The non-local nature of structure functions

Kolmogorov's two-thirds, ((Δv) 2) ∼ e 2/ 3r 2/ 3, and five-thirds, E ∼ e 2/ 3k -5/ 3, laws are formally equivalent in the limit of vanishing viscosity, v → 0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s 2/ 3, in accordance with Kolmogorov's 1941 law, and we vary the range of scales, γ = s max/s min, in any one realisation from γ = 25 to γ = 800. This is equivalent to varying the Reynolds number in an experiment from R λ = 60 to R λ = 600. While there is some evidence of a five-thirds law for g > 50 (R λ > 100), the two-thirds law only starts to become apparent when g approaches 200 (R λ ∼ 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, ((Δv) 2) takes the form of a mixed power-law, a 1+a 2r 2+a 3r 2/ 3, where a 2r 2 tracks the variation in enstrophy and a 3r 2/ 3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r 2/ 3 law by the enstrophy contribution, a 2r 2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency.

Measuring the composition of AlGaN layers in GaN based structures grown on 150 mm Si substrates using (2 0 5) reciprocal space maps

A critical element for the successful growth of GaN device layers on Si is accurate control of the AlGaN buffer layers used to manage strain. Here we present a method for measuring the composition of the AlGaN buffer layers in device structures which makes use of a one-dimensional x-ray detector to provide efficient measurement of a reciprocal space map which covers the full compositional range from AlN to GaN. Combining this with a suitable x-ray reflection with low strain sensitivity it is possible to accurately determine the Al fraction of the buffer layers independent of their relaxation state. © 2013 IOP Publishing Ltd.

Effect of dry oxidation on the energy gap and chemical composition of CVD graphene on nickel

The findings presented herein show that the electronic properties of CVD graphene on nickel can be altered from metallic to semiconducting by introducing oxygen adsorbates via UV/ozone or oxygen plasma treatment. These properties can be partially recovered by removing the oxygen adsorbates via vacuum annealing treatment. The effect of oxidation is studied by scanning tunneling microscopy/spectroscopy (STM/STS) and X-ray photoelectron spectroscopy (XPS). As probed by STM/STS, an energy gap opening of 0.11-0.15 eV is obtainable as the oxygen/carbon atomic ratio reaches 13-16%. The corresponding XPS spectra show a significant monotonic increase in the concentration of oxygenated functional groups due to the oxidation treatments. This study demonstrates that the opening of energy gap in CVD graphene can be reasonably controlled by a combination of UV/ozone or oxygen plasma treatment and vacuum annealing treatment. © 2013 Elsevier B.V.