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.

Analytical model and experimental validation of friction laws for composites under low loads

In order to account for interfacial friction of composite materials, an analytical model based on contact geometry and local friction is proposed. A contact area includes several types of microcontacts depending on reinforcement materials and their shape. A proportion between these areas is defined by in-plane contact geometry. The model applied to a fibre-reinforced composite results in the dependence of friction on surface fibre fraction and local friction coefficients. To validate this analytical model, an experimental study on carbon fibrereinforced epoxy composites under low normal pressure was performed. The effects of fibre volume fraction and fibre orientation were studied, discussed and compared with analytical model results. © Springer Science+Business Media, LLC 2012.

Local hydrogen reactions of H*2 in a-Si:H

Hydrogen rearrangements at the H*2 complex are used as a model of low energy, local transitions in the two-hydrogen density of states of hydrogenated amorphous silicon (a-Si:H). These are used to account for the low activation energy motion of H observed by nuclear magnetic resonance, the low energy defect annealing of defects formed by bias stress in thin film transistors, and the elimination of hydrogen from the growth zone during the low temperature plasma deposition of a-Si:H. © 1998 Elsevier Science B.V. All rights reserved.