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     

Surface vibrations and the nature of the adsorption state: C2H2 on Pt(111)

Molecular vibrations of C₂H₂ and C₂D₂ adsorbed on Pt(111) at 140 K and ∼300K have been measured by high resolution electron energy loss spectroscopy. The comparison of C₂H₂ and C₂D₂ spectra allows an unambiguous assignment of the observed losses to the excitation of C−H bending, C−H stretching, and C−C stretching modes of nondissociatively adsorbed acetylene. From the relative intensities of losses the hybridisation state is determined to be nearsp ². The C−C stretching frequency indicates a C−C bond order of ∼1.8.     

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Use of chromatographic pre-concentration for routine uranium bioassay analysis by ICP-MS

Routine monitoring of urine is an effective way to detect occupational intake of radioactive material. Historically, determinations of uranium isotopic ratios have been performed by radiochemical separation followed by alpha spectrometry. With recent advancements in technology, inductively coupled plasma-mass spectrometry (ICP-MS) has become widely available for the determination of trace metals as well as radioactive nuclides with long half-lives, such as ²³⁸U in urine. Furthermore, ICP-MS measurements of ²³⁸U do not require radiochemical separation since the number of atoms in the sample is determined instead of the number of alpha particles emitted. However, this method does not provide good sensitivity for the determination of ²³⁵U due to its shorter half-life. An improved procedure using pre-concentration of uranium and determination by ICP-MS decreases the detection limit by a factor of ten or greater with only slight increase in total analysis time. The method also has the capability of accurately determining the isotopic ratio of the sample, which is very important in cases where enriched or depleted uranium is involved.     

Optical absorption by surface plasmons in deep sub-wavelength channels

The interaction of visible light with surface plasmons in a periodic array of silver channels is studied experimentally and theoretically. Channels of width 130 nm and depth 280 nm on a pitch of 468 nm were fabricated using electron beam lithography. Measurements of the reflectance of the channels show strong absorption for a specific angle of incidence at a given wavelength of the light. It is shown using a simple geometric model that this is consistent with the excitation and propagation of surface plasmons in the deep sub-wavelength channels. A numerical simulation of the electromagnetic fields excited in the channels confirms this result.     

Point-sensitive and point-free patch constructions

Using the category of frames we consider various generalizations of the patch space of a topological space. Some of these constructions are old and some are new. We consider how these variants interact and under what circumstances they agree.     

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.     

Coordination of acetonitrile (CH3CN) to platinum (111): Evidence for an η2(C,N) species

Acetonitrile (CH₃CN) coordination to a Pt(111) surface has been studied with electron energy loss vibrational spectroscopy (EELS), XPS, thermal desorption and work function measurements. We compare data for the surface states with known acetonitrile coordination complexes. For CH₃CN adsorbed on Pt(111) at 100 K, the molecule is rehybridized and adsorbs with the CN bond parallel or slightly inclined to the surface plane in an η²(C, N) configuration. The ν(CN) frequency is 1615 cm^?1 and the C ls and N ls binding energies are 284.6 eV and 397.2 eV respectively. By contrast, weakly adsorbed multilayer acetonitrile exhibits a ν(CN) vibrational frequency of 2270 cm^?1, and C ls and N ls binding energies of 286.9 eV and 400.1 eV respectively. Both the EELS and XPS results are consistent with rehybridization of the CN triple bond to a double bond with both C and N atoms of the CN group attached to the surface. In addition to this majority η²(C, N) monolayer state, evidence is found for a second, more strongly bound minority molecular state in thermal desorption spectra. As a result of the low coverage of this state, EELS was unable to spectroscopically identify it and we tentatively assign it as an η⁴(C, N) species associated with accidental step sites. By contrast to the surface complexes, almost all of the known platinum-nitrile coordination complexes are end-bonded via the N lone-pair orbital. Several cases of side-on bonding are known, however, and we compare the results with the known complex Fe₃(η²-NCCH₃)(CO)₉. The difference in the coordinative properties of a Pt(111) surface versus a single Pt atom must be due to the increased ability of multi-atom arrays to back-donate electrons into the π¹ system of acetonitrile. Previously published EELS and XPS results for monolayer acetonitrile on Ni(111) and polycrystalline films are almost identical to the present results on Pt(111). We believe that the monolayer of $\text{CH}{}_3\text{CN}\text{Ni}\text{(111)}$ is also an η²(C, N) species, not an end-bonded species previously proposed by Friend, Muetterties and Gland.