83 research outputs found
Global Hopf bifurcation in the ZIP regulatory system
Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been
modeled by a system of ordinary differential equations based on the uptake of
zinc, expression of a transporter protein and the interaction between an
activator and inhibitor. For certain parameter choices the steady state of this
model becomes unstable upon variation in the external zinc concentration.
Numerical results show periodic orbits emerging between two critical values of
the external zinc concentration. Here we show the existence of a global Hopf
bifurcation with a continuous family of stable periodic orbits between two Hopf
bifurcation points. The stability of the orbits in a neighborhood of the
bifurcation points is analyzed by deriving the normal form, while the stability
of the orbits in the global continuation is shown by calculation of the Floquet
multipliers. From a biological point of view, stable periodic orbits lead to
potentially toxic zinc peaks in plant cells. Buffering is believed to be an
efficient way to deal with strong transient variations in zinc supply. We
extend the model by a buffer reaction and analyze the stability of the steady
state in dependence of the properties of this reaction. We find that a large
enough equilibrium constant of the buffering reaction stabilizes the steady
state and prevents the development of oscillations. Hence, our results suggest
that buffering has a key role in the dynamics of zinc homeostasis in plant
cells.Comment: 22 pages, 5 figures, uses svjour3.cl
Generalized N=1 Orientifold Compactifications and the Hitchin functionals
The four-dimensional N=1 supergravity theories arising in compactifications
of type IIA and type IIB on generalized orientifold backgrounds with background
fluxes are discussed. The Kahler potentials are derived for reductions on SU(3)
structure orientifolds and shown to consist of the logarithm of the two Hitchin
functionals. These are functions of even and odd forms parameterizing the
geometry of the internal manifold, the B-field and the dilaton. The
superpotentials induced by background fluxes and the non-Calabi-Yau geometry
are determined by a reduction of the type IIA and type IIB fermionic actions on
SU(3) and generalized SU(3) x SU(3) manifolds. Mirror spaces of Calabi-Yau
orientifolds with electric and part of the magnetic NS-NS fluxes are
conjectured to be certain SU(3) x SU(3) structure manifolds. Evidence for this
identification is provided by comparing the generalized type IIA and type IIB
superpotentials.Comment: 57 pages, references adde
Geometric Transitions on non-Kaehler Manifolds
This article is based on the author's PhD--thesis. We study geometric
transitions on the supergravity level using the basic idea of
arXiv:hep-th/0403288, where a pair of non-Kaehler backgrounds was constructed,
which are related by a geometric transition. Here we embed this idea into an
orientifold setup as suggested in arXiv:hep-th/0511099. The non-Kaehler
backgrounds we obtain in type IIA are non-trivially fibered due to their
construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate
that these non-Kaehler manifolds are not half-flat and show that a symplectic
structure exists on them at least locally.
We also review the construction of new non-Kaehler backgrounds in type I and
heterotic theory as proposed in arXiv:hep-th/0408192. They are found by a
series of T- and S-duality and can be argued to be related by geometric
transitions as well. A local toy model is provided that fulfills the flux
equations of motion in IIB and the torsional relation in heterotic theory, and
that is consistent with the U-duality relating both theories. For the heterotic
theory we also propose a global solution that fulfills the torsional relation
because it is similar to the Maldacena-Nunez background.Comment: 127 pages, based on PhD-thesis, v2 some references added, this
version to appear in Fort. Phy
The Most Probable Size of the Universe
It has recently been suggested, by Firouzjahi, Sarangi, and Tye, that
string-motivated modifications of the Hartle-Hawking wave function predict that
our Universe came into existence from "nothing" with a de Sitter-like spacetime
geometry and a spacetime curvature similar to that of "low-scale" models of
Inflation. This means, however, that the Universe was quite large at birth. It
would be preferable for the initial scale to be close to the string scale, or
perhaps the Planck scale. The problem with this, however, is to explain how any
initial homogeneity is preserved during the pre-inflationary era, so that
Inflation can indeed begin. Here we modify a suggestion due to Linde and assume
that the Universe was born with the topology of a torus; however, we propose
that the size of the torus is to be predicted by the FST wave function. The
latter does predict an initial size for the torus at about the string scale,
and it also predicts a pre-inflationary spacetime geometry such that chaotic
mixing preserves any initial homogeneity until Inflation can begin at a
relatively low scale.Comment: References added; accepted by Nuclear Physics
Pre-Inflationary Spacetime in String Cosmology
Seiberg and Witten have shown that the non-perturbative stability of string
physics on conformally compactified spacetimes is related to the behaviour of
the areas and volumes of certain branes as the brane is moved towards infinity.
