Large NN reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Breaking a Chaotic Cryptographic Scheme Based on Composition Maps

Recently, a chaotic cryptographic scheme based on composition maps was proposed. This paper studies the security of the scheme and reports the following findings: 1) the scheme can be broken by a differential attack with $6+\lceil\log_L(MN)\rceil$ chosen-plaintext, where $MN$ is the size of plaintext and $L$ is the number of different elements in plain-text; 2) the scheme is not sensitive to the changes of plaintext; 3) the two composition maps do not work well as a secure and efficient random number source.Comment: 9 pages, 7 figure

La boîte à outils géotechnique de demain: conception des structures géotechniques selon EN 1997: 202x

This paper shows how three new concepts – ‘Design Cases’ (introduced in prEN 1990), the ‘Geotechnical Design Model’ (prEN 1997-1), and the ‘Ground Model’ (prEN 1997-2) – are combined (in prEN 1997-3) to provide a comprehensive and flexible set of tools for the design of specific geotechnical structures. The paper presents flow charts divided between: a) reliability management, b) ground modelling, c) verification of the design, and d) structure execution, which provide guidelines for navigating prEN 1990 and prEN 1997.Postprint (published version

Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.

VLTI/AMBER spectro-interferometry of the late-type supergiants V766 Cen (=HR 5171 A), sigma Oph, BM Sco, and HD 206859

We add four warmer late-type supergiants to our previous spectro-interferometric studies of red giants and supergiants. V766 Cen (=HR 5171 A) is found to be a high-luminosity log(L/L_sun)=5.8+-0.4 source of Teff 4290+-760 K and radius 1490+-540 Rsun located close to both the Hayashi and Eddington limits; this source is consistent with a 40 Msun evolutionary track without rotation and current mass 27-36 Msun. It exhibits NaI in emission arising from a shell of radius 1.5 Rphot and a photocenter displacement of about 0.1 Rphot. V766 Cen shows strong extended molecular (CO) layers and a dusty circumstellar background component. This suggest an optically thick pseudo-photosphere at about 1.5 Rphot at the onset of the wind. V766 Cen is a red supergiant located close to the Hayashi limit instead of a yellow hypergiant already evolving back toward warmer Teff as previously discussed. The stars sigma Oph, BM Sco, and HD 206859 are found to have lower luminosities of about log(L/Lsun)=3.4-3.5 and Teff of 3900-5300 K, corresponding to 5-9 Msun tracks. They do not show extended molecular layers as observed for higher luminosity red supergiants of our sample. BM Sco shows an unusually strong contribution by an over-resolved circumstellar dust component. These stars are more likely high-mass red giants instead of red supergiants. This leaves us with an unsampled locus in the HR diagram corresponding to luminosities log(L/Lsun)~3.8-4.8 or masses 10-13 Msun, possibly corresponding to the mass region where stars explode as type II-P supernovae during the RSG stage. Our previously found relation of increasing strength of extended molecular layers with increasing luminosities is now confirmed to extend to double our previous luminosities and up to the Eddington limit. This might further point to steadily increasing radiative winds with increasing luminosity. [Abridged]Comment: 16 pages, 14 figures, accepted for publication in Astronomy and Astrophysics (A&A

Bogomolny equations for vortices in the noncommutative torus

We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discussed how vortex solutions are constructed. We also consider the extension to an $U(2)\times U(1)$ model, a simplified prototype of the noncommutative standard model.Comment: 23 pages, no figure