Bi-paracontact structures and Legendre foliations

We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold $(M,\eta)$, then under some natural assumptions of integrability, $M$ carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures are defined on a contact manifold, then $M$ admits an almost bi-paracontact structure. We define a canonical connection on an almost bi-paracontact manifold and we study its curvature properties, which resemble those of the Obata connection of an anti-hypercomplex (or complex-product) manifold. Further, we prove that any contact metric manifold whose Reeb vector field belongs to the $(\kappa,\mu)$-nullity distribution canonically carries an almost bi-paracontact structure and we apply the previous results to the theory of contact metric $(\kappa,\mu)$-spaces.Comment: To appear on: Kodai Mathematical Journa

Tachyon Effects on the 2-Dim Black Hole Geometry

We study solutions of the tree level string effective action in the presence of the tachyon mode.We find that the 2-dim. static black hole is stable against tachyonic perturbations.For a particular ansatz for the tachyon field we find an exact solution of the equations of motion which exhibits a naked singularity.In the case of static fields we find numerically that the full system has a black hole solution,with the tachyon regular at the horizon.Comment: NTUA 45/94, Pages 11, Latex, 3 Figures on reques

Cosmological Evolution of a Purely Conical Codimension-2 Brane World

We study the cosmological evolution of isotropic matter on an infinitely thin conical codimension-two brane-world. