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.     

Use of 73Ge NMR spectroscopy for the study of electronic interactions

The lack of understanding of the structural and electronic factors that affect the often difficult to observe germanium resonance has been a major deterrent to studies of bonding interactions at germanium. We utilized the symmetrical system GeR 4 to determine what structural factors inherent in the R group affect the shape and position of the (73)Ge resonance. The (73)Ge resonances of symmetrical tetrakis germanium compounds of the type GeR 4 (R = alkyl, aryl), GeX 4 (X = F, Cl, Br, I), Ge(OR) 4 (R = alkyl, methoxyalkyl, dimethylaminoalkyl), Ge(NR 2) 4 (R = alkyl), and Ge(SR) 4 (R = alkyl, dimethylaminoalkyl) were examined for evidence of intramolecular coordination. Although many of these compounds have sharp resonances due to idealized tetrahedral symmetry with relatively long relaxation times, others have broad or no observable resonances due to fast quadrupolar relaxation. We hypothesize that the perturbation of symmetry by even weak Lewis interactions or conformational changes causes broadening of the resonance before the interaction can become sufficiently strong to cause the significant low-frequency shift generally associated with hypercoordination in most nuclei. Intermolecular coordination to GeCl 4 is believed to be responsible for the low-frequency shifts in (73)Ge resonances and the associated changes in peak widths in mixtures with bases such as tributylphosphine oxide (TBPO) and triethylphosphine oxide (TEPO). Adduct formation with these bases is confirmed by broad (31)P resonances that are resolved into five peaks at -40 degrees C. The exchange-broadened resonances due to the 1:1 and 1:2 TEPO adducts are also observed at -40 degrees C in the (73)Ge spectrum. Thus, relatively strong bonding to the germanium in GeCl 4 results in both low-frequency shifts and broadening of the resonance. The broad (73)Ge resonances that occur in some compounds may be in part due to exchange as well as quadrupolar relaxation.     

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.     

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.     

Exploring the reactivity of flavonoid compounds with metal-associated amyloid-β species

Metal ions associated with amyloid-β (Aβ) peptides have been suggested to be involved in the development of Alzheimer's disease (AD), but this remains unclear and controversial. Some attempts to rationally design or select small molecules with structural moieties for metal chelation and Aβ interaction (i.e., bifunctionality) have been made to gain a better understanding of the hypothesis. In order to contribute to these efforts, four synthetic flavonoid derivatives FL1-FL4 were rationally selected according to the principles of bifunctionality and their abilities to chelate metal ions, interact with Aβ, inhibit metal-induced Aβ aggregation, scavenge radicals, and regulate the formation of reactive oxygen species (ROS) were studied using physical methods and biological assays. The compounds FL1-FL3 were able to chelate metal ions, but showed limited solubility in aqueous buffered solutions. In the case of FL4, which was most compatible with aqueous conditions, its binding affinities for Cu(2+) and Zn(2+) (nM and μM, respectively) were obtained through solution speciation studies. The direct interaction between FL4 and Aβ monomer was weak, which was monitored by NMR spectroscopy and mass spectrometry. Employing FL1-FL4, no noticeable inhibitory effect on metal-mediated Aβ aggregation was observed. Among FL1-FL4, FL3, having 3-OH, 4-oxo, and 4'-N(CH(3))(2) groups, exhibited similar antioxidant activity to the vitamin E analogue, Trolox, and ca. 60% reduction in the amount of hydrogen peroxide (H(2)O(2)) generated by Cu(2+)-Aβ in the presence of dioxygen (O(2)) and a reducing agent. Overall, the studies here suggest that although four flavonoid molecules were selected based on expected bifunctionality, their properties and metal-Aβ reactivity were varied depending on the structure differences, demonstrating that bifunctionality must be well tuned to afford desirable reactivity.     

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.     

Development of bifunctional stilbene derivatives for targeting and modulating metal-amyloid-β species

Amyloid-β (Aβ) peptides and their metal-associated aggregated states have been implicated in the pathogenesis of Alzheimer's disease (AD). Although the etiology of AD remains uncertain, understanding the role of metal-Aβ species could provide insights into the onset and development of the disease. To unravel this, bifunctional small molecules that can specifically target and modulate metal-Aβ species have been developed, which could serve as suitable chemical tools for investigating metal-Aβ-associated events in AD. Through a rational structure-based design principle involving the incorporation of a metal binding site into the structure of an Aβ interacting molecule, we devised stilbene derivatives (L1-a and L1-b) and demonstrated their reactivity toward metal-Aβ species. In particular, the dual functions of compounds with different structural features (e.g., with or without a dimethylamino group) were explored by UV-vis, X-ray crystallography, high-resolution 2D NMR, and docking studies. Enhanced bifunctionality of compounds provided greater effects on metal-induced Aβ aggregation and neurotoxicity in vitro and in living cells. Mechanistic investigations of the reaction of L1-a and L1-b with Zn(2+)-Aβ species by UV-vis and 2D NMR suggest that metal chelation with ligand and/or metal-ligand interaction with the Aβ peptide may be driving factors for the observed modulation of metal-Aβ aggregation pathways. Overall, the studies presented herein demonstrate the importance of a structure-interaction-reactivity relationship for designing small molecules to target metal-Aβ species allowing for the modulation of metal-induced Aβ reactivity and neurotoxicity.