7,634 research outputs found
Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
We determine, for all three-dimensional non-unimodular Lie groups equipped
with a Lorentzian metric, the set of homogeneous geodesics through a point.
Together with the results of [C] and [CM2], this leads to the full
classification of three-dimensional Lorentzian g.o. spaces and naturally
reductive spaces
Coherent states for a particle on a sphere
The coherent states for a particle on a sphere are introduced. These states
are labelled by points of the classical phase space, that is the position on
the sphere and the angular momentum of a particle. As with the coherent states
for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J.
Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space
related with quantum fluctuations. The expectation values of the position and
the angular momentum in the coherent states are regarded as the best possible
approximation of the classical phase space. The correctness of the introduced
coherent states is illustrated by an example of the rotator.Comment: LaTeX, 16 pages, 2 figure
Homogeneity and plane-wave limits
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave
limits along homogeneous geodesics the limit is known to be homogeneous and we
exhibit the limiting metric in terms of Lie algebraic data. This simplifies
many calculations and we illustrate this with several examples. We also
investigate the behaviour of (reductive) homogeneous structures under the
plane-wave limit.Comment: In memory of Stanley Hobert, 33 pages. Minor corrections and some
simplification of Section 4.3.
Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of
signature (2s,s) which are not locally homogeneous but whose curvature tensors
never the less exhibit a number of important symmetry properties. They are
curvature homogeneous; their curvature tensor is modeled on that of a local
symmetric space. They are spacelike Jordan Osserman with a Jacobi operator
which is nilpotent of order 3; they are not timelike Jordan Osserman. They are
k-spacelike higher order Jordan Osserman for ; they are k-timelike
higher order Jordan Osserman for , and they are not k timelike
higher order Jordan Osserman for .Comment: Update bibliography, fix minor misprint
Investment in Latin America Will Limit Migration North
The refugee crisis at the US Southern Border is due to multiple compounding factors: Latin Americaâs over-reliance on commodities, failure to economically diversify to innovation, and a lack of coherent US strategic engagement with the region. The situation is hemispheric; imploding states and a serious humanitarian calamity loom ever larger on the southern horizon. Since this represents a long-term problem requiring strategic and sustainable development initiatives, a new Alliance for Progress for the 21st Century is proposed which will build partnerships to advance innovation-driven development across the region
First Detection of a Strong Magnetic Field on a Bursty Brown Dwarf: Puzzle Solved
We report the first direct detection of a strong, 5 kG magnetic field on the
surface of an active brown dwarf. LSR J1835+3259 is an M8.5 dwarf exhibiting
transient radio and optical emission bursts modulated by fast rotation. We have
detected the surface magnetic field as circularly polarized signatures in the
819 nm sodium lines when an active emission region faced the Earth. Modeling
Stokes profiles of these lines reveals the effective temperature of 2800 K and
log gravity acceleration of 4.5. These parameters place LSR J1835+3259 on
evolutionary tracks as a young brown dwarf with the mass of 554 M and age of 224 Myr. Its magnetic field is at least 5.1 kG and covers
at least 11% of the visible hemisphere. The active region topology recovered
using line profile inversions comprises hot plasma loops with a vertical
stratification of optical and radio emission sources. These loops rotate with
the dwarf in and out of view causing periodic emission bursts. The magnetic
field is detected at the base of the loops. This is the first time that we can
quantitatively associate brown dwarf non-thermal bursts with a strong, 5 kG
surface magnetic field and solve the puzzle of their driving mechanism. This is
also the coolest known dwarf with such a strong surface magnetic field. The
young age of LSR J1835+3259 implies that it may still maintain a disk, which
may facilitate bursts via magnetospheric accretion, like in higher-mass T
Tau-type stars. Our results pave a path toward magnetic studies of brown dwarfs
and hot Jupiters.Comment: ApJ, in pres
The relativistic massless harmonic oscillator
A detailed study of the relativistic classical and quantum mechanics of the
massless harmonic oscillator is presented.Comment: 15 pages, 4 figure
Distributed Deterministic Broadcasting in Uniform-Power Ad Hoc Wireless Networks
Development of many futuristic technologies, such as MANET, VANET, iThings,
nano-devices, depend on efficient distributed communication protocols in
multi-hop ad hoc networks. A vast majority of research in this area focus on
design heuristic protocols, and analyze their performance by simulations on
networks generated randomly or obtained in practical measurements of some
(usually small-size) wireless networks. %some library. Moreover, they often
assume access to truly random sources, which is often not reasonable in case of
wireless devices. In this work we use a formal framework to study the problem
of broadcasting and its time complexity in any two dimensional Euclidean
wireless network with uniform transmission powers. For the analysis, we
consider two popular models of ad hoc networks based on the
Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links,
and the other with randomly disturbed SINR. In the former model, we show that
one of our algorithms accomplishes broadcasting in rounds, where
is the number of nodes and is the diameter of the network. If nodes
know a priori the granularity of the network, i.e., the inverse of the
maximum transmission range over the minimum distance between any two stations,
a modification of this algorithm accomplishes broadcasting in
rounds.
Finally, we modify both algorithms to make them efficient in the latter model
with randomly disturbed SINR, with only logarithmic growth of performance.
Ours are the first provably efficient and well-scalable, under the two
models, distributed deterministic solutions for the broadcast task.Comment: arXiv admin note: substantial text overlap with arXiv:1207.673
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