20,595 research outputs found
On Effective Constraints for the Riemann-Lanczos System of Equations
There have been conflicting points of view concerning the Riemann--Lanczos
problem in 3 and 4 dimensions. Using direct differentiation on the defining
partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar
(in dimensions n > 2) have argued that there are effective constraints so that
not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of
integrability of ideals of differential forms Bampi and Caviglia have argued
that there are no such constraints in dimensions n < 5, and that, in these
dimensions, all Riemann tensors can have Lanczos potentials. In this paper we
give a simple direct derivation of a constraint equation, confirm explicitly
that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue
that the Bampi and Caviglia conclusion must therefore be flawed. In support of
this, we refer to the recent work of Dolan and Gerber on the three dimensional
problem; by a method closely related to that of Bampi and Caviglia, they have
found an 'internal identity' which we demonstrate is precisely the three
dimensional version of the effective constraint originally found by Massa and
Pagani, and Edgar.Comment: 9pages, Te
Formation and morphology of anomalous solar circular polarization
The morphology of spectral line polarization is the most valuable observable
to investigate the magnetic and dynamic solar atmosphere. However, in order to
develop solar diagnosis, it is fundamental to understand the different kinds of
anomalous solar signals that have been routinely found in linear and circular
polarization (LP,CP). The goal of this paper has been to explain and
characterize the morphology of solar CP signals by understanding the combined
effect of magnetic fields, velocity gradients, and atomic orientation in
general NLTE regime. To that aim, an analytical two-layer model of the
polarized radiative transfer equation is developed and used to solve the NLTE
problem with atomic polarization in a semi-parametric way. The formation of
polarization is thus insightfully described with certain precision without
resorting in MHD models or sacrifying key physical ingredients. The potential
of the model for reproducing solar anomalous CP is shown with detailed
calculations. The essential physical behavior of dichroism and atomic
orientation is described, introducing the concepts of dichroic inversion,
neutral and reinforcing medium, critic intensity spectrum, and critic source
function. It is shown that the zero-crossings of the CP spectrum are useful to
classify its morphology and understand its formation. This led to identify and
explain the morphology of the seven most characteristics CP signals that a
single (depth-resolved) scattering layer can produce. Futhermore, it is found
that a minimal number of two magnetic layers along the LOS is required to fully
explain anomalous solar CP signals, and that the morphology and polarity of
Stokes V depends on magnetic, radiative and atomic polarities. Some
implications of these results are presented through a preliminar modeling of
anomalous CP signals in the Na I D and Fe I 1564.8 nm lines.Comment: 18 pages, 18 figures. Accepted for publication in A&A. Typos and
language correcte
The Lanczos potential for Weyl-candidate tensors exists only in four dimensions
We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd
does not generally exist for dimensions higher than four. The technique is
simply to assume the existence of such a potential in dimension n, and then
check the integrability conditions for the assumed system of differential
equations; if the integrability conditions yield another non-trivial
differential system for L_abc and W_abcd, then this system's integrability
conditions should be checked; and so on. When we find a non-trivial condition
involving only W_abcd and its derivatives, then clearly Weyl candidate tensors
failing to satisfy that condition cannot be written in terms of a Lanczos
potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200
A Grounded theory study of the job-seeking experiences of foreign graduates on the German job market
Old and new results for superenergy tensors from dimensionally dependent tensor identities
It is known that some results for spinors, and in particular for superenergy
spinors, are much less transparent and require a lot more effort to establish,
when considered from the tensor viewpoint. In this paper we demonstrate how the
use of dimensionally dependent tensor identities enables us to derive a number
of 4-dimensional identities by straightforward tensor methods in a signature
independent manner. In particular, we consider the quadratic identity for the
Bel-Robinson tensor and also the new conservation laws for the
Chevreton tensor, both of which have been obtained by spinor means; both of
these results are rederived by {\it tensor} means for 4-dimensional spaces of
any signature, using dimensionally dependent identities, and also we are able
to conclude that there are no {\it direct} higher dimensional analogues. In
addition we demonstrate a simple way to show non-existense of such identities
via counter examples; in particular we show that there is no non-trivial Bel
tensor analogue of this simple Bel-Robinson tensor quadratic identity. On the
other hand, as a sample of the power of generalising dimensionally dependent
tensor identities from four to higher dimensions, we show that the symmetry
structure, trace-free and divergence-free nature of the four dimensional
Bel-Robinson tensor does have an analogue for a class of tensors in higher
dimensions.Comment: 18 pages; TeX fil
Obtaining a class of Type N pure radiation metrics using invariant operators
We develop further the integration procedure in the generalised invariant
formalism, and demonstrate its efficiency by obtaining a class of Petrov type N
pure radiation metrics without any explicit integration, and with comparatively
little detailed calculations. The method is similar to the one exploited by
Edgar and Vickers when deriving the general conformally flat pure radiation
metric. A major addition to the technique is the introduction of non-intrinsic
elements in generalised invariant formalism, which can be exploited to keep
calculations manageable.Comment: This work was presented in July 2004, in the Gr17 meeting held in
Dublin-Irelan
Hypergeometric L-functions in average polynomial time
We describe an algorithm for computing, for all primes , the
mod- reduction of the trace of Frobenius at of a fixed hypergeometric
motive in time quasilinear in . This combines the Beukers--Cohen--Mellit
trace formula with average polynomial time techniques of Harvey et al.Comment: 15 pages, 1 figure; v4 several exposition improvements as suggested
the referee
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