Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of hyperbolic 3-manifolds is presented. We discuss briefly L^2 - analytical and topological torsions of a manifold with boundary.Comment: 12 pages, LaTeX fil

Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds

We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.Comment: Int. Journ. Modern Physics A, vol. 18 (2003), 2041-205

On Useful Conformal Tranformations In General Relativity

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical purposes and represents a collection of exercises concerning local conformal transformations and dimensional reduction. To be published in "Gravitation and Cosmology

Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_\infty$-property.Comment: 6 page

Phase diagram of a random-anisotropy mixed-spin Ising model

We investigate the phase diagram of a mixed spin-1/2--spin-1 Ising system in the presence of quenched disordered anisotropy. We carry out a mean-field and a standard self-consistent Bethe--Peierls calculation. Depending on the amount of disorder, there appear novel transition lines and multicritical points. Also, we report some connections with a percolation problem and an exact result in one dimension.Comment: 8 pages, 4 figures, accepted for publication in Physical Review

Ab-initio study of the relation between electric polarization and electric field gradients in ferroelectrics

The hyperfine interaction between the quadrupole moment of atomic nuclei and the electric field gradient (EFG) provides information on the electronic charge distribution close to a given atomic site. In ferroelectric materials, the loss of inversion symmetry of the electronic charge distribution is necessary for the appearance of the electric polarization. We present first-principles density functional theory calculations of ferroelectrics such as BaTiO3, KNbO3, PbTiO3 and other oxides with perovskite structures, by focusing on both EFG tensors and polarization. We analyze the EFG tensor properties such as orientation and correlation between components and their link with electric polarization. This work supports previous studies of ferroelectric materials where a relation between EFG tensors and polarization was observed, which may be exploited to study ferroelectric order when standard techniques to measure polarization are not easily applied.Comment: 9 pages, 6 figures, 5 tables, corrected typos, as published in Phys. Rev.

The Safe-Port project: an approach to port surveillance and protection

SAFE-PORT is a recently started project addressing the complex issue of determining the best configurations of resources for harbour and port surveillance and protection. More specifically, the main goal is to find, for any given scenario, an adequate set of configuration solutions — i.e., number and type of sensors and equipments, their locations and operating modes, the corresponding personnel and other support resources — that maximize protection over a specific area. The project includes research and development of sensors models, novel algorithms for optimization and decision support, and a computer-based decision support system (DSS) to assist decision makers in that task. It includes also the development of a simulation environment for modelling relevant aspects of the scenario (including sensors used for surveillance, platforms, threats and the environment), capable to incorporate data from field-trials, used to test and validate solutions proposed by the DSS. Test cases will consider the use of intelligent agents to model the behaviour of threats and of NATO forces in a realistic way, following experts’ definitions and parameters