63,075 research outputs found
An Introduction to Conformal Ricci Flow
We introduce a variation of the classical Ricci flow equation that modifies
the unit volume constraint of that equation to a scalar curvature constraint.
The resulting equations are named the Conformal Ricci Flow Equations because of
the role that conformal geometry plays in constraining the scalar curvature.
These equations are analogous to the incompressible Navier-Stokes equations of
fluid mechanics inasmuch as a conformal pressure arises as a Lagrange
multiplier to conformally deform the metric flow so as to maintain the scalar
curvature constraint. The equilibrium points are Einstein metrics with a
negative Einstein constant and the conformal pressue is shown to be zero at an
equilibrium point and strictly positive otherwise. The geometry of the
conformal Ricci flow is discussed as well as the remarkable analytic fact that
the constraint force does not lose derivatives and thus analytically the
conformal Ricci equation is a bounded perturbation of the classical
unnormalized Ricci equation. That the constraint force does not lose
derivatives is exactly analogous to the fact that the real physical pressure
force that occurs in the Navier-Stokes equations is a bounded function of the
velocity. Using a nonlinear Trotter product formula, existence and uniqueness
of solutions to the conformal Ricci flow equations is proven. Lastly, we
discuss potential applications to Perelman's proposed implementation of
Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur
What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement
The infrared behaviour of Landau gauge QCD vertex functions is investigated
employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group
equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon
vertex functions are presented. Positivity violation of the gluon propagator,
and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger
equations for a finite volume are compared to corresponding lattice data. It is
analytically demonstrated that a linear rising potential between heavy quarks
can be generated by infrared singularities in the dressed quark-gluon vertex.
The selfconsistent mechanism that generates these singularities necessarily
entails the scalar Dirac amplitudes of the full vertex and the quark
propagator. These can only be present when chiral symmetry is broken, either
explicitly or dynamically.Comment: 13 pages, 13 figures; to appear in the Proceedings of ``X Hadron
Physics 2007'', Florianopolis, Brazil, March 26 - 31, 200
Speed Limits in General Relativity
Some standard results on the initial value problem of general relativity in
matter are reviewed. These results are applied first to show that in a well
defined sense, finite perturbations in the gravitational field travel no faster
than light, and second to show that it is impossible to construct a warp drive
as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum
Gravit
Hybridization and spin decoherence in heavy-hole quantum dots
We theoretically investigate the spin dynamics of a heavy hole confined to an
unstrained III-V semiconductor quantum dot and interacting with a narrowed
nuclear-spin bath. We show that band hybridization leads to an exponential
decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips,
and that the accordant single-hole-spin decoherence time T2 can be tuned over
many orders of magnitude by changing external parameters. In particular, we
show that, under experimentally accessible conditions, it is possible to
suppress hyperfine-mediated nuclear-pair-flip processes so strongly that
hole-spin quantum dots may be operated beyond the `ultimate limitation' set by
the hyperfine interaction which is present in other spin-qubit candidate
systems.Comment: 7 pages, 3 figure
Sub-10 nm colloidal lithography for integrated spin-photo-electronic devices
Colloidal lithography [1] is how patterns are reproduced in a variety of
natural systems and is used more and more as an efficient fabrication tool in
bio-, opto-, and nano-technology. Nanoparticles in the colloid are made to form
a mask on a given material surface, which can then be transferred via etching
into nano-structures of various sizes, shapes, and patterns [2,3]. Such
nanostructures can be used in biology for detecting proteins [4] and DNA [5,6],
for producing artificial crystals in photonics [7,8] and GHz oscillators in
spin-electronics [9-14]. Scaling of colloidal patterning down to 10-nm and
below, dimensions comparable or smaller than the main relaxation lengths in the
relevant materials, including metals, is expected to enable a variety of new
ballistic transport and photonic devices, such as spin-flip THz lasers [15]. In
this work we extend the practice of colloidal lithography to producing
large-area, near-ballistic-injection, sub-10 nm point-contact arrays and
