67 research outputs found
Uniform stability estimates for the discrete Calderon problems
In this article, we focus on the analysis of discrete versions of the
Calderon problem in dimension d \geq 3. In particular, our goal is to obtain
stability estimates for the discrete Calderon problems that hold uniformly with
respect to the discretization parameter. Our approach mimics the one in the
continuous setting. Namely, we shall prove discrete Carleman estimates for the
discrete Laplace operator. A main difference with the continuous ones is that
there, the Carleman parameters cannot be taken arbitrarily large, but should be
smaller than some frequency scale depending on the mesh size. Following the
by-now classical Complex Geometric Optics (CGO) approach, we can thus derive
discrete CGO solutions, but with limited range of parameters. As in the
continuous case, we then use these solutions to obtain uniform stability
estimates for the discrete Calderon problems.Comment: 38 pages, 2 figure
Shape optimization for the generalized Graetz problem
We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared
Proposal for new experimental schemes to realize the Avogadro constant
We propose two experimental schemes to determine and so to realize the
Avogadro constant at the level of 10 or better with a watt
balance experiment and a cold atom experiment measuring (where is
the Planck constant and the mass of the atom ). We give some
prospects about achievable uncertainties and we discuss the opportunity to test
the existence of possible unknown correction factors for the Josephson effect
and quantum Hall effect
Background Light in Potential Sites for the ANTARES Undersea Neutrino Telescope
The ANTARES collaboration has performed a series of {\em in situ}
measurements to study the background light for a planned undersea neutrino
telescope. Such background can be caused by K decays or by biological
activity. We report on measurements at two sites in the Mediterranean Sea at
depths of 2400~m and 2700~m, respectively. Three photomultiplier tubes were
used to measure single counting rates and coincidence rates for pairs of tubes
at various distances. The background rate is seen to consist of three
components: a constant rate due to K decays, a continuum rate that
varies on a time scale of several hours simultaneously over distances up to at
least 40~m, and random bursts a few seconds long that are only correlated in
time over distances of the order of a meter. A trigger requiring coincidences
between nearby photomultiplier tubes should reduce the trigger rate for a
neutrino telescope to a manageable level with only a small loss in efficiency.Comment: 18 pages, 8 figures, accepted for publication in Astroparticle
Physic
Sedimentation and Fouling of Optical Surfaces at the ANTARES Site
ANTARES is a project leading towards the construction and deployment of a
neutrino telescope in the deep Mediterranean Sea. The telescope will use an
array of photomultiplier tubes to detect the Cherenkov light emitted by muons
resulting from the interaction with matter of high energy neutrinos. In the
vicinity of the deployment site the ANTARES collaboration has performed a
series of in-situ measurements to study the change in light transmission
through glass surfaces during immersions of several months. The average loss of
light transmission is estimated to be only ~2% at the equator of a glass sphere
one year after deployment. It decreases with increasing zenith angle, and tends
to saturate with time. The transmission loss, therefore, is expected to remain
small for the several year lifetime of the ANTARES detector whose optical
modules are oriented downwards. The measurements were complemented by the
analysis of the ^{210}Pb activity profile in sediment cores and the study of
biofouling on glass plates. Despite a significant sedimentation rate at the
site, in the 0.02 - 0.05 cm.yr^{-1} range, the sediments adhere loosely to the
glass surfaces and can be washed off by water currents. Further, fouling by
deposits of light-absorbing particulates is only significant for surfaces
facing upwards.Comment: 18 pages, 14 figures (pdf), submitted to Astroparticle Physic
The ANTARES Optical Module
The ANTARES collaboration is building a deep sea neutrino telescope in the
Mediterranean Sea. This detector will cover a sensitive area of typically 0.1
km-squared and will be equipped with about 1000 optical modules. Each of these
optical modules consists of a large area photomultiplier and its associated
electronics housed in a pressure resistant glass sphere. The design of the
ANTARES optical module, which is a key element of the detector, has been
finalized following extensive R & D studies and is reviewed here in detail.Comment: 26 pages, 15 figures, to be published in NI
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