Spin tunneling in magnetic molecules: Quantitative estimates for Fe8 clusters

Spin tunneling in the particular case of the magnetic molecular cluster octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows for an angle-based description of the process. The presence of an external magnetic field along the easy axis is also taken into account in this description. Analytic expressions for the energy levels and barriers are obtained from a harmonic approximation of the potential function which give results in good agreement with the experimental results. The energy splittings due to spin tunneling is treated in an adapted WKB approach and it is shown that the present description can give results to a reliable degree of accuracy.Comment: 17 pages, 2 figures, preprint submitted to Physica

Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

Solar type II radio bursts associated with CME expansions as shown by EUV waves

We investigate the physical conditions of the sources of two metric Type-II bursts associated with CME expansions with the aim of verifying the relationship between the shocks and the CMEs, comparing the heights of the radio sources and the heights of the EUV waves associated with the CMEs. The heights of the EUV waves associated with the events were determined in relation to the wave fronts. The heights of the shocks were estimated by applying two different density models to the frequencies of the Type-II emissions and compared with the heights of the EUV waves. For the 13 June 2010 event, with band-splitting, the shock speed was estimated from the frequency drifts of the upper and lower branches of the harmonic lane, taking into account the H/F frequency ratio fH/fF = 2. Exponential fits on the intensity maxima of the branches revealed to be more consistent with the morphology of the spectrum of this event. For the 6 June 2012 event, with no band-splitting and with a clear fundamental lane on the spectrum, the shock speed was estimated directly from the frequency drift of the fundamental emission, determined by linear fit on the intensity maxima of the lane. For each event, the most appropriate density model was adopted to estimate the physical parameters of the radio source. The 13 June 2010 event presented a shock speed of 664-719 km/s, consistent with the average speed of the EUV wave fronts of 609 km/s. The 6 June 2012 event was related to a shock of speed of 211-461 km/s, also consistent with the average speed of the EUV wave fronts of 418 km/s. For both events, the heights of the EUV wave revealed to be compatible with the heights of the radio source, assuming a radial propagation of the shock.Comment: Accepted for publication in Astronomy and Astrophysic

Meson decay in the Fock-Tani Formalism

The Fock-Tani formalism is a first principle method to obtain effective interactions from microscopic Hamiltonians. Usually this formalism was applied to scattering, here we introduced it to calculate partial decay widths for mesons.Comment: Presented at HADRON05 XI. "International Conference on Hadron Spectroscopy" Rio de Janeiro, Brazil, August 21 to 26, 200

A potential library for primary MFL pedagogy: the case of Young Pathfinders

As readers of this journal will know very well, 2010 will see all KS2 (ages 7-11) pupils in England entitled to learn a modern foreign language in normal curriculum time. This development of the commitment to primary language learning should provide an excellent opportunity and experience for pupils, whilst at the same time requiring some radical changes for many teachers, schools and much of the wider language learning community. Recent research has indicated general trends suggesting an increase in primary languages already, in anticipation of this development and even beforehand. One of the most recent studies indicates that 43% of primary children currently learn a foreign language at KS2, either in class or as an extra-curricular activity, although the extent of this learning varies considerably (Driscoll, Jones and Macrory, 2004). It has also been suggested (Muijs et al, 2005) that there are certain aspects of the process that will be particularly demanding if the challenge of providing this entitlement are to be met