have been observed. We show from first-principles, based on calculations of the electronic spectra and Fermi surfaces of Al-Ge substitutional solid solutions, that an electronic topological transition (ETT) takes place in the system. We predict anomalies in transport properties to be revealed experimentally for Al-Ge solid solutions with the Ge concentration ≈10 at.%. The influence of the ETT on the thermodynamic properties of the system is discussed and, in particular, concentration dependence of the Debye temperature is reproduced in good agreement with experiment.     

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.