If, as is particularly natural in quantum cosmology, the spatial sections of an
accelerating cosmological model are flat and compact, then the spacetime is on
the brink of disaster: it turns out that the version of inflationary spacetime
geometry with toral spatial sections is marginally stable in the Seiberg-Witten
sense. The question is whether the system remains stable before and after
Inflation, when the spacetime geometry is distorted away from the inflationary
form but still has flat spatial sections. We show that it is indeed possible to
avoid disaster, but that requiring stability at all times imposes non-trivial
conditions on the spacetime geometry of the early Universe in string cosmology.
This in turn allows us to suggest a candidate for the structure which, in the
earliest Universe, forbids cosmological singularities.Comment: Final version to appear in NPB, 27 pages including 1 eps figur
Accidental Inflation in String Theory
We show that inflation in type IIB string theory driven by the volume modulus
can be realized in the context of the racetrack-based Kallosh-Linde model (KL)
of moduli stabilization. Inflation here arises through the volume modulus
slow-rolling down from a flat hill-top or inflection point of the scalar
potential. This situation can be quite generic in the landscape, where by
uplifting one of the two adjacent minima one can turn the barrier either to a
flat saddle point or to an inflection point supporting eternal inflation. The
resulting spectral index is tunable in the range of 0.93 < n_s < 1, and there
is only negligible production of primordial gravitational waves r < 10^{-6}.
The flatness of the potential in this scenario requires fine-tuning, which may
be justified taking into account the exponential reward by volume factors
preferring the regions of the universe with the maximal amount of slow-roll
inflation. This consideration leads to a tentative prediction of the spectral
index or depending on whether the
potential has a symmetry phi -> - phi or not.Comment: 15 pages, 6 figures, LaTeX, uses RevTex
LSST: from Science Drivers to Reference Design and Anticipated Data Products
(Abridged) We describe here the most ambitious survey currently planned in
the optical, the Large Synoptic Survey Telescope (LSST). A vast array of
science will be enabled by a single wide-deep-fast sky survey, and LSST will
have unique survey capability in the faint time domain. The LSST design is
driven by four main science themes: probing dark energy and dark matter, taking
an inventory of the Solar System, exploring the transient optical sky, and
mapping the Milky Way. LSST will be a wide-field ground-based system sited at
Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m
effective) primary mirror, a 9.6 deg field of view, and a 3.2 Gigapixel
camera. The standard observing sequence will consist of pairs of 15-second
exposures in a given field, with two such visits in each pointing in a given
night. With these repeats, the LSST system is capable of imaging about 10,000
square degrees of sky in a single filter in three nights. The typical 5
point-source depth in a single visit in will be (AB). The
project is in the construction phase and will begin regular survey operations
by 2022. The survey area will be contained within 30,000 deg with
, and will be imaged multiple times in six bands, ,
covering the wavelength range 320--1050 nm. About 90\% of the observing time
will be devoted to a deep-wide-fast survey mode which will uniformly observe a
18,000 deg region about 800 times (summed over all six bands) during the
anticipated 10 years of operations, and yield a coadded map to . The
remaining 10\% of the observing time will be allocated to projects such as a
Very Deep and Fast time domain survey. The goal is to make LSST data products,
including a relational database of about 32 trillion observations of 40 billion
objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures
available from https://www.lsst.org/overvie
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