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     

Isotopic effects in hydrogen-bonded crystals with order–disorder type phase transitions

The influence of geometric isotopic effects on the Curie temperature of hydrogen-containing crystals was considered. The experimental pressure and concentration dependencies of the Curie temperature have been explained in a framework of the pseudo-spin Ising model, by taking into account the changes in geometry of hydrogen bonds under pressure and due to isotopic exchange.     

I NQR and spectroscopic investigation of impurity-doped and mixed lithium iodate Li1−xHxIO3 crystals

The ¹²⁷I NQR, IR absorption and Raman spectra of impurity-doped and mixed lithium iodate Li_1−xH_xIO₃ crystals grown from water solutions with different LiIO₃/HIO₃ ratios were investigated depending on the content of the impurity hydrogen x. The NQR results suggested that, at small concentration of doping iodic acid x<0.22, the lattice dynamics of the crystal grown from water solution changes significantly though the crystal retains hexagonal symmetry. Spectroscopic studies are compatible with average hexagonal symmetry of the grown doped crystals. From the results of Raman studies at room temperature and 100 K, the concentration range of hydrogen dopant 0.22<x<0.36 was found where disordered solid solution crystals Li_1−xH_xIO₃ are formed.     

Search forββ decay of76Ge to the excited states in76Se

Lower limits on the half-life of theββ(2v+0v) decay of⁷⁶Ge to the excited states in⁷⁶Se have been obtained using the results of low-background measurements with a HPGe detector surrounded by passive germanium shielding: T_1/2(0⁺ → 2 ₁ ⁺ ) >1.1 · 10²¹ y, T_1/2(0⁺ → 0 ₁ ⁺ ) > 1.7 · 10²¹ y, T_1/2(0⁺ → 2^2/+) > 1.4 ·10²¹ y.     

Determination of the energy measurement accuracy for charged particles by their range in nuclear photoemulsion

Ranges of monochromatic muons in nuclear photoemulsion, produced in the ?? ?? ??? _?? decay, are measured by the coordinate method to determine their energy by the range. The variance of the muon energymeasured by this method ?? _?? = (0.11±0.01) MeV, which corresponds to the accuracy of the determination of the charged particle energy by the range in nuclear emulsion ??3.1%. The developed technique will allow electron energy measurements in the 2??-decay (??3 MeV)with an accuracy of (5?C6)%.     

Experiment double beta decay: Historical review of 75 years of research

The main achievements during 75 years of research on double beta decay have been reviewed. The existing experimental data have been presented and the capabilities of the next-generation detectors have been demonstrated.     

Search for double beta decay of Mo with liquid argon ionization chamber (first results)

First two runs with 138.7 g of ¹⁰⁰Mo were done 9202 h and 238 h). Limits on half-lives for 0ν- and 0νχ⁰-decays of ¹⁰⁰Mo were obtained, > 2.3 · 10²¹ y and 0.8 · 10²⁰ y, respectively at 90% CL. Also the limit on the content of radioactive ⁴²Ar in the natural Ar was obtained, < 5 · 10⁻²¹ g/g. Perspectives for the future are discussed.     

Investigation of double-beta decay with the NEMO-3 detector

The double-beta-decay experiment NEMO-3 has been taking data since February 2003. The aim of this experiment is to search for neutrinoless (0 νββ) decay and investigate two neutrino doublebeta decay in seven different isotopically enriched samples (¹⁰⁰Mo, ⁸²Se, ⁴⁸Ca, ⁹⁶Zr, ¹¹⁶Cd, ¹³⁰Te, and ¹⁵⁰Nd). After analysis of the data corresponding to 3.75 yr, no evidence for 0 νββ decay in the 100Mo and 82Se samples was found. The half-life limits at the 90% C.L. are 1.1 × 10²⁴ and 3.6 × 10²³ yr, respectively. Additionally for 0 νββ decay the following limits at the 90% C.L. were obtained, >1.3 × 10²² yr for ⁴⁸Ca, >9.2 × 10²¹ yr for ⁹⁶Zr, and >1.8 × 10²² yr for 150Nd. The 2 νββ decay half-life values were precisely measured for all investigated isotopes.     

Nemo double-beta-decay experiments

To investigate double beta decay processes the NEMO collaboration developed an electron tracking detector made of Geiger cells for track reconstruction and plastic scintillators for energy measurements. The prototype, NEMO-2, is described and results onββ decay of¹⁰⁰Mo,¹¹⁶Cd,⁸²Se and⁹⁶Zr are given. A brief presentation of the status and design parameters of a new detector NEMO-3, which is approximately 20 times larger, will also be given.     

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.