71,330 research outputs found
The principle of equivalence and projective structure in space-times
This paper discusses the extent to which one can determine the space-time
metric from a knowledge of a certain subset of the (unparametrised) geodesics
of its Levi-Civita connection, that is, from the experimental evidence of the
equivalence principle. It is shown that, if the space-time concerned is known
to be vacuum, then the Levi-Civita connection is uniquely determined and its
associated metric is uniquely determined up to a choice of units of
measurement, by the specification of these geodesics. It is further
demonstrated that if two space-times share the same unparametrised geodesics
and only one is assumed vacuum then their Levi-Civita connections are again
equal (and so the other metric is also a vacuum metric) and the first result
above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit
On the Theory of Killing Orbits in Space-Time
This paper gives a theoretical discussion of the orbits and isotropies which
arise in a space-time which admits a Lie algebra of Killing vector fields. The
submanifold structure of the orbits is explored together with their induced
Killing vector structure. A general decomposition of a space-time in terms of
the nature and dimension of its orbits is given and the concept of stability
and instability for orbits introduced. A general relation is shown linking the
dimensions of the Killing algebra, the orbits and the isotropies. The
well-behaved nature of "stable" orbits and the possible miss-behaviour of the
"unstable" ones is pointed out and, in particular, the fact that independent
Killing vector fields in space-time may not induce independent such vector
fields on unstable orbits. Several examples are presented to exhibit these
features. Finally, an appendix is given which revisits and attempts to clarify
the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur
A new species of Colletes (Hymenoptera: Apoidea: Colletidae) from northern Florida and Georgia, with notes on the Colletes of those states
Colletes ultravalidus Hall & Ascher, new species, is described from several sites in northwestern Florida and southeastern Georgia. It is a member of the inaequalis species group, very similar to C. validus Cresson, a specialist of Ericaceae, but can be distinguished by an even more elongate malar area and the absence of conspicuous tergal fascia. Colletes ultravalidus has been found flying from early winter to early spring when it forms nest aggregations in xeric sites adjacent to shrub bog or basin swamp, the habitat of Pieris phyllyreifolia (Hook.) DC. (Ericaceae), the most likely, but as yet unconfirmed, host plant of the new species. State records of Colletes for Florida and Georgia are reviewed and discrepancies in taxonomy and distributional limits between Stephen’s 1954 revision of the genus and Mitchell’s 1960 monograph of eastern North American bees are noted. We concur with Stephen that the distributions of several taxa in Colletes are more limited than that reported by Mitchell
Fish -- More Than Just Another Commodity
This brief highlights the contribution of wild capture fisheries to nutritional security in fish dependent developing countries. It is intended to stimulate debate around two broad themes: (1) when should the focus of fisheries policies be on local food security and human well-being as opposed to revenue generation, and (2) how does the current research agenda, with its emphasis on environmental and economic issues, assist or impair decision making processes
Coulomb plus power-law potentials in quantum mechanics
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the
Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q >
-2 and q \ne 0. We show by envelope theory that the discrete eigenvalues
E_{n\ell} of H may be approximated by the semiclassical expression
E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.
Values of mu and nu are prescribed which yield upper and lower bounds.
Accurate upper bounds are also obtained by use of a trial function of the form,
psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for
V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with
comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure
Decay of an isolated monopole into a Dirac monopole configuration
We study numerically the detailed structure and decay dynamics of isolated
monopoles in conditions similar to those of their recent experimental
discovery. We find that the core of a monopole in the polar phase of a spin-1
Bose-Einstein condensate contains a small half-quantum vortex ring. Well after
the creation of the monopole, we observe a dynamical quantum phase transition
that destroys the polar phase. Strikingly, the resulting ferromagnetic order
parameter exhibits a Dirac monopole in its synthetic magnetic field.Comment: 6 pages, 5 figure
Radiobiological studies with monoenergetic neutrons
The Radiological Research Accelerator Facility (RARAF) has the capability of
producing essentially monoenergetic neutron beams, ranging in energy from 16.4 MeV
down to 220 keV. In addition, two lower energy neutron beams are available which
consist of a wide spectrum of energies and are described as the 110 keV and 60 keV
spectra. Seedlings of Vicia faba have been used to measure the oxygen enhancement
ratio (OER) and the relative biological effectiveness (RBE) of each of these neutron
beams. The OER decreases as the neutron energy is reduced between 15.4 MeV and
220 keV, but does not appear to decrease further for lower energy neutrons. RBE increases
as the neutron energy is reduced from 15.4 AleV to 440 keV; the curve then
goes through a maximum at around 350 keV, and for lower energies the RBE falls again
Semiclassical energy formulas for power-law and log potentials in quantum mechanics
We study a single particle which obeys non-relativistic quantum mechanics in
R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2,
then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may
be represented exactly by the semiclassical expression E_{n\ell}(q) =
min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) =
ln(r). By writing one power as a smooth transformation of another, and using
envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are
monotone increasing. Recent refinements to the comparison theorem of QM in
which comparison potentials can cross over, allow us to prove for n = 1 that
Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q}
is monotone decreasing. Thus P(q) cannot increase too slowly. This result
yields some sharper estimates for power-potential eigenvlaues at the bottom of
each angular-momentum subspace.Comment: 20 pages, 5 figure
The School Improvement Partnership Programme: Using Collaboration and Enquiry to tackle Educational Inequity
No abstract available
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