1,066 research outputs found
A general wavelet-based profile decomposition in the critical embedding of function spaces
We characterize the lack of compactness in the critical embedding of
functions spaces having similar scaling properties in the
following terms : a sequence bounded in has a subsequence
that can be expressed as a finite sum of translations and dilations of
functions such that the remainder converges to zero in as
the number of functions in the sum and tend to . Such a
decomposition was established by G\'erard for the embedding of the homogeneous
Sobolev space into the in dimensions with
, and then generalized by Jaffard to the case where is a Riesz
potential space, using wavelet expansions. In this paper, we revisit the
wavelet-based profile decomposition, in order to treat a larger range of
examples of critical embedding in a hopefully simplified way. In particular we
identify two generic properties on the spaces and that are of key use
in building the profile decomposition. These properties may then easily be
checked for typical choices of and satisfying critical embedding
properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older
and BMO spaces.Comment: 24 page
Sparse Deterministic Approximation of Bayesian Inverse Problems
We present a parametric deterministic formulation of Bayesian inverse
problems with input parameter from infinite dimensional, separable Banach
spaces. In this formulation, the forward problems are parametric, deterministic
elliptic partial differential equations, and the inverse problem is to
determine the unknown, parametric deterministic coefficients from noisy
observations comprising linear functionals of the solution.
We prove a generalized polynomial chaos representation of the posterior
density with respect to the prior measure, given noisy observational data. We
analyze the sparsity of the posterior density in terms of the summability of
the input data's coefficient sequence. To this end, we estimate the
fluctuations in the prior. We exhibit sufficient conditions on the prior model
in order for approximations of the posterior density to converge at a given
algebraic rate, in terms of the number of unknowns appearing in the
parameteric representation of the prior measure. Similar sparsity and
approximation results are also exhibited for the solution and covariance of the
elliptic partial differential equation under the posterior. These results then
form the basis for efficient uncertainty quantification, in the presence of
data with noise
Precision Tests of the Standard Model
30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part
by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe
Conditioning bounds for traveltime tomography in layered media
This paper revisits the problem of recovering a smooth, isotropic, layered
wave speed profile from surface traveltime information. While it is classic
knowledge that the diving (refracted) rays classically determine the wave speed
in a weakly well-posed fashion via the Abel transform, we show in this paper
that traveltimes of reflected rays do not contain enough information to recover
the medium in a well-posed manner, regardless of the discretization. The
counterpart of the Abel transform in the case of reflected rays is a Fredholm
kernel of the first kind which is shown to have singular values that decay at
least root-exponentially. Kinematically equivalent media are characterized in
terms of a sequence of matching moments. This severe conditioning issue comes
on top of the well-known rearrangement ambiguity due to low velocity zones.
Numerical experiments in an ideal scenario show that a waveform-based model
inversion code fits data accurately while converging to the wrong wave speed
profile
Concentration analysis and cocompactness
Loss of compactness that occurs in may significant PDE settings can be
expressed in a well-structured form of profile decomposition for sequences.
Profile decompositions are formulated in relation to a triplet , where
and are Banach spaces, , and is, typically, a
set of surjective isometries on both and . A profile decomposition is a
representation of a bounded sequence in as a sum of elementary
concentrations of the form , , , and a remainder that
vanishes in . A necessary requirement for is, therefore, that any
sequence in that develops no -concentrations has a subsequence
convergent in the norm of . An imbedding with this
property is called -cocompact, a property weaker than, but related to,
compactness. We survey known cocompact imbeddings and their role in profile
decompositions
Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
We generalize the concept of separable dual-space Gaussian pseudopotentials
to the relativistic case. This allows us to construct this type of
pseudopotential for the whole periodic table and we present a complete table of
pseudopotential parameters for all the elements from H to Rn. The relativistic
version of this pseudopotential retains all the advantages of its
nonrelativistic version. It is separable by construction, it is optimal for
integration on a real space grid, it is highly accurate and due to its analytic
form it can be specified by a very small number of parameters. The accuracy of
the pseudopotential is illustrated by an extensive series of molecular
calculations
Discovery of the Transiting Planet Kepler-5B
We present 44 days of high duty cycle, ultra precise photometry of the 13th magnitude star Kepler-5 (KIC 8191672, T(eff) = 6300 K, log g = 4.1), which exhibits periodic transits with a depth of 0.7%. Detailed modeling of the transit is consistent with a planetary companion with an orbital period of 3.548460 +/- 0.000032 days and a radius of 1.431(-0.052)(+0.041) R(J). Follow-up radial velocity measurements with the Keck HIRES spectrograph on nine separate nights demonstrate that the planet is more than twice as massive as Jupiter with a mass of 2.114(-0.059)(+0.056) M(J) and a mean density of 0.894 +/- 0.079 g cm(-3).NASA's Science Mission DirectorateAstronom
The K2-ESPRINT Project. I. Discovery of the Disintegrating Rocky Planet K2-22b with a Cometary Head and Leading Tail
We present the discovery of a transiting exoplanet candidate in the K2
Field-1 with an orbital period of 9.1457 hr: K2-22b. The highly variable
transit depths, ranging from 0\% to 1.3\%, are suggestive of a planet
that is disintegrating via the emission of dusty effluents. We characterize the
host star as an M-dwarf with K. We have obtained
ground-based transit measurements with several 1-m class telescopes and with
the GTC. These observations (1) improve the transit ephemeris; (2) confirm the
variable nature of the transit depths; (3) indicate variations in the transit
shapes; and (4) demonstrate clearly that at least on one occasion the transit
depths were significantly wavelength dependent. The latter three effects tend
to indicate extinction of starlight by dust rather than by any combination of
solid bodies. The K2 observations yield a folded light curve with lower time
resolution but with substantially better statistical precision compared with
the ground-based observations. We detect a significant "bump" just after the
transit egress, and a less significant bump just prior to transit ingress. We
interpret these bumps in the context of a planet that is not only likely
streaming a dust tail behind it, but also has a more prominent leading dust
trail that precedes it. This effect is modeled in terms of dust grains that can
escape to beyond the planet's Hill sphere and effectively undergo `Roche lobe
overflow,' even though the planet's surface is likely underfilling its Roche
lobe by a factor of 2.Comment: 22 pages, 16 figures. Final version accepted to Ap
Simulations of Aerodynamic Damping for MEMS Resonators
Aerodynamic damping for MEMS resonators is studied based on the numerical solution of Boltzmann-ESBGK equation. A compact model is then developed based on numerical simulations for a wide range of Knudsen numbers. The damping predictions are compared with both Reynold equation based models and several sets of experimental data. It has been found that the structural damping is dominant at low pressures (high Knudsen numbers). For cases with small length-to-width ratios and large vibration amplitudes, the threedimensionality effects must be taken into account. Finally, an uncertainty quantification approach based on the probability transformation method has been applied to assess the influence of pressure and geometric uncertainties. The output probability density functions (PDF) of the damping ratio has been studied for various input PDF of beam geometry and ambient pressure
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