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Propagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.
The exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.
In 1986 the programme “The Northern Cone of Metagalaxy” has been finished with the 6-meter Telescope. In the course of the programme redshifts of all very rich compact clusters of galaxies inside the cone with galactic latitude and indirect estimates of redshifts ZLB < 0.28 have been measured. The total volume of the investigated region is V ≈ 500·106 Mpc3 (we accept Hubble constant H=50 km/s Mpc−1). A number of possible indications of existence of inhomogeneities in the Universe on scales greater than 100 Mpc are obtained: 1) the void of 400 Mpc in size; 2) the flat stratum of 150 Mpc thickness and 1000 Mpc diameter; 3) two-point space correlation function ξ (R = 200–300 Mpc) = 0.5±0.2. We found no indications that topology of the Universe is non-Euclidean on scales of 20–200 Mpc.
We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin–Lighthill conjecture for flows with values of Bernoulli’s constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.
This study examines how to stop the pyrolysis of fir needles, birch leaves, aspen twigs and their mixture using the minimum volumes of water. The combustion of forest fuels is suppressed by spraying water on their surface. The temperature of thermal decomposition is monitored throughout the layer of forest fuel by thermocouples. A high-speed camera and optical techniques allow us to study water spraying and its interaction with forest fuels. Finally, the study specifies the ranges of the minimum water volumes and the times of ending of the thermal decomposition of forest fuels. When analyzing the energy balance in the thermally decomposing forest fuel, a mathematical expression is formulated to predict the water volume sufficient to suppress thermal decomposition of forest fuel. This expression takes into account the ratio between the heat energy spent on water evaporation in pores of forest fuel and the heat energy of the reacting layer of forest fuel. The obtained dimensionless factor considers the main parameters of water spraying and the properties of forest fuel. This factor enables us to apply the research findings to forest fuel in various regions of the world.
Newly obtained radiocarbon measurements are used to suggest that the initial settlement of the northeastern Baltic area was largely controlled by the Ladoga-Baltic waterway in the north of the Karelian Isthmus, which emerged ∼11,500 cal BP and remained in action for ∼7000 yr. The transgression of Ladoga Lake started ∼5000 cal BP and reached its maximum at ∼3000 cal BP (∼1100–1000 cal BC). The formation of a new outlet via the Neva River led to a rapid regression of the lake that stimulated the spread of farming populations.
The classical problem of determining the secular retardation of the Earth's rotation due to the effect of tides (oceanic and bodily) has an important geophysical value in determining the possible existence of processes inside the Earth, which lead to secular variations of rotation of the whole Earth or its external layers.
Using new cotidal charts of the world ocean calculated by Bogdanov for the main tidal waves M2, S2, K1 and O1 and using the method of moments of tidal forces the retarding moment was found to be 8.3 × 1023 dyn cm. This is twice the amount of previous evaluations. (This method is superior to the method of calculating the dissipation of energy or the moments of frictional forces). This amount corresponds to a retardation of 3.8 μs/century in the speed of the Earth's rotation. But the observations of the Sun give only 1.9 μs/century for the retardation. Thus, there seem to be nontidal and probably internal processes, which accelerate the Earth's rotation by about 2 μs/century. And this is without taking account of additional smaller effects of bodily tides. The search for these processes is an important problem.
The full text of the paper will be published in the magazine Physics of the Earth, No. 2, 1972.
Available spectroscopic evidence of various circumstellar gaseous structures in the well-known binary β Lyr is confronted with the results of 3-D gas-dynamical simulations of mass transfer between the binary components, obtained for the currently best available basic physical properties of the system. It appears that the gas-dynamical model is capable to explain, at least qualitatively, the formation of all basic observed components of the circumstellar matter, including the jet-like structures, recently found from interferometry and polarimetry of the object.
Thermal conductivity of single-crystal boron-doped diamond (BDD) was studied in comparison with high-quality pure IIa-type diamond in the temperature range from 20 to 400 K. Boron content in BDD was about 1019 cm−3 that is a typical value of p+ substrates used for power device applications. The thermal conductivity of BDD is about 10 times less than that of IIa diamond near 100 K, but above room temperature the difference is <30%. The observed deviation mostly takes place due to acoustic phonon scattering on extended structural defects occurring in synthetic diamond at high boron content.
The results of a numerical simulation of heat and mass transfer during evaporation of a water droplet with solid inclusion in air at temperature as high as 1000K are presented. Typical heating steps of droplet until it reaches the conditions of intensive evaporation (i.e. the interface “solid inclusion – liquid” reaches the boiling temperature) are described. The roles played by the external air temperature and by the main properties of inclusion are detailed. The droplet size, the relation between the sizes of inclusion and a liquid layer during the heating up is determined. The necessary and sufficient conditions of intensive evaporation in the system “water droplet with solid inclusion in high-temperature air” are pointed out.
When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.
For the problem describing steady gravity waves with vorticity on a two-dimensional unidirectional flow of finite depth the following results are obtained. (i) Bounds are found for the free-surface profile and for Bernoulli’s constant. (ii) If only one parallel shear flow exists for a given value of Bernoulli’s constant, then there are no wave solutions provided the vorticity distribution is subject to a certain condition.
