Compositions with distinct parts

The number of compositionsC(n) of a positive integern into distinct parts can be considered as a natural analogue of the numberq(n) of distinct partitions ofn. We obtain an asymptotic estimate forC(n) and in addition show that the sequence {C(n, k)} of distinct compositions ofn withk distinct parts is unimodal. Our analysis is more complicated than is usual for composition problems. The results imply however that the behaviour of these functions is of comparable complexity to partition problems.     

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of Ωt of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at three points (triads) and allow the explicit removal of pressure fluctuations. We first extend the formalism to anisotropic rotating turbulence with ‘production’, in the presence of mean velocity gradients in the rotating frame. Second, we compare the spectral approach at three points to the two-point approach directly performed in physical space, in which we consider the transport of the scalar second-order structure function ?(δq)²?. This calls into play componental third-order correlations ?(δq)²δu?(r) in axisymmetric turbulence. This permits to discuss inhomogeneous anisotropic effects from spatial decay, shear, or production, as in the central region of a rotating round jet. We show that the above-mentioned important statistical quantities can be estimated from experimental planar particle image velocimetry, and that explicit passage relations systematically exist between one- and two-point statistics in physical and spectral space for second-order tensors, but also sometimes for third-order tensors that are involved in the dynamics.     

Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

Stationarity and invertibility of simple bilinear models

Necessary and sufficient conditions for strict stationarity and invertibility are found for one-parameter bilinear models. These conditions involve the expectations of the logarithms of the absolute values of the input and output sequences.     

A note on stability of some parametrically excited structural elastic systems

An analogue simulation study for the stability investigations of nonlinear parametrically excited structural systems, exhibiting hard and soft spring characteristics is undertaken as a feasible alternative to current asymptotic and other analytic methods. It is shown that this technique locates the position of an unstable limit cycle, identifying the point of change of equilibrium states, which is ordinarily obscured in using the other existing schemes.     

The effect of InxGa1−xN back-barriers on the dislocation densities in Al0.31Ga0.69N/AlN/GaN/InxGa1−xN/GaN heterostructures (0.05 ≤ x ≤ 0.14)

Al_0.31Ga_0.69N/AlN/GaN/In_xGa_1?xN/GaN heterostructures grown with the metal-organic chemical vapor deposition (MOCVD) technique with different In_xGa_1?xN back-barriers with In mole fractions of 0.05 ≤ x ≤ 0.14 were investigated by using XRD measurements. Screw, edge, and total dislocations, In mole fraction of back-barriers, Al mole fraction, and the thicknesses of front-barriers and lattice parameters were calculated. Mixed state dislocations with both edge and screw type dislocations were observed. The effects of the In mole fraction difference in the back-barrier and the effect of the thickness of front-barrier on crystal quality are discussed. With the increasing In mole fraction, an increasing dislocation trend is observed that may be due to the growth temperature difference between ultrathin In_xGa_1?xN back-barrier and the surrounding layers.     

Multiwall-carbon nanotube/cobalt ferrite hybrid: Synthesis,magnetic and conductivity characterization

Functionalized multiwall carbon nanotubes (MWCNT-COOH) were decorated with crystalline cobalt ferrite nanoparticles (CoFe₂O₄ NPs) by co-precipitation reaction to form MWCNT-COOH/CoFe₂O₄ hybrid. The hybrid was characterized by X-ray diffraction analysis, transmission electron microscopy (TEM), Fourier transfom infrared spectroscopy and vibrating sample magnetometry. The results confirmed that MWCNTs and CoFe₂O₄ NPs coexisted in the hybrid. The TEM results showed a thick layer of CoFe₂O₄ was intimately connected to the surface of MWCNTs. The saturation magnetization value of the hybrid was 11.5 emu/g. There has been a high frequency fluctuation in conductivity, however, above all dc conductivity changes and resulting activation energy is calculated from the Arrhenius plots. It is found to vary with the temperature regions. This can be attributed to the existence of a conventional temperature independent tunneling conduction mechanism, which can be also explained that the metallic conduction is a dominant mechanism around room temperature. The ac conductivity of MWCNT-COOH/CoFe₂O₄ hybrid might also be a consequence of the predictions of the universal dynamic response and the ‘n’ power exponents could be determined with lower concentration of the addition in the hybrids.     

Plasmon effects in electron energy loss and gain spectra in aluminium

Oberservations of the low energy secondary and Auger electron spectra and the electron energy loss spectra from a clean aluminium surface have been made and the results are compared with other recent studies including that of Jenkins and Chung (1971). Low energy emissions at 5.7 eV and 10.3 eV are associated with the creation of single electron excitations in the valence band by plasmon decay. An apparent anomaly in the plasmon loss and gain peaks associated with the Auger spectrum is discussed.     

Long-life batteries for sound level meters

The use of rechargeable, nickel-cadmium batteries instead of the throw-away type is suggested for sound level meters. The advantages are saving of money, and greater convenience in the use of sound level meters on site visits. A simple method for recharging the batteries is discussed, which should be of interest to engineers and public health inspectors, as well as acoustic specialists.