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.     

Characteristics of electrical properties of wide temperature range TGB phases in liquid crystal dimers

4-n-decyloxy-4′-(cholesteryloxycarbonyl-1-butyloxy) chalcone and its two successive homologous are optically active dimeric compound derived from cholesterol. They possess wide temperature ranges of two twist grain boundary (TGB) phases namely TGBA and TGBC*. Comprehensive dielectric studies have been carried out for these compounds in the frequency range of 1 Hz to 10 MHz for different conditions of molecular anchoring. Various electrical parameter viz. dielectric permittivity, dielectric anisotropy, dc conductivity, and activation energy have been determined for these two TGB phases. Weak relaxation processes have been detected under planar anchoring of molecules in the TGBA and TGBC* phases presumably due to amplitude (soft mode) and phase (Goldstone mode) fluctuations.     

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.     

Effect of Atomic‐Scale Differences on the Self‐Assembly of Thiophene‐based Polycatenars in Liquid Crystalline and Organogel States

Two series of polycatenars are reported that contain a central thiophene moiety connected to two substituted oxadiazole or thiadiazole units. The number, position, and length of the peripheral chains connected to these molecules were varied. The oxadiazole‐based polycatenars exhibited columnar phases with rectangular and hexagonal or oblique symmetry, whereas the thiadiazole‐based polycatenars exhibited columnar phases with rectangular and/or hexagonal symmetry. All of the compounds exhibited bright emission in the solution and thin‐film states. Two oxadiazole‐based molecules and one thiadiazole‐based molecule exhibited supergelation ability in hydrocarbon solvents, which is mainly supported by attractive π–π interactions. These gels showed aggregation‐induced enhanced emission, which is of high technological importance for applications in solid‐state emissive displays. X‐ray diffraction studies of the xerogel fibers of oxadiazole‐based polycatenars revealed a columnar rectangular organization, whereas a hexagonal columnar arrangement was observed for thiadiazole‐based polycatenars. Rheological measurements carried out on the samples quantitatively confirmed the formation of gels and showed that these gels are mechanically robust. The impact of an atomic‐scale difference (oxygen to sulfur, <2 % of the molecular weight) on the self‐assembly and the macroscopic properties of those self‐assembled structures are clearly visualized.     

Glass-forming organic radical compounds with cholesterol and benzylideneamine cores

Several organic radical compounds based on TEMPO radical with cholesterol and benzylideneamine cores (3a-c) were prepared. The radical compounds were found to freeze into glassy state when cooled from their isotropic liquid state and characteristic heat-responsive magnetic properties were observed in the radicals due to the phase transitions.     

Dielectric spectroscopy of unsymmetrical liquid crystal dimers showing wide temperature range TGBA and TGBC* phases

The electrical properties of frustrated twist grain boundary (TGB) phase are a matter of curiosity. Some studies have indicated the existence of soft and Goldstone modes in TGBA and TGBC* phases respectively. However, the experimental results are still not very conclusive. In the present work, we report dielectric studies of wide temperature range TGBA and TGBC* phases of an optically active dimeric compound 4‐n‐decyloxy‐4′‐(cholesteryloxycarbonyl‐1‐butyloxy) chalcone in the frequency range of 1 Hz to 35 MHz for the planar and homeotropic anchoring of the molecules. Two different relaxation processes have been detected for the planar anchoring of molecules in the TGBA and TGBC^* phases. The soft mode like behaviour is obtained due to tilt fluctuation of molecules in the megahertz region for both TGBA and TGBC* phases. Goldstone mode like behaviour due to phase fluctuation of molecules has been detected for the TGBC* phase in the low frequency region (～200–300 Hz). Activation energies for DC conductivity have also been determined for various phases of the material.