Two-dimensional steady gravity waves with vorticity are considered on water of finite depth. The dispersion equation is analysed for general vorticity distributions, but under assumptions valid only for unidirectional shear flows. It is shown that for these flows (i) the general dispersion equation is equivalent to the Sturm–Liouville problem considered by Constantin & Strauss (Commun. Pure Appl. Math., vol. 57, 2004, pp. 481–527; Arch. Rat. Mech. Anal., vol. 202, 2011, pp. 133–175), (ii) the condition guaranteeing bifurcation of Stokes waves with constant wavelength is fulfilled. Moreover, a necessary and sufficient condition that the Sturm–Liouville problem mentioned in (i) has an eigenvalue is obtained.
Gallium nitride films were successfully grown by HVPE technique on p-type 6H-SiC substrate. The layers exhibit high crystal quality as was determined by X-ray diffraction. Photoluminescence (PL) of these films was measured. The PL spectra were dominated by band edge emission. Concentration Nd-Na in undoped epitaxial layers ranged from 2×1017 to 1×1019cm−3. Mesa-structures formed by reactive ion etching showed good rectifying current-voltage characteristics for GaN/SiC pn heterojunctions.
We have studied epitaxial GaN layers grown by hydride vapour phase epitaxy (HVPE) on porous GaN sublayers formed on SiC substrates. It was shown that these layers can be grown with good surface morphology and high crystalline quality. X-ray, Raman and photoluminescent (PL) measurements showed that the stress in the layers grown on porous GaN was reduced to 0.1-0.2 GPa, while the stress in the layers grown directly on 6H-SiC substrates remains at its usual level of about 1 GPa. Thus, we have shown that growth on porous GaN sublayer is a promising method for fabrication of high quality epitaxial layers of GaN with low strain values.
In this paper, we have developed an approximate method for modelling the flow of embryonic fluid in a ventral node. We simplified the problem as flow in a two-dimensional cavity; the effect of rotating cilia was modelled by specifying a constant vorticity at the edge of the ciliated layer. We also developed an approximate solution for morphogen transport in the nodal pit. The solutions were obtained utilizing the proper generalized decomposition (PGD) method. We compared our approximate solutions with the results of numerical simulation of flow caused by the rotation of 81 cilia, and obtained reasonable agreement in most of the flow domain. We discuss locations where agreement is less accurate. The obtained semi-analytical solutions simplify the analysis of flow and morphogen distribution in a nodal pit.
Defect density and stress reduction in heteroepitaxial GaN and AlN materials is one of the main issues in group III nitride technology. Recently, significant progress in defect density reduction in GaN layers has been achieved using lateral overgrowth technique. In this paper, we describe a novel technique based on nano-scale epitaxial lateral overgrowth.
GaN layers were overgrown by hydride vapour phase epitaxy (HVPE) on porous GaN. Porous GaN was formed by anodization of GaN layers grown previously on SiC ŝubstrates. Pore's size was in nano-scale range.
Thickness of overgrown layers ranged from 2 to 120 microns. It was shown that GaN layers overgrown on porous GaN have good surface morphology and high crystalline quality. The surface of overgrown GaN material was uniform and flat without any traces of porous structure. Raman spectroscopy measurements indicated that the stress in the layers grown on porous GaN was reduced down to 0.1 - 0.2 GPa, while the stress in the layers grown directly on 6H-SiC substrates remains at its usual level of about 1.3 GPa.
Preliminary experiments were done on HVPE growth of AlN layer on porous substrates. Improvement of surface morphology and crack density reduction has been observed.
Here we present the result of measurements of electrical resistivity and magnetoresistivity of graphite/diamond nanocomposites (GDNC) and onion-like carbon (OLC) prepared by vacuum annealing of nanodiamond (ND) at various fixed temperatures. GDNC contain particles with a diamond core covered by closed curved graphitic shells. The electrical resistivity of annealed ND is characteristic of systems with localized electrons and can be described in terms of variable hopping-length hopping conductivity (VHLHC). The magnetoresistivity of OLC is negative in the range of field 0<B<2 T, and is positive at B>2 T. The conduction carrier concentration for OLC samples was estimated in the framework of the theory of negative magnetoresistance in semiconductors in the hopping conduction region. The free path length for conducting electrons at liquid helium temperature was estimated from the data on positive magnetoresistivity. The localization length of current carriers was also estimated. The determined parameters are in agreement with proposed structure model of OLC constructed using HRTEM data.
Annealing of nanodiamond at moderate temperature makes it possible to produce structures being intermediate in the carbon transformation from sp3- to sp2-state (graphite/diamond nanocomposites) and onion-like carbon (OLC). Electron microscopy shows such structures involve cage shells with spacing close to graphite. X-ray emission spectroscopy has been applied to examine the electronic structure of OLC and graphite/diamond nanocomposites. The CKα-spectra of OLC produced in the temperature range of 1600-1900 K were found to be markedly different from the spectrum of particles formed at 2140 K and characterized by better ordering of graphitic shells. The latter spectrum was shown to be very similar to the CKα-spectrum of polycrystalline graphite, while the former ones exhibited a significant increase of high-energy maximum that might be caused by the holed defect structure of graphitic networks forming at the intermediate annealing temperatures. To interpret experimental spectra, the quantum-chemical semiempirical AM1 calculation of icosahedral C540 cage and that with holed defects was carried out. The lack of at least 22% atoms in an internal carbon cage was found to be essential to provide an increase of density of high-energy electronic states similar to that observed in the spectrum of OLC produced at 1900 K.