On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Magnetic anisotropy in strained manganite films and bicrystal junctions

Transport and magnetic properties of LSMO manganite thin films and bicrystal junctions were investigated. Manganite films were epitaxially grown on STO, LAO, NGO and LSAT substrates and their magnetic anisotropy were determined by two techniques of magnetic resonance spectroscopy. Compare with cubic substrates a small (about 0.3 persentage), the anisotropy of the orthorhombic NGO substrate leads to a uniaxial anisotropy of the magnetic properties of the films in the plane of the substrate. Samples with different tilt of crystallographic basal planes of manganite as well as bicrystal junctions with rotation of the crystallographic axes (RB - junction) and with tilting of basal planes (TB - junction) were investigated. It was found that on vicinal NGO substrates the value of magnetic anisotropy could be varied by changing the substrate inclination angle from 0 to 25 degrees. Measurement of magnetic anisotropy of manganite bicrystal junction demonstrated the presence of two ferromagnetically ordered spin subsystems for both types of bicrystal boundaries RB and TB. The magnitude of the magnetoresistance for TB - junctions increased with decreasing temperature and with the misorientation angle even misorientation of easy axes in the parts of junction does not change. Analysis of the voltage dependencies of bicrystal junction conductivity show that the low value of the magnetoresistance for the LSMO bicrystal junctions can be caused by two scattering mechanisms with the spin- flip of spin - polarized carriers due to the strong electron - electron interactions in a disordered layer at the bicrystal boundary at low temperatures and the spin-flip by anti ferromagnetic magnons at high temperatures.Comment: 26 pages, 10 figure

СТРУКТУРА И МЕХАНИЧЕСКИЕ СВОЙСТВА СЛИТКОВ И ПРОФИЛЕЙ ИЗ АЛЮМИНИЕВОГО СПЛАВА НА ОСНОВЕ СИСТЕМЫ AL-MG-MN

Commercial ingots and hot-pressed rolled sections of Al-Mg-Mn alloy doped with zinc, scandium, zirconium, chromium, and vanadium have been studied using optical microscopy, thermal analysis, electron microscopy, and electron-probe microanalysis. The compositions of the phase constituents and aluminum matrix of the alloy are determined. The sensitivity of the alloy to the formation of complex intermetallic compounds during solidification is revealed. The mechanical properties of ingots and rolled sections are determined. © 2013 Pleiades Publishing, Ltd

Hybrid heterostructures with superconducting/antiferromagnetic interfaces

We report on structural, DC, X-ray and neutron studies of hybrid superconducting mesa-heterostructures with a cuprate antiferromagnetic interlayer Ca1-xSrxCuO2 (CSCO). The upper electrode was bilayer Nb/Au superconductor and copper oxide superconductor YBa2Cu3O7 (YBCO) was the bottom electrode. It was experimentally shown that during the epitaxial growth of the two films YBCO and CSCO a charge carrier doping takes place in the CSCO interlayer with a depth about 20 nm. The conductivity of the doped part of CSCO layer is close to the metal type, while the reference CSCO film, deposited directly on NdGaO3 substrate, behaves as Mott insulator with the hopping conductivity. The interface Au/CSCO is clearly seen on bright-field image of the cross-section of heterostructure and gives the main contribution to the total resistance of mesa-heterostructure.Comment: 16 pages, 9 figure

Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the curl of the fluid velocity. A main result of the classification in the kinematic case is that the only equation of state found to be distinguished by admitting extra $n$-dimensional conserved integrals, apart from mass, momentum, energy, angular momentum and Galilean momentum (which are admitted for all equations of state), is the well-known polytropic equation of state with dimension-dependent exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of state are found to arise, and here the main result of the classification is that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's two-dimensional circulation theorem is obtained for a general equation of state.Comment: 24 pages; published version with misprints correcte

Negative high-frequency differential conductivity in semiconductor superlattices

We examine the high-frequency differential conductivity response properties of semiconductor superlattices having various miniband dispersion laws. Our analysis shows that the anharmonicity of Bloch oscillations (beyond tight-binding approximation) leads to the occurrence of negative high-frequency differential conductivity at frequency multiples of the Bloch frequency. This effect can arise even in regions of positive static differential conductivity. The influence of strong electron scattering by optic phonons is analyzed. We propose an optimal superlattice miniband dispersion law to achieve high-frequency field amplification

Synchrotron X-ray Diffraction Study of BaFe2As2 and CaFe2As2 at High Pressures up to 56 GPa: Ambient and Low-Temperatures Down to 33 K

We report high pressure powder synchrotron x-ray diffraction studies on MFe2As2 (M=Ba, Ca) over a range of temperatures and pressures up to about 56 GPa using a membrane diamond anvil cell. A phase transition to a collapsed tetragonal phase is observed in both compounds upon compression. However, at 300 (33) K in the Ba-compound the transition occurs at 26 (29) GPa, which is a much higher pressure than 1.7 (0.3) GPa at 300 (40) K in the Ca-compound, due to its larger volume. It is important to note that the transition in both compounds occurs when they are compressed to almost the same value of the unit cell volume and attain similar ct/at ratios. We also show that the FeAs4 tetrahedra are much less compressible and more distorted in the collapsed tetragonal phase than their nearly regular shape in the ambient pressure phase. We present a detailed analysis of the pressure dependence of the structures as well as equation of states in these important BaFe2As2 and CaFe2As2 compounds.Comment: 26 pages, 12 figure

Invariants of differential equations defined by vector fields

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the second order. A result on the characterization of classes of these equations by the invariant functions is also given.Comment: 13 page