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

Strong Spin Dependence of Correlation Effects in Ni Due to Stoner Excitations

Using high resolution angle resolved photoemission, we observe a strong spin dependent renormalization and lifetime broadening of the quasiparticle excitations in the electronic band structure of Ni 111 in an energy window of amp; 8764;0.3 eV below the Fermi level. We derive a quantitative result for the spin dependent lifetime broadening by comparing the scattering rates of majority and minority d states, and further show that spin dependent electron correlations are instead negligible for sp states. From our analysis we experimentally determine the effective on site Coulomb interaction U caused by Stoner like interband transitions between majority and minority d states. The present results demonstrate the remarkable impact of spin dependent electron correlation effects originating from single particle excitations in a prototypical 3d transition metal, paving the way for further refinement of current many body theoretical approache

Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems

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

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

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

Accurate prediction of H₃O⁺ and D₃O⁺ sensitivity coefficients to probe a variable proton-to-electron mass ratio

The mass sensitivity of the vibration–rotation–inversion transitions of H316O+, H318O+, and D316O+ is investigated variationally using the nuclear motion program TROVE (Yurchenko, Thiel & Jensen). The calculations utilize new high-level ab initio potential energy and dipole moment surfaces. Along with the mass dependence, frequency data and Einstein A coefficients are computed for all transitions probed. Particular attention is paid to the Δ|k| = 3 and Δ|k − l| = 3 transitions comprising the accidentally coinciding |J, K = 0, v2 = 0+〉 and |J, K = 3, v2 = 0−〉 rotation–inversion energy levels. The newly computed probes exhibit sensitivities comparable to their ammonia and methanol counterparts, thus demonstrating their potential for testing the cosmological stability of the proton-to-electron mass ratio. The theoretical TROVE results are in close agreement with sensitivities obtained using the non-rigid and rigid inverter approximate models, confirming that the ab initio theory used in the present study is adequate

Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.Comment: 13 pages, 3 figure

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