Sub-Riemannian Geodesics on the 3-D Sphere

The unit sphere can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding Lie algebra define a 2-step sub-Riemannian manifold. We study sub-Riemannian geodesics on this sub-Riemannian manifold making use of the Hamiltonian formalism and solving the corresponding Hamiltonian system. The first author is partially supported by a research grant from the United State Army Research Office and a Hong Kong RGC competitive earmarked research grant #600607. The second and the third authors have been supported by the grant of the Norwegian Research Council #177355/V30, and by the European Science Foundation Research Networking Programme HCAA.     

Diffraction of a Gaussian light beam at the right-angle edges of a plate and the interference pattern in the shadow region

A circular Gaussian beam of monochromatic laser radiation is normally incident to the plane of a right-angle thin metal plate and diffracts at the edges of the plate angle. It is revealed that two main fragments of a composite diffracted wave with cylindrical wave fronts whose axes are mutually orthogonal occur and interfere with each other in the shadow region behind the plate. This is found from the characteristic interference pattern on a flat screen behind the plate. This interference pattern consists of intensive curvilinear, wedge-shaped bands that are located symmetrically in pairs with respect to the bisector of the direct central angle of the circular shadow sector.     

Experimental evidence of self-localized and propagating spin wave modes in obliquely magnetized current-driven nanocontacts

Through detailed experimental studies of the angular dependence of spin wave excitations in nanocontact-based spin-torque oscillators, we demonstrate that two distinct spin wave modes can be excited, with different frequency, threshold currents, and frequency tunability. Using analytical theory and micromagnetic simulations we identify one mode as an exchange-dominated propagating spin wave, and the other as a self-localized nonlinear spin wave bullet. Wavelet-based analysis of the simulations indicates that the apparent simultaneous excitation of both modes results from rapid mode hopping induced by the Oersted field.     

EPR study of the Jahn-Teller effect of Cu2+ ions in ZnGa2O4

The Jahn-Teller effect in the ZnGa₂O₄ spinel single crystal has been investigated using electron paramagnetic resonance of Cu²⁺ ions in the temperature range 110–560 K. It has been shown that copper ions occupy octahedral sites 16d in the ZnGa₂O₄ crystal with cubic symmetry O _h ⁷ (Fd-3m). At T < 560 K, the octahedra undergo tetragonal distortions (predominantly tension) and rotation around the fourfold axes by the angle θ ≈ 2.6°. The parameters of the spin Hamiltonian, which characterize the prolate (g _‖ = 2.355, g _⊥ = 2.077, A _‖ = 116 Oe, A _tp = 12 Oe) and oblate (g _‖ = 2.018, g _⊥ = 2.246, A _‖ = 75 Oe, A _⊥ = 44 Oe) octahedra, have been determined. At temperatures above 560 K, the static Jahn-Teller effect transforms into the dynamic effect and the spectrum of the magnetic resonance becomes isotropic with g = 2.116 (the experimental frequency corresponds to the X band).     

Electron microscopy investigation of AlMg6 aluminum alloy surface defects caused by microorganisms extracted in space stations

The surfaces of AMg6 (aluminum-magnesium) alloy samples that have passed accelerated biocorrosion tests have been investigated in a Quanta-3D scanning electron microscope. The alloy samples have been treated with the Ulocladium botrytis Preuss fungus, which is an active destructive fungus and was previously extracted on surfaces of the International Space Station. Biocorrosion pits 2–10 μm in diameter, cavities the depths of which can reach 70–250 μm depth, and spots of modified color are found to be the most typical defects. The surfaces of large cavities consist of faceted cubic particles that are formed when the acid products of fungus metabolism interact with the alloy surface. The particles have an average size of 30 μm, which is close to the size of alloy grains. The microstructure of a biocorrosion layer has been investigated in a Quanta-3D microscope with the use of a focused Ga⁺ ion beam. The samples of 12-μm-wide transverse slices are obtained near large cavities and investigated in a Tecnai G₂₃0ST transmission electron microscope. The X-ray microanalysis of the defective layer has revealed the high concentration of oxygen in this layer. Obtained images indicate that the corrosion cavity surface has a complex porous structure.     

Failure of Structural Material as a Nonequilibrium Phase Transition

The initial stage of instability in the failure of a structural material treated as a nonequilibrium phase transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).     

Regularized extragradient method for solving parametric multicriteria equilibrium programming problem

A regularized extragradient method is designed for solving unstable multicriteria equilibrium programming problems. The convergence of the method is investigated, and a regularizing operator is constructed.     

Surface monitoring of HEMT structures

The data of Atomic Force Microscopy (AFM) surface monitoring and of mobility investigations in the HEMT structures based on the AlGaAs/InGaAs/GaAs heterostructures with pseudomorphic InGaAs channel are presented. The level of HEMT nanomaterial self-organization (LNSO) were obtained using the treatment the AFM data by the method of multifractal analysis. Direct correlation between the mobility values and LNSO was found for the most of studied HEMT structures that reflect the close relation between the LNSO values and the HEMT bulk properties. In the structures with LNSO changing from 1.13 to 1.45 the 1.5 time mobility decrease at 300 K and 4 times at 77 K was observed. The results obtained allow to suppose that the LNSO calculation based on surface monitoring of HEMT structures can be used for the optimization of their parameters and of their formation process.     

Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L _p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L _p -space.     

Study of process e + e − → π+π−π0π0 at energies √s < 1 GeV with the spherical neutral detector

The cross section for the process e ⁺ e ^? → π⁺π^?π⁰π⁰ has been measured in an experiment with a spherical neutral detector, with the cross section at energies √s < 920 MeV having been measured for the first time. The model of vector dominance describes well the data obtained if the ρ, ρ′, and ρ″ resonances are taken into account. The probability of the decay ρ → π⁺π^?π⁰π⁰ is B(ρ → π⁺π^?π⁰π⁰) = (1.60 ± 0.74 ± 0.18) × 10^?5. The upper limit for the decay ω → π⁺π^?π⁰π⁰ has been improved by two orders of magnitude compared to previous measurements and is B(ω → π⁺π^?π⁰π⁰) < 2 × 10^?4 at a 90% confidence level.