A RANS 3D model with unbounded eddy viscosities

We consider the Reynolds Averaged Navier–Stokes (RANS) model of order one (u,p,k)$(\mathbf{u},p,k)$ set in R³${\mathbb{R}}^3$ which couples the Stokes Problem to the equation for the turbulent kinetic energy by k-dependent eddy viscosities in both equations and a quadratic term in the k  -equation. We study the case where the velocity and the pressure satisfy periodic boundary conditions while the turbulent kinetic energy is defined on a cell with Dirichlet boundary conditions. The corresponding eddy viscosity in the fluid equation is extended to R³${\mathbb{R}}^3$ by periodicity. Our contribution is to prove that this system has a solution when the eddy viscosities are nondecreasing, smooth, unbounded functions of k, and the eddy viscosity in the fluid equation is a concave function.     

Impedance studies on polyacrylonitrile–CuX2–DMSO (X=Cl, Br, CF3SO3) solid polymer electrolyte

A series of polyacrylonitrile–dimethylsulfoxide–CuX₂ (X=CF₃SO₃⁻, Cl⁻, Br⁻), films (foils) were prepared by means of the solution cast technique. The thickness of the foils was between 0.04 and 0.09 cm and they contained 70–80 wt.% of the solvent. Conductivities of the solid electrolytes were obtained from impedance measurements. The conductivity increases with the increase of the salt content up to 8 wt.%; at higher concentrations (>8 wt.%) the conductivity is more or less stable, and reaches, in the case of Cu(CF₃SO₃)₂ and CuCl₂, the level of ca. 10⁻³ Ω⁻¹ cm⁻¹ at room temperature. The foils based on the CuBr₂ show even higher conductivity, close to 10⁻² Ω⁻¹ cm⁻¹ at room temperature, a value comparable to that characteristic for liquid solutions. The temperature variation of the conductivity for all the systems studied is of the Arrhenius type. The activation energy, determined from linear plots lnσ=f(T⁻¹), is of the order ca. 14 kJ mol⁻¹ for the PAN/CuBr₂/DMSO and of ca. 21 kJ mol⁻¹ for the PAN/CuCl₂/DMSO and the PAN/Cu(CF₃SO₃)₂/DMSO systems.     

Experimental and theoretical studies on vibrational structure of metal complexes with m-halogenobenzoic acids

The effects of alkaline metals and halogen substituent on the vibrational structure of m-halogenobenzoates have been investigated by Infrared (IR), Raman, and quantum chemical methods. A complete assignments of vibrational spectra are based on the previous literature data and present theoretical approach. A good correspondence between experimental and calculated (density functional theory) vibrational spectra has been observed. The changes in vibrational structure caused by halogen substituent indicate perturbation of the electronic charge distribution in the aromatic ring. The effect of alkaline metal is much weaker and hidden by overwhelming effect of halogen. A linear relationships between vibrational frequencies of selected bands and ionic potential as well as electronegativity of halogen substituent have been established. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62 : 385–392, 1997     

Study of free convective boundary layer of isothermal lateral surface of axisymmetrical horizontal body

Approximate analytical solution of simplified Navier–Stokes and Fourier–Kirchhoff equations describing free convective heat transfer from isothermal surface has been presented. It is supposed that the surface has the horizontal axis of symmetry and its axial cross-section lateral boundary is a concave function. The equation for the boundary layer thickness is derived for typical for natural convection assumptions. The most important are that the convective fluid flow is stationary and the normal to the surface component of velocity is negligibly small in comparison with the tangential one. The theoretical results are verified by two characteristic cases of the revolution surfaces namely for horizontal conic and vertical round plate. Both limits of presented solution coincide with known formulas.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

Influence of a strontium-enriched intergranular cluster network on the electrical conductivity of In2O3-SrO ceramics

