6,238 research outputs found
An analytical proof of Hardy-like inequalities related to the Dirac operator
We prove some sharp Hardy type inequalities related to the Dirac operator by
elementary, direct methods. Some of these inequalities have been obtained
previously using spectral information about the Dirac-Coulomb operator. Our
results are stated under optimal conditions on the asymptotics of the
potentials near zero and near infinity.Comment: LaTex, 22 page
Urban structure and growth
Most economic activity occurs in cities. This creates a tension between local increasing returns, implied by the existence of cities, and aggregate constant returns, implied by balanced growth. To address this tension, we develop a theory of economic growth in an urban environment. We show how the urban structure is the margin that eliminates local increasing returns to yield constant returns to scale in the aggregate, thereby implying a city size distribution that is well described by a power distribution with coefficient one: Zipf's Law. Under strong assumptions our theory produces Zipf's Law exactly. More generally, it produces the systematic deviations from Zipf's Law observed in the data, namely, the underrepresentation of small cities and the absence of very large ones. In these cases, the model identifies the standard deviation of industry productivity shocks as the key element determining dispersion in the city size distribution. We present evidence that the dispersion of city sizes is consistent with the dispersion of productivity shocks in the data.
The radial abundance gradient of oxygen towards the Galactic anticentre
We present deep optical spectroscopy of eight HII regions located in the
anticentre of the Milky Way. The spectra were obtained at the 10.4m GTC and
8.2m VLT. We determined Te([NII]) for all objects and Te([OIII]) for six of
them. We also included in our analysis an additional sample of 13 inner-disc
Galactic Hii regions from the literature that have excellent T_e
determinations. We adopted the same methodology and atomic dataset to determine
the physical conditions and ionic abundances for both samples. We also detected
the CII and OII optical recombination lines in Sh 2-100, which enables
determination of the abundance discrepancy factor for this object. We found
that the slopes of the radial oxygen gradients defined by the HII regions from
R_25 (= 11.5 kpc) to 17 kpc and those within R_25 are similar within the
uncertainties, indicating the absence of flattening in the radial oxygen
gradient in the outer Milky Way. In general, we found that the scatter of the
O/H ratios of Hii regions is not substantially larger than the observational
uncertainties. The largest possible local inhomogeneities of the oxygen
abundances are of the order of 0.1 dex. We also found positive radial gradients
in Te([O III]) and Te([N II]) across the Galactic disc. The shapes of these
temperature gradients are similar and also consistent with the absence of
flattening of the metallicity distribution in the outer Galactic disc.Comment: 20 pages, 11 figures. Accepted for publication in Monthly Notices of
the Royal Astronomical Societ
A physics-based life prediction methodology for thermal barrier coating systems
A novel mechanistic approach is proposed for the prediction of the life of
thermal barrier coating (TBC) systems. The life prediction methodology is based
on a criterion linked directly to the dominant failure mechanism. It relies on
a statistical treatment of the TBC's morphological characteristics,
non-destructive stress measurements and on a continuum mechanics framework to
quantify the stresses that promote the nucleation and growth of microcracks
within the TBC. The last of these accounts for the effects of TBC constituents'
elasto-visco-plastic properties, the stiffening of the ceramic due to sintering
and the oxidation at the interface between the thermally insulating yttria
stabilized zirconia (YSZ) layer and the metallic bond coat. The mechanistic
approach is used to investigate the effects on TBC life of the properties and
morphology of the top YSZ coating, metallic low-pressure plasma sprayed bond
coat and the thermally grown oxide. Its calibration is based on TBC damage
inferred from non-destructive fluorescence measurements using
piezo-spectroscopy and on the numerically predicted local TBC stresses
responsible for the initiation of such damage. The potential applicability of
the methodology to other types of TBC coatings and thermal loading conditions
is also discussed
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