26,785 research outputs found
Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave
Coulomb wave functions are difficult to compute numerically for extremely low
energies, even with direct numerical integration. Hence, it is more convenient
to use asymptotic formulas in this region. It is the object of this paper to
derive analytical asymptotic formulas valid for arbitrary energies and partial
waves. Moreover, it is possible to extend these formulas for complex values of
parameters.Comment: 5 pages, 2 figure
Structure of smectic defect cores: an X-ray study of 8CB liquid crystal ultra-thin films
We study the structure of very thin liquid crystal films frustrated by
antagonistic anchorings in the smectic phase. In a cylindrical geometry, the
structure is dominated by the defects for film thicknesses smaller than 150 nm
and the detailed topology of the defects cores can be revealed by x-ray
diffraction. They appear to be split in half tube-shaped Rotating Grain
Boundaries (RGB). We determine the RGB spatial extension and evaluate its
energy per unit line. Both are significantly larger than the ones usually
proposed in the literatureComment: 4 page
Polynomial Relations in the Centre of U_q(sl(N))
When the parameter of deformation q is a m-th root of unity, the centre of
U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new
generators, which are basically the m-th powers of all the Cartan generators of
U_q(sl(N)). All these central elements are however not independent. In this
letter, generalising the well-known case of U_q(sl(2)), we explicitly write
polynomial relations satisfied by the generators of the centre. Application to
the parametrization of irreducible representations and to fusion rules are
sketched.Comment: 8 pages, minor TeXnical revision to allow automatic TeXin
Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites
In conventional approaches to the homogenization of random particulate
composites, both the distribution and size of the component phase particles are
often inadequately taken into account. Commonly, the spatial distributions are
characterized by volume fraction alone, while the electromagnetic response of
each component particle is represented as a vanishingly small depolarization
volume. The strong-permittivity-fluctuation theory (SPFT) provides an
alternative approach to homogenization wherein a comprehensive description of
distributional statistics of the component phases is accommodated. The
bilocally-approximated SPFT is presented here for the anisotropic homogenized
composite which arises from component phases comprising ellipsoidal particles.
The distribution of the component phases is characterized by a two-point
correlation function and its associated correlation length. Each component
phase particle is represented as an ellipsoidal depolarization region of
nonzero volume. The effects of depolarization volume and correlation length are
investigated through considering representative numerical examples. It is
demonstrated that both the spatial extent of the component phase particles and
their spatial distributions are important factors in estimating coherent
scattering losses of the macroscopic field.Comment: Typographical error in eqn. 16 in WRM version is corrected in arxiv
versio
Partial discharge testing of defective three-phase PILC cable under rated conditions
The ability to accurately monitor the health of power distribution plant is a very attractive prospect for utility companies. This capability would provide a system that engineers could use to assess the real-time state of the network. Analysis of the data produced could allow for more informed decisions to be made in the areas of asset replacement and maintenance scheduling amongst others. It is widely accepted that partial discharge activity is linked with the electrical ageing/degradation of high voltage equipment. Work at Southampton is focused on obtaining a better understanding of the characteristics and trends of partial discharge events associated with medium voltage cables under, 'real life' conditions. An experiment has been developed that allows for service conditions to be applied to defective paper insulated lead covered cable samples. The samples under investigation were exposed to mechanical damage designed to replicate typical problems found on an active circuit. Partial discharge measurement was undertaken during the stressing process
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