A metastable hexagonal R-phase is revealed in polycrystalline In₂O₃-SrO samples, which has the form of a network made up of mesoscopic clusters (60–180 Å in size). The clusters arise from strontium-enriched regions near grain boundaries in the main cubic structure of indium oxide. It is shown that annealing in oxygen at T _a ? 300°C saturates dangling bonds between the R-phase and the matrix and makes the system metastable. This state shows up in the presence of (i) solitary diffuse maxima from the R-phase imposed on Debye lines from the main phase in the X-ray diffraction pattern and (ii) the electron cyclotron resonance (ECR) line with g = 1.875. In addition, the sample in this state acquires a high resistivity (ρ ～ 10⁶ Ω cm). Relaxation at T ? 300°C after annealing at T _a > 300°C disrupts bonds between the strontium-enriched clusters of the R-phase and the indium oxide matrix. This causes spatial separation of the clusters, disruption of their coherent bonds with the matrix structure, and escape of excess oxygen from the sample along grain boundaries. As a result, a new stable state forms, which is characterized by (i) a series of diffuse maxima from the R-phase imposed on lines assigned to the main phase, (ii) the presence of the ECR line with g = 2 with the line with g = 1.875 retained, and (iii) the transition of the sample to a low-resistivity state (ρ ～ 100 Ω cm).     

Laminar free convection heat transfer from a horizontal ring

The analytical solution of laminar free convective heat transfer in an unlimited space from an isothermal horizontal ring with an adiabatic plug is presented. The results of theoretical considerations are presented as relation of the Nusselt and Rayleigh numbers: $$Nu_D = 1.151 \cdot (Ra_D )^{1/5} \cdot \Phi (\phi _0 )$$ \] where Φ(φ₀) is a function of shape coefficient of the ring (φ₀=d/D). The solution presented has been verified experimentally with rings of constant external diameter (D=0.06 [m]) and various internal diameters (d=0, 0.01, 0.02, 0.04 and 0.05 [m]). The fluid tested was glycerin. The theoretical predictions agree well with the experimental results.     

A rapid,spatially dispersive frequency comb spectrograph aimed at gas phase chemical reaction kinetics

This New Views article will highlight some recent advances in high sensitivity gas detection using direct infrared absorption frequency comb laser spectroscopy, with a focus on frequency comb use in chemical reaction kinetics and our own contribution to this field. Our recently implemented detection technique uses a combination of a 12.9?GHz free spectral range virtually imaged phased array and diffraction grating to spatially disperse the mid-infrared frequency comb onto a camera. Individual frequencies or ‘comb teeth’ of a 250?MHz repetition-rate frequency comb are able to be resolved. High molecular sensitivity is achieved by increasing the interaction path length using a Herriott multipass cell. High spectral resolution, broadband spectral coverage, and high molecular sensitivity are all achieved on an adjustable 1–50 µs timescale, making this frequency comb apparatus ideal for measuring chemical reaction kinetics where multiple absorbing species can be monitored simultaneously. This New Views article will also discuss some of the challenges and decisions that chemists might face in implementing this advanced physics technology in their own laboratory.

Spatially dispersed 250 MHz mid-infrared frequency comb laser, with absorption of some frequencies by a dilute sample of methane.     

Preparation and Characterization of Carbon Nano‐Onion/PEDOT:PSS Composites

Composites of unmodified or oxidized carbon nano‐onions (CNOs/ox‐CNOs) with poly(3,4‐ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) are prepared with different compositions. By varying the ratio of PEDOT:PSS relative to CNOs, CNO/PEDOT:PSS composites with various PEDOT:PSS loadings are obtained and the corresponding film properties are studied as a function of the polymer. X‐ray photoelectron spectroscopy characterization is performed for pristine and ox‐CNO samples. The composites are characterized by scanning and transmission electron microscopy and differential scanning calorimetry studies. The electrochemical properties of the nanocomposites are determined and compared. Doping the composites with carbon nanostructures significantly increases their mechanical and electrochemical stabilities. A comparison of the results shows that CNOs dispersed in the polymer matrices increase the capacitance of the CNO/PEDOT:PSS and ox‐CNO/PEDOT:PSS composites.