89,577 research outputs found
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
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