379 research outputs found
Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows
The general Ericksen-Leslie system for the flow of nematic liquid crystals is
reconsidered in the non-isothermal case aiming for thermodynamically consistent
models. The non-isothermal model is then investigated analytically. A fairly
complete dynamic theory is developed by analyzing these systems as quasilinear
parabolic evolution equations in an -setting. First, the existence of
a unique, local strong solution is proved. It is then shown that this solution
extends to a global strong solution provided the initial data are close to an
equilibrium or the solution is eventually bounded in the natural norm of the
underlying state space. In these cases, the solution converges exponentially to
an equilibrium in the natural state manifold
The -boundedness of a family of integral operators on UMD Banach function spaces
We prove the -boundedness of a family of integral operators with an
operator-valued kernel on UMD Banach function spaces. This generalizes and
simplifies earlier work by Gallarati, Veraar and the author, where the
-boundedness of this family of integral operators was shown on Lebesgue
spaces. The proof is based on a characterization of -boundedness as
weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665
Maximal regularity for non-autonomous equations with measurable dependence on time
In this paper we study maximal -regularity for evolution equations with
time-dependent operators . We merely assume a measurable dependence on time.
In the first part of the paper we present a new sufficient condition for the
-boundedness of a class of vector-valued singular integrals which does not
rely on H\"ormander conditions in the time variable. This is then used to
develop an abstract operator-theoretic approach to maximal regularity.
The results are applied to the case of -th order elliptic operators
with time and space-dependent coefficients. Here the highest order coefficients
are assumed to be measurable in time and continuous in the space variables.
This results in an -theory for such equations for .
In the final section we extend a well-posedness result for quasilinear
equations to the time-dependent setting. Here we give an example of a nonlinear
parabolic PDE to which the result can be applied.Comment: Application to a quasilinear equation added. Accepted for publication
in Potential Analysi
FACT -- The G-APD revolution in Cherenkov astronomy
Since two years, the FACT telescope is operating on the Canary Island of La
Palma. Apart from its purpose to serve as a monitoring facility for the
brightest TeV blazars, it was built as a major step to establish solid state
photon counters as detectors in Cherenkov astronomy. The camera of the First
G-APD Cherenkov Telesope comprises 1440 Geiger-mode avalanche photo diodes
(G-APD), equipped with solid light guides to increase the effective light
collection area of each sensor. Since no sense-line is available, a special
challenge is to keep the applied voltage stable although the current drawn by
the G-APD depends on the flux of night-sky background photons significantly
varying with ambient light conditions. Methods have been developed to keep the
temperature and voltage dependent response of the G-APDs stable during
operation. As a cross-check, dark count spectra with high statistics have been
taken under different environmental conditions. In this presentation, the
project, the developed methods and the experience from two years of operation
of the first G-APD based camera in Cherenkov astronomy under changing
environmental conditions will be presented.Comment: Proceedings of the Nuclear Science Symposium and Medical Imaging
Conference (IEEE-NSS/MIC), 201
Search for non-relativistic Magnetic Monopoles with IceCube
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting
of Antarctic ice. The detector can be used to search for
signatures of particle physics beyond the Standard Model. Here, we describe the
search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand
Unified Theory) era shortly after the Big Bang. These monopoles may catalyze
the decay of nucleons via the Rubakov-Callan effect with a cross section
suggested to be in the range of to
. In IceCube, the Cherenkov light from nucleon decays
along the monopole trajectory would produce a characteristic hit pattern. This
paper presents the results of an analysis of first data taken from May 2011
until May 2012 with a dedicated slow-particle trigger for DeepCore, a
subdetector of IceCube. A second analysis provides better sensitivity for the
brightest non-relativistic monopoles using data taken from May 2009 until May
2010. In both analyses no monopole signal was observed. For catalysis cross
sections of the flux of non-relativistic
GUT monopoles is constrained up to a level of at a 90% confidence level,
which is three orders of magnitude below the Parker bound. The limits assume a
dominant decay of the proton into a positron and a neutral pion. These results
improve the current best experimental limits by one to two orders of magnitude,
for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure
Lateral Distribution of Muons in IceCube Cosmic Ray Events
In cosmic ray air showers, the muon lateral separation from the center of the
shower is a measure of the transverse momentum that the muon parent acquired in
the cosmic ray interaction. IceCube has observed cosmic ray interactions that
produce muons laterally separated by up to 400 m from the shower core, a factor
of 6 larger distance than previous measurements. These muons originate in high
pT (> 2 GeV/c) interactions from the incident cosmic ray, or high-energy
secondary interactions. The separation distribution shows a transition to a
power law at large values, indicating the presence of a hard pT component that
can be described by perturbative quantum chromodynamics. However, the rates and
the zenith angle distributions of these events are not well reproduced with the
cosmic ray models tested here, even those that include charm interactions. This
discrepancy may be explained by a larger fraction of kaons and charmed
particles than is currently incorporated in the simulations
Flavor Ratio of Astrophysical Neutrinos above 35 TeV in IceCube
A diffuse flux of astrophysical neutrinos above has been
observed at the IceCube Neutrino Observatory. Here we extend this analysis to
probe the astrophysical flux down to and analyze its flavor
composition by classifying events as showers or tracks. Taking advantage of
lower atmospheric backgrounds for shower-like events, we obtain a shower-biased
sample containing 129 showers and 8 tracks collected in three years from 2010
to 2013. We demonstrate consistency with the
flavor ratio at Earth
commonly expected from the averaged oscillations of neutrinos produced by pion
decay in distant astrophysical sources. Limits are placed on non-standard
flavor compositions that cannot be produced by averaged neutrino oscillations
but could arise in exotic physics scenarios. A maximally track-like composition
of is excluded at , and a purely shower-like
composition of is excluded at .Comment: 8 pages, 3 figures. Submitted to PR
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