`Interpolating' differential reductions of multidimensional integrable hierarchies

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the second heavenly equation and its generalization proposed by Dunajski. We give a characterization of differential reductions in terms of the Lax-Sato equations as well as in the framework of the dressing method based on nonlinear Riemann-Hilbert problem.Comment: Based on the talk at NLPVI, Gallipoli, 15 page

On the Ehrenfest theorem of quantum mechanics

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.Comment: To appear in J. Math. Phy

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

FeNi-based magnetoimpedance multilayers: Tailoring of the softness by magnetic spacers

The microstructure and magnetic properties of sputtered permalloy films and FeNi(170 nm)/X/FeNi(170 nm) (X=Co, Fe, Gd, Gd-Co) sandwiches were studied. Laminating of the thick FeNi film with various spacers was done in order to control the magnetic softness of FeNi-based multilayers. In contrast to the Co and Fe spacers, Gd and Gd-Co magnetic spacers improved the softness of the FeNi/X/FeNi sandwiches. The magnetoimpedance responses were measured for [FeNi/Ti(6 nm)] 2/FeNi and [FeNi/Gd(2 nm)] 2/FeNi multilayers in a frequency range of 1-500 MHz: for all frequencies under consideration the highest magnetoimpedance variation was observed for [FeNi/Gd(2 nm)] 2/FeNi multilayers. © 2012 American Institute of Physics

Rotationally resolved spectroscopy of (20000) Varuna in the near-infrared

Models of the escape and retention of volatiles by minor icy objects exclude any presence of volatile ices on the surface of TNOs smaller than ~1000km in diameter at the typical temperature in this region of the solar system, whereas the same models show that water ice is stable on the surface of objects over a wide range of diameters. Collisions and cometary activity have been used to explain the process of surface refreshing of TNOs and Centaurs. These processes can produce surface heterogeneity that can be studied by collecting information at different rotational phases. The aims of this work are to study the surface composition of (20000)Varuna, a TNO with a diameter ~650km and to search for indications of rotational variability. We observed Varuna during two consecutive nights in January 2011 with NICS@TNG obtaining a set of spectra covering the whole rotation period of Varuna. After studying the spectra corresponding to different rotational phases, we did not find any indication of surface variability. In all the spectra, we detect an absorption at 2{\mu}m, suggesting the presence of water ice on the surface. We do not detect any other volatiles on the surface, although the S/N is not high enough to discard their presence. Based on scattering models, we present two possible compositions compatible with our set of data and discuss their implications in the frame of the collisional history of the Kuiper Belt. We find that the most probable composition for the surface of Varuna is a mixture of amorphous silicates, complex organics, and water ice. This composition is compatible with all the materials being primordial. However, our data can also be fitted by models containing up to a 10% of methane ice. For an object with the characteristics of Varuna, this volatile could not be primordial, so an event, such as an energetic impact, would be needed to explain its presence on the surface.Comment: 6 pages, 5 figures, to be published in A&

Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation

It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type singularities are presented.Comment: 19 page

Quantum Resonances of Kicked Rotor and SU(q) group

The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order $q$, we relate the problem to the {\it regular} motion along a circle in a $(q^2-1)$-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the $SU(q)$ group. This motion is in parallel with the classical phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure

Iron oxide nanoparticles fabricated by electric explosion of wire: Focus on magnetic nanofluids

Nanoparticles of iron oxides (MNPs) were prepared using the electric explosion of wire technique (EEW). The main focus was on the fabrication of de-aggregated spherical nanoparticles with a narrow size distribution. According to XRD the major crystalline phase was magnetite with an average diameter of MNPs, depending on the fraction. Further separation of air-dry EEW nanoparticles was performed in aqueous suspensions. In order to provide the stability of magnetite suspension in water, we found the optimum concentration of the electrostatic stabilizer (sodium citrate and optimum pH level) based on zeta-potential measurements. The stable suspensions still contained a substantial fraction of aggregates which were disintegrated by the excessive ultrasound treatment. The separation of the large particles out of the suspension was performed by centrifuging. The structural features, magnetic properties and microwave absorption of MNPs and their aqueous solutions confirm that we were able to obtain an ensemble in which the magnetic contributions come from the spherical MNPs. The particle size distribution in fractionated samples was narrow and they showed a similar behaviour to that expected of the superparamagnetic ensemble. Maximum obtained concentration was as high as 5 % of magnetic material (by weight). Designed assembly of de-aggregated nanoparticles is an example of on-purpose developed magnetic nanofluid. Copyright © 2012 Author(s)