The statistics of energy transfer is studied by using the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R and grid points up to approximately 1130 and 4096 3 , respectively. The data show that the energy transfer T across the wave number k is highly intermittent and the skewness S and flatness F of T increase with k approximately as S / ðkLÞ S , F / ðkLÞ F in the inertial subrange, where S $ 2=3, F $ 1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T, the energy dissipation rate and its average r over a domain of scale r shows that T is less intermittent than , while there is a certain similarity between the probability distribution functions of T and r .

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We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

The surface energy band diagrams and the electron affinity of hydrogen-terminated and oxygen-terminated highly phosphorous-doped single crystal diamond (111) surfaces have been studied by ultraviolet photoelectron spectroscopy, secondary electron spectroscopy, X-ray photoelectron spectroscopy and photoemission electron microspectroscopy. A hydrogen-terminated boron-doped diamond (001) surface was used as a reference of surface energy band diagram. The electron affinity of the H-terminated heavily P-doped diamond was determined to be 0.2 ± 0.15 eV, thus close to zero. The electron affinity of the O-terminated highly P-doped diamond was determined to be 0.0 ± 0.15 eV, thus can be negative. However, the surface energy bands for the two highly P-doped samples were found to have large amounts (3 eV) of upward bending toward surface.

We studied the behaviors of contrast in backscattered electron (BSE) images of cross-sectional heattreated steel under various accelerating voltages and take-off angles. Changes in these conditions resulted in dramatic changes in contrast. Low accelerating voltage and low take-off angle improved the surface information and channeling contrast, whereas high accelerating voltage and high take-off angle enhanced the bulk information and reduced channeling contrast, resulting in improved contrast. Such behavior can be understood by the ratio of low-loss electrons (LLEs), which are related to channeling contrast, to the inelastic BSE components detected. The distribution of these components varies with the accelerating voltage and take-off angle: the detection ratio of LLE to inelastic BSE increases with decreasing accelerating voltage and take-off angle. The results obtained in this study will be useful for obtaining and crystallographic information separately in BSE images for the material of interest.