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 $q$). At imaginary $q$ it is IR singular, and at the point \o=0, $q^2=-3m^2$ it coincides with the result of Rebhan for next-to-leading order Debye screening. When $q$ 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