demonstrate their integration in to spin-photo-electronic devices.Comment: 15 pages, 5 figure
A Search for Lost Planets in the Kepler Multi-planet Systems and the Discovery of the Long-period, Neptune-sized Exoplanet Kepler-150 f
The vast majority of the 4700 confirmed planets and planet candidates
discovered by the Kepler mission were first found by the Kepler pipeline. In
the pipeline, after a transit signal is found, all data points associated with
those transits are removed, creating a "Swiss cheese"-like light curve full of
holes, which is then used for subsequent transit searches. These holes could
render an additional planet undetectable (or "lost"). We examine a sample of
114 stars with confirmed planets to evaluate the effect of this "Swiss
cheesing". A simulation determines that the probability that a transiting
planet is lost due to the transit masking is low, but non-negligible, reaching
a plateau at lost in the period range of days. We then
model all planet transits and subtract out the transit signals for each star,
restoring the in-transit data points, and use the Kepler pipeline to search the
transit-subtracted (i.e., transit-cleaned) light curves. However, the pipeline
did not discover any credible new transit signals. This demonstrates the
validity and robustness of the Kepler pipeline's choice to use transit masking
over transit subtraction. However, a follow-up visual search through all the
transit-subtracted data, which allows for easier visual identification of new
transits, revealed the existence of a new, Neptune-sized exoplanet (Kepler-150
f) and a potential single transit of a likely false positive (Kepler-208).
Kepler-150 f ( days, R)
is confirmed with confidence using a combination of the planet
multiplicity argument, a false positive probability analysis, and a transit
duration analysis.Comment: 11 pages, 5 figures, 2 tables. Accepted into A
QCD Propagators at non-vanishing temperatures
We investigate the behaviour of the gluon and ghost propagators, especially
their infrared properties, at non-vanishing temperatures. To this end we solve
their Dyson-Schwinger equations on a torus and find an infrared enhanced ghost
propagator and an infrared vanishing gluon propagator.Comment: 2 pages, 2 figures; talk given by B.G. at the Erice summer school on
Nuclear Physics, Sept. 16 -- 24, 2003, Erice, Ital
Perturbations of Spatially Closed Bianchi III Spacetimes
Motivated by the recent interest in dynamical properties of topologically
nontrivial spacetimes, we study linear perturbations of spatially closed
Bianchi III vacuum spacetimes, whose spatial topology is the direct product of
a higher genus surface and the circle. We first develop necessary mode
functions, vectors, and tensors, and then perform separations of (perturbation)
variables. The perturbation equations decouple in a way that is similar to but
a generalization of those of the Regge--Wheeler spherically symmetric case. We
further achieve a decoupling of each set of perturbation equations into
gauge-dependent and independent parts, by which we obtain wave equations for
the gauge-invariant variables. We then discuss choices of gauge and stability
properties. Details of the compactification of Bianchi III manifolds and
spacetimes are presented in an appendix. In the other appendices we study
scalar field and electromagnetic equations on the same background to compare
asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear
in Class. Quant. Gravi
Testing of pear trees on their own roots in comparison with important used rootstocks under organic farming conditions with special regard to fire blight (E. amylovora)
Pear trees on their own roots are tested in comparison to grafted trees in growth and yield
characteristics and with special regard to the tolerance to diseases, above all fire blight
(Erwinia amylovora). In spring 2004 15 randomized trees of the cultivar 'Williams' from
three variants (self rooted in vitro, self rooted long cuttings, grafted on Quince A) were
planted in a pear orchard, which was heavily infected with fire blight (Erwinia amylovora)
the previous years. The trees were left untreated. Growth and yield characteristics, plant
diseases and tree losses were observed. After four years the in vitro self rooted trees were
significantly more vigorous in growth than those grafted on quince A. The self rooted long
cuttings were comparable in growth with grafts on quince, but showed high tree losses
probably due to frost damages in the first winter one year after planting. However no
infections with Erwinia amylovora could be observed so far. In a field trial with more
cultivars and rootstock variants planted in 2006 at two organically managed sites more
significant effects are expected in the next years
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