13,032 research outputs found
Descent Via Isogeny on Elliptic Curves with Large Rational Torsion Subgroups.
We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities which aid the computation of members of the Tate-Shafarevich group. We apply these techniques to several examples: in one case we use descent via 9-isogeny to determine the rank of an elliptic curve; in another case we find nontrivial members of the 9-part of the Tate-Shafarevich group, and in a further case, nontrivial members of the 13-part of the Tate-Shafarevich group
K dwarfs and the chemical evolution of the Solar cylinder
K-dwarfs have life-times older than the present age of the Galactic disc, and
are thus ideal stars to investigate the disc's chemical evolution. We have
developed several photometric metallicity indicators for K dwarfs, based an a
sample of accurate spectroscopic metallicities for 34 disc and halo G and K
dwarfs. The photometric metallicities lead us to develop a metallicity index
for K dwarfs based only on their position in the colour absolute-magnitude
diagram. Metallicities have been determined for 431 single K dwarfs drawn from
the Hipparcos catalog, selecting the stars by absolute magnitude and removing
multiple systems. The sample is essentially a complete reckoning of the metal
content in nearby K dwarfs. We use stellar isochrones to mark the stars by
mass, and select a subset of 220 of the stars which is complete in a narrow
mass interval. We fit the data with a model of the chemical evolution of the
Solar cylinder. We find that only a modest cosmic scatter is required to fit
our age metallicity relation. The model assumes two main infall episodes for
the formation of the halo-thick disc and thin disc respectively. The new data
confirms that the solar neighbourhood formed on a long timescale of order 7
Gyr.Comment: 14 pages, 15 figures, accepted by MNRA
Heavy Quark Physics From Lattice QCD
We review the application of lattice QCD to the phenomenology of b- and
c-quarks. After a short discussion of the lattice techniques used to evaluate
hadronic matrix elements and the corresponding systematic uncertainties, we
summarise results for leptonic decay constants, B--Bbar mixing, semileptonic
and rare radiative decays. A discussion of the determination of heavy quark
effective theory parameters is followed by an explanation of the difficulty in
applying lattice methods to exclusive nonleptonic decays.Comment: 52 pages LaTeX with 10 eps files. Requires: hfsprocl.sty (included)
plus axodraw.sty, rotating.sty and array.sty. To appear in Heavy Flavours
(2nd edition) edited by A J Buras and M Lindner (World Scientific,
Singapore). Revised version corrects typo in axis labelling of Fig 1
Accurate fundamental parameters for Lower Main Sequence Stars
We derive an empirical effective temperature and bolometric luminosity
calibration for G and K dwarfs, by applying our own implementation of the
InfraRed Flux Method to multi-band photometry. Our study is based on 104 stars
for which we have excellent BVRIJHK photometry, excellent parallaxes and good
metallicities. Colours computed from the most recent synthetic libraries
(ATLAS9 and MARCS) are found to be in good agreement with the empirical colours
in the optical bands, but some discrepancies still remain in the infrared.
Synthetic and empirical bolometric corrections also show fair agreement. A
careful comparison to temperatures, luminosities and angular diameters obtained
with other methods in literature shows that systematic effects still exist in
the calibrations at the level of a few percent. Our InfraRed Flux Method
temperature scale is 100K hotter than recent analogous determinations in the
literature, but is in agreement with spectroscopically calibrated temperature
scales and fits well the colours of the Sun. Our angular diameters are
typically 3% smaller when compared to other (indirect) determinations of
angular diameter for such stars, but are consistent with the limb-darkening
corrected predictions of the latest 3D model atmospheres and also with the
results of asteroseismology. Very tight empirical relations are derived for
bolometric luminosity, effective temperature and angular diameter from
photometric indices. We find that much of the discrepancy with other
temperature scales and the uncertainties in the infrared synthetic colours
arise from the uncertainties in the use of Vega as the flux calibrator. Angular
diameter measurements for a well chosen set of G and K dwarfs would go a long
way to addressing this problem.Comment: 34 pages, 20 figures. Accepted by MNRAS. Landscape table available
online at http://users.utu.fi/luccas/IRFM
A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored
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