Stable Ergodicity and Frame Flows

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Permeability of N2, Ar,He, O2, and CO2 through as‐extruded amorphous and biaxially oriented polyester films: Dependence on chain mobility

For as‐extruded amorphous and biaxially orientated polyester films based on poly(ethylene terephthalate), poly(ethylene naphthalate), and copolymers containing poly(ethylene terephthalate) and poly(ethylene naphthalate) moieties, permeability, diffusion, and solubility coefficients are interpreted in terms of chain mobility. The influence of polymer morphology is determined by comparison of the data for as‐extruded amorphous sheets and materials produced with different biaxial draw ratios. The crystallinities of the samples were assessed using differential scanning calorimetry and density measurements. Changes in mobility at a molecular level were investigated using dielectric spectroscopy and dynamic mechanical thermal analysis. The study, in conjunction with our earlier work, leads to the conclusion that the key to understanding differences in gas transport is the difference in local chain motions rather than in free volume. This was illustrated by the permeability results for He, Ar, N₂, and O₂ in the range of polyesters. However, the permeability of CO₂ was found to require alternative explanations because of polymer–penetrant interactions. For biaxially oriented samples, the differences in diffusivity are not only due to differences in local chain motions, but also additional constraints resulting from the increased crystallinity and chain rigidity—which also act to hinder segmental mobility. The effectiveness of the reduction in permeability in the biaxially oriented films is consequently determined by the ability of the polymer chains to effectively align and form crystalline structures. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2916–2929, 2004     

Steady-state electrolysis at a grooved or ridged plane

This study concerns an infinite plane whose smoothness is marred by a single defect: either a groove or a ridge. The blemished plane serves as an electrode supporting a diffusion-controlled steady-state process. By using a convenient coordinate transformation, the local current density at all points on the surface is determined exactly. The results are found to confirm intuitive expectations. Thus, compared with normal values on the plane remote from a groove, the electron transfer rate is diminished within the groove but enhanced along its margins. Similarly, an abnormally large transfer rate is encountered high on the ridge but the rate is subnormal on its lower flanks. The total current is demonstrated to be unchanged by the presence of the blemish. Received: 27 September 1996 / Accepted: 11 March 1997     

The potential of pyrolysis/gas chromatography/mass spectrometry for determining the progress of lignification: An investigation of maturing asparagus sclerenchyma tissue

Sclerenchyma tissues from semi-mature and mature asparagus spears were analysed by pyrolysis/gas chromatography/mass spectrometry and by conventional chemical methods in order to determine the degree of lignification and compare analytical techniques. The pyrolysis data are similar to those obtained by a chemical method involving alkaline extraction at 70°C followed by spectrophotometric determination of phenolic content. The pyrolysis method was more rapid, sensitive and informative than the chemical technique and shows considerable potential for studying the chemical basis of the textural development of plant foods.     

Catalytic air oxidation of ambient temperature hydrocarbons

Catalytic air oxidation of the aliphatic hydrocarbons n-decane, hexanes, gasoline and diesel fuel was conducted at ambient temperature with novel iron catalysts. The concentration of n-decane in water was reduced from 1.42 g in 100 ml to 0.07 g in 100 ml in 5 h at room temperature forming carbon monoxide and water by means of intermediate aldehydes. Results of FT–IR and GC–MS analyses demonstrated formation of aldehydes and unsaturated alcohols. Carbon monoxide was detected on catalyst residues and in the vapor phase. The indicated catalytic reaction mechanisms are discussed.     

Electrode “edge effects” analyzed by the Green function method

An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive.     

The central limit problem for convex bodies

It is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately Gaussian. Several quite broad classes of bodies are shown to satisfy the condition.