1,048 research outputs found
Certificates of infeasibility via nonsmooth optimization
An important aspect in the solution process of constraint satisfaction
problems is to identify exclusion boxes which are boxes that do not contain
feasible points. This paper presents a certificate of infeasibility for finding
such boxes by solving a linearly constrained nonsmooth optimization problem.
Furthermore, the constructed certificate can be used to enlarge an exclusion
box by solving a nonlinearly constrained nonsmooth optimization problem.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0802
Cb-TRAM: Tracking and monitoring severe convection from onset over rapid development to mature phase using multi-channel Meteosat-8 SEVIRI data
Cb-TRAM is a new fully automated tracking and nowcasting algorithm. Intense convective
cells are detected, tracked and discriminated with respect to onset, rapid development,
and mature phase. Finally, short range forecasts are provided. The detection is
based on Meteosat-8 SEVIRI (Spinning Enhanced Visible and Infra-Red Imager) data
from the broad band high resolution visible, infra-red 6.2 micrometer (water vapour),
and the infra-red 10.8 micrometer channels. Areas of convection initiation, of rapid
vertical development, and mature thunderstorm cells (cumulonimbus Cb) are identified.
For the latter, tropopause temperature data from ECMWF operational model
analyses is utilised as an adaptive detection criterion. The tracking is based on geographical
overlap between current detections and first guess patterns of cells detected
in preceeding time steps. The first guess patterns as well as the short range forecasts
are obtained with the aid of a new image matching algorithm providing complete fields
of approximate differential cloud motion. Based on the so called pyramid matcher an
interpolation and extrapolation technique is presented which can also be used to generate
synthetic intermediate data fields between two known fields as well as nowcasts
of motion and development of detected areas. Examples of application are presented
for thunderstorm tracks over the Mediterranean
Nova Geminorum 1912 and the Origin of the Idea of Gravitational Lensing
Einstein's early calculations of gravitational lensing, contained in a
scratch notebook and dated to the spring of 1912, are reexamined. A hitherto
unknown letter by Einstein suggests that he entertained the idea of explaining
the phenomenon of new stars by gravitational lensing in the fall of 1915 much
more seriously than was previously assumed. A reexamination of the relevant
calculations by Einstein shows that, indeed, at least some of them most likely
date from early October 1915. But in support of earlier historical
interpretation of Einstein's notes, it is argued that the appearance of Nova
Geminorum 1912 (DN Gem) in March 1912 may, in fact, provide a relevant context
and motivation for Einstein's lensing calculations on the occasion of his first
meeting with Erwin Freundlich during a visit in Berlin in April 1912. We also
comment on the significance of Einstein's consideration of gravitational
lensing in the fall of 1915 for the reconstruction of Einstein's final steps in
his path towards general relativity.Comment: 31 p
Variational principles for involutive systems of vector fields
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector
field can be characterized by means of a variational principle based on a
one-form. We discuss how a vector field on a manifold can also be characterized
in a similar way by means of an higher order variational principle, and how
this extends to involutive systems of vector fields.Comment: 31 pages. To appear in International Journal of Geometric Methods in
Modern Physics (IJGMMP
Magnetic screening in the hot gluon system
The gluon transverse self-energy of the pure Yang-Mills system at
high-temperature is analysed in the static limit and at fourth order in the
coupling. Possible contributions to this function are collected, seen to be
gauge-fixing independent subsets and shown to vanish all, except those which
are either regulators or constituents of the self-energy of Euklidean 3D
Yang-Mills theory at zero temperature. The latter self-energy, in turn, is
known from the non-perturbative analysis by Karabali and Nair.Comment: 11 pages, latex, correction of prefactor in (24
Teaching Theoretical Physics: the cases of Enrico Fermi and Ettore Majorana
We report on theoretical courses by Fermi and Majorana, giving evidence of
the first appearance and further development of Quantum Mechanics teaching in
Italy. On the basis of original documents, we make a comparison between Fermi's
and Majorana's approaches. A detailed analysis is carried out of Fermi's course
on Theoretical Physics attended by Majorana in 1927-28. Three (previously
unknown) programs on advanced Physics courses submitted by Majorana to the
University of Rome between 1933 and 1936 and the course he held in Naples in
1938 complete our analysis: Fermi's phenomenological approach resounded in
Majorana, who however combined it with a deeper theoretical approach, closer to
the modern way of presenting Quantum Mechanics.Comment: latex, 21 pages; a contribution in the centenary of the birth of
Ettore Majoran
Geometrothermodynamics
We present the fundamentals of geometrothermodynamics, an approach to study
the properties of thermodynamic systems in terms of differential geometric
concepts. It is based, on the one hand, upon the well-known contact structure
of the thermodynamic phase space and, on the other hand, on the metric
structure of the space of thermodynamic equilibrium states. In order to make
these two structures compatible we introduce a Legendre invariant set of
metrics in the phase space, and demand that their pullback generates metrics on
the space of equilibrium states. We show that Weinhold's metric, which was
introduced {\it ad hoc}, is not contained within this invariant set. We propose
alternative metrics which allow us to redefine the concept of thermodynamic
length in an invariant manner and to study phase transitions in terms of
curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy
Thermodynamic Geometry Of Charged Rotating BTZ Black Holes
We study the thermodynamics and the thermodynamic geometries of charged
rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the
thermodynamics of these systems within the context of the Weinhold and
Ruppeiner thermodynamic geometries and the recently developed formalism of
geometrothermodynamics (GTD). Considering the behavior of the heat capacity and
the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot
describe completely the thermodynamics of these black holes and of their
limiting case of vanishing electric charge. In contrast, the Legendre
invariance imposed on the metric in GTD allows one to describe the CR-BTZ black
holes and their limiting cases in a consistent and invariant manner
On the Gluon Plasmon Self-Energy at O(g)
The next-to-leading order contribution \d\P\omn (\o ,\vc q ) to the
polarization function of the hot gluon system is analysed at non-zero wave
vectors \vc q \,. Using Braaten-Pisarski resummation and general covariant
gauges, \d\P\omn is found to be gauge-fixing independent and transverse on
the longitudinal mass-shell. The real part of the longitudinal component
\d\P_\ell is UV and IR stable (for real ). At imaginary it is IR
singular, and at the point \o=0, it coincides with the result of
Rebhan for next-to-leading order Debye screening. When approaches the
lightcone, \d\P_\ell diverges like 1 / \wu {\o^2 - q^2} , reflecting the
breakdown of the Braaten-Pisarski decomposition scheme in this limit.Comment: 14 pages, LaTe
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