Size effect and the quadratic temperature dependence of the transverse magnetoresistivity in "size-effect" tungsten single crystals

The transverse magnetoresistivity of pure tungsten single crystals with a residual resistivity ratio ρ293K/ρ4.2K of about 75000 was measured from 4.2 to 20 K and in magnetic fields of up to 15 T. The size effect, i.e. the linear dependence of the magnetoconductivity on the inverse cross sample dimensions, was studied in detail at high fields. We show that the size effect can be used for the separation of the contributions from the electron-surface and the electron-phonon scattering mechanisms to the full conductivity. We demonstrate that the electron-phonon scattering leads to the exponential temperature dependence of the conductivity, and the interference between the electron-phonon and the electron-surface processes leads to a new scattering mechanism "electron-phonon-surface" with a quadratic temperature dependence of the magnetoconductivity. © Published under licence by IOP Publishing Ltd

On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

Interaction of the radiation of the high-power ytterbium-fiber laser with inhomogeneous dielectric targets

The action of the radiation of the ytterbium-fiber laser (λ = 1.07 μm) on the Nd3+Y2O3 target with nonuniform transparency in the course of the nanopowder production is studied. It is demonstrated that the laser irradiation leads to an extremely rough surface with the stalagmite roughness due to a relatively large melting depth. The resulting powder consists of two fractions. The first fraction (99% of the total mass of the powder) consists of nanoparticles with a mean size of 29 nm (BET data). The second fraction consists of micro- and submicroparticles that represent circular drops condensed from the melt and shapeless debris of the target. The peaks on the diameter distribution of the drops at 2, 8, and 80 μm are determined by different effects. The laser heating of the inhomogeneous target with the nonlinear refractive index is numerically analyzed. It is demonstrated that the melting of the target is initiated at a mean laser power of 700 W, a power density of 5.6 × 105 W/cm2, and an irradiation time of 150 μs. © 2013 Pleiades Publishing, Ltd

The influence of HfO2 additives on the optical properties of Nd3+-doped Y2O3 ceramics

Transparent yttria ceramics were fabricated by sintering a mixture of 1 at.% Nd:Y2O3 and HfO2 nanopowders produced by laser synthesis method. The best transmittance was 80.96% at the wavelength of λ=1080 nm in 6 mol.% HfO2 doped sample (1.5 mm thick). The additives of hafnium broaden both pumping and luminescence bands of Nd3+ ion in yttria ceramics. The luminescence intensity of 4F3/2→4I11/2 transition was little affected by hafnium concentration. The effective lifetime of 4F3/2 level in Nd:Y2O3 ceramics enhanced by 30% at 10 mol.% HfO2 doping concentration and the decay kinetics of laser transition attains Förster's behavior. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim