Epigroups whose subepigroup lattice is lower semimodular

We characterize epigroups mentioned in the title. © 2012 Springer Science+Business Media, LLC

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

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

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

Electronic and magnetic structure of epitaxial NiO/Fe3_3O4_4(001) heterostructures grown on MgO(001) and Nb-doped SrTiO3_3(001)

We study the underlying chemical, electronic and magnetic properties of a number of magnetite based thin films. The main focus is placed onto NiO/Fe$_3$O$_4$(001) bilayers grown on MgO(001) and Nb-SrTiO$_3$(001) substrates. We compare the results with those obtained on pure Fe$_3$O$_4$(001) thin films. It is found that the magnetite layers are oxidized and Fe$^{3+}$ dominates at the surfaces due to maghemite ($\gamma$-Fe$_2$O$_3$) formation, which decreases with increasing magnetite layer thickness. From a layer thickness of around 20 nm on the cationic distribution is close to that of stoichiometric Fe$_3$O$_4$. At the interface between NiO and Fe$_3$O$_4$ we find the Ni to be in a divalent valence state, with unambiguous spectral features in the Ni 2p core level x-ray photoelectron spectra typical for NiO. The formation of a significant NiFe$_2$O$_4$ interlayer can be excluded by means of XMCD. Magneto optical Kerr effect measurements reveal significant higher coercive fields compared to magnetite thin films grown on MgO(001), and a 45$^{\circ}$ rotated magnetic easy axis. We discuss the spin magnetic moments of the magnetite layers and find that the moment increases with increasing thin film thickness. At low thickness the NiO/Fe$_3$O$_4$ films grown on Nb-SrTiO$_3$ exhibits a significantly decreased spin magnetic moments. A thickness of 20 nm or above leads to spin magnetic moments close to that of bulk magnetite

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

Polaron physics and crossover transition in magnetite probed by pressure-dependent infrared spectroscopy

The optical properties of magnetite at room temperature were studied by infrared reflectivity measurements as a function of pressure up to 8 GPa. The optical conductivity spectrum consists of a Drude term, two sharp phonon modes, a far-infrared band at around 600 cm$^{-1}$, and a pronounced mid-infrared absorption band. With increasing pressure both absorption bands shift to lower frequencies and the phonon modes harden in a linear fashion. Based on the shape of the MIR band, the temperature dependence of the dc transport data, and the occurrence of the far-infrared band in the optical conductivity spectrum the polaronic coupling strength in magnetite at room temperature should be classified as intermediate. For the lower-energy phonon mode an abrupt increase of the linear pressure coefficient occurs at around 6 GPa, which could be attributed to minor alterations of the charge distribution among the different Fe sites.Comment: 7 pages, 7 figure

Novel Regime of Operation for Superconducting Quantum Interference Filters

A new operating regime of the Superconducting Quantum Interference Filter (SQIF) is investigated. The voltage to magnetic field response function, V(H), is determined by a Fraunhofer dependence of the critical current and magnetic flux focusing effect in Josephson junctions (F-mode). For SQIF-arrays made of high-Tc superconducting bicrystal Josephson junctions the F-mode plays a predominant role in the voltage-field response V(H). The relatively large superconducting loops of the SQIF are used for inductive coupling to the external input circuit. It is shown that the output noise of a SQIF-array measured with a cooled amplifier in the 1-2 GHz range is determined by the slope of the V(H) characteristic. Power gain and saturation power were evaluated using low frequency SQIF parameters. Finally, we consider the influence of the spread in the parameters of Josephson junctions in the SQIF-array on the V(H) characteristic of the whole structure.Comment: 7 pages, 4 figure

Electronic structure studies of BaFe2As2 by angle-resolved photoemission spectroscopy

We report high resolution angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of BaFe$_2$As$_2$, which is one of the parent compounds of the Fe-pnictide superconductors. ARPES measurements have been performed at 20 K and 300 K, corresponding to the orthorhombic antiferromagnetic phase and the tetragonal paramagnetic phase, respectively. Photon energies between 30 and 175 eV and polarizations parallel and perpendicular to the scattering plane have been used. Measurements of the Fermi surface yield two hole pockets at the $\Gamma$-point and an electron pocket at each of the X-points. The topology of the pockets has been concluded from the dispersion of the spectral weight as a function of binding energy. Changes in the spectral weight at the Fermi level upon variation of the polarization of the incident photons yield important information on the orbital character of the states near the Fermi level. No differences in the electronic structure between 20 and 300 K could be resolved. The results are compared with density functional theory band structure calculations for the tetragonal paramagnetic phase.Comment: 11 pages, 5 figure