On an evasion problem on a semi-infinite interval for a class of controlled distributed systems

In this paper, we study an evasion problem in systems described by equations of parabolic type. We consider four versions of constraints on the control parameters.     

On the structure of finite coverings of compact connected groups

Finite-sheeted covering mappings onto compact connected groups are studied. We show that for a covering mapping from a connected Hausdorff topological space onto a compact (in general, non-abelian) group there exists a topological group structure on the covering space such that the mapping becomes a homomorphism of groups. To prove this fact we construct an inverse system of covering mappings onto Lie groups which approximates the given covering mapping. As an application, it is shown that a covering mapping onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by degree of the mapping. We also get a criterion for triviality of coverings in terms of means and prove that each finite covering of G is equivalent to a polynomial covering.     

Corn stover fractions and bioenergy

Information is presented on structure, composition, and response to enzymes of corn stover related to barriers for bioconversion to ethanol. Aromatic compounds occurred in most tissue cell walls. Ferulic acid esterase treatment before cellulase treatment significantly improved dry weight loss and release of phenolic acids and sugars in most fractions over cellulase alone. Leaf fractions were considerably higher in dry weight loss and released sugars with esterase treatment, but stem pith cells gave up the most phenolic acids. Results help identify plant fractions more appropriate for coproducts and bioconversion and those more suitable as residues for soil erosion control.     

A Study of premixed propagating flame vortex interaction

Experimental data is presented for the interaction between a propagating flame and a simple vortex flow field structure generated in the wake of solid obstacles. The interaction between gas movement and obstacles creates vortex shedding forming a simple flow field recirculation. The presence of the simple turbulent structure within the gas mixture curls the flame front increasing curvature and enhancing burning rate. A novel twin camera Particle Image Velocimetry, PIV, was employed to characterise the flow field recirculation and the interaction with the flame front. The technique allowed the quantification of the flame/vortex interaction. The twin camera technique provides data to define the spatial variation of both the velocity of the flow field and flame front. Experimentally obtained values of local flame displacement speed and flame stretch rate are presented for simple flame/vortex interactions.     

Cosmic γ-ray bursts: Observations and modeling

It is now commonly accepted that cosmic γ-ray bursts (GRBs) are of cosmological origin. This conclusion is based on the statistical analysis of GRBs and the measurements of line redshifts in GRB optical afterglows, i.e., in the so-called long GRBs. In this review, the models of radiation and models of GRB sources are considered. In most of these models, if not in all of them, the isotropic radiation cannot provide the energy release necessary for the appearance of a cosmological GRB. No correlation is noted between the redshift, the GRB-spectrum shape, and the total detected energy. The comparison between data obtained in the Soviet experiment KONUS and the American experiment BATSE shows that they substantially differ in statistical properties and the detection of hard x-ray lines. The investigation of hard gamma (0.1–10 GeV) afterglows, the measurement of prompt optical spectra during the GRB detection, and the further investigation of hard x-ray lines is of obvious importance for gaining insight into the GRB origin. Observations of two bright optical GRB afterglows point to the fact that an initially bright optical flare is directly related to the GRB itself, and the subsequent weak and much more continuous optical radiation is of a different nature. The results of observations of optical GRB afterglows are discussed. They point to the fact that the GRBs originate in distant galaxies with a high matter density, where intense star formation takes place. The interaction of the cosmological GRB radiation with a dense surrounding molecular cloud results in the appearance of long-duration (up to 10 years) weak optical afterglows associated with the heating and reradiation of gas. Results of 2D numerical simulation of the heating and reradiation of gas in various variants of the relative disposition of GRB and molecular clouds are presented. In conclusion, the possible relation between the so-called short GRBs and recurrent sources of soft γ rays in our Galaxy, the so-called “soft gamma repeaters,” is discussed.     

Nonstoichiometry and low-temperature magnetic properties of FeSi crystals

The results of experimental and theoretical studies of the low-temperature properties of FeSi crystals are presented. The specific features of the magnetic susceptibility are shown to be related to the superparamagnetic behavior of impurity clusters. The thermomagnetic hysteresis phenomena observed are explained using the model of exchange-coupled clusters.     

Use of random numbers in computer simulation of magnetic resonance signals

The proton magnetic resonance spectra of water molecules diffusing over regular sites in natrolite are numerically simulated. Experimental data and the results of simulation are found to be in good agreement in a wide temperature interval including the transition range, where the magnetic resonance spectrum is a superposition of a wide unaveraged spectrum and a spectrum averaged by the motion of molecules. The simulation uses generators of pseudorandom-number Markovian sequences. For a binary Markovian process, it is shown, in particular, that the time within which a physical quantity remains constant is described by an exponentially distributed random number.     

A fractal model of reinforcement of elastoplastic nanocomposites

Within the framework of fractal analysis and percolation theory, an alternative model of reinforcement of filled polymers is offered. Practically, this model can be used only to describe the reinforcement of nanocomposites, because, according to the treatment considered, a pronounced reinforcement can be reached only at ratios of filler particle diameter to the statistical segment length of about 10 and less. A theoretical calculation showed a good qualitative and quantitative agreement with experiments. The type of reinforcement mechanism of composites is determined by the type of the space (fractal or Euclidean) in which the structure of the polymeric matrix is formed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 797–802, November–Decem ber, 2006.     

High resolution X-ray diffraction of GaN grown on Si (1 1 1) by MOVPE

High temperature GaN layers have been grown on Si (1 1 1) substrate by metalorganic vapor phase epitaxy (MOVPE). AlN was used as a buffer layer and studied as a function of thickness and growth temperature. The growth was monitored by in situ laser reflectometry. High resolution X-ray diffraction (HRXRD) revealed that optimized monocrystalline GaN was obtained for a 40 nm AlN grown at 1080 °C. This is in good agreement with the results of morphological study by scanning electron microscopy (SEM) and also confirmed by atomic force microscopy (AFM) observations. The best morphology of AlN with columnar structure and lower rms surface roughness is greatly advantageous to the coalescence of the GaN epilayer. Symmetric and asymmetric GaN reflections were combined for twist and stress measurements in monocrystalline GaN. It was found that mosaicity and biaxial tensile stress are still high in 1.7 μm GaN. Curvature radius measurement was also done and correlated to the cracks observations over the GaN surface.