On local and global aspects of the 1:4 resonance in the conservative cubic H\'enon maps

We study the 1:4 resonance for the conservative cubic H\'enon maps $\mathbf{C}_\pm$ with positive and negative cubic term. These maps show up different bifurcation structures both for fixed points with eigenvalues $\pm i$ and for 4-periodic orbits. While for $\mathbf{C}_-$ the 1:4 resonance unfolding has the so-called Arnold degeneracy (the first Birkhoff twist coefficient equals (in absolute value) to the first resonant term coefficient), the map $\mathbf{C}_+$ has a different type of degeneracy because the resonant term can vanish. In the last case, non-symmetric points are created and destroyed at pitchfork bifurcations and, as a result of global bifurcations, the 1:4 resonant chain of islands rotates by $\pi/4$. For both maps several bifurcations are detected and illustrated.Comment: 21 pages, 13 figure

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

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

Observation of the second harmonic in superconducting current-phase relation of Nb/Au/(001)YBa2Cu3Ox heterojunctions

The superconducting current-phase relation (CPR) of Nb/Au/(001)YBa2Cu3Ox heterojunctions prepared on epitaxial c-axis oriented YBa2Cu3Ox thin films has been measured in a single-junction interferometer. For the first time, the second harmonic of the CPR of such junctions has been observed. The appearance of the second harmonic and the relative sign of the first and second harmonics of the CPR can be explained assuming, that the macroscopic pairing symmetry of our YBa2Cu3Ox thin films is of the d+s typeComment: 11 pages, 4 figure

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

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