Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.

Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

"Available online 22 March 2016"

Induced magnetoelectric effect driven by magnetization in BaFe12O19 -/P(VDF-TrFE) composites

Films of BaFe12O19/P(VDF-TrFE) composites with 5, 10 and 20 %wt Barium ferrite content have been fabricated. BaFe12O19 microparticles have the shape of thin hexagonal platelets, the easy direction of magnetization remaining along the c axis, which is perpendicular to the plates. This fact allows for ferrite particles orientation in-plane and out-of-plane within the composite films, as confirmed by measured hysteresis loops. While the in-plane induced magnetoelectric effect (ME) is practically zero, these composite films show a good out-of-plane magnetoelectric effect. with maximum ME coupling coefficient changes of 3, 17 and 2 mV/cm.Oe for the 5, 10 and 20%wt Barium ferrite content films, respectively. We infer that this ME behavior appears as driven by the magnetization process arising when we applied the external magnetic field. We have also measured linear and reversible magnetoelectric effect for low applied bias field, when magnetization process is still reversible.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζτ(k) controlling the singularities for both the longitudinal  and transverse (τ = t) dynamical structure factors for the whole momentum range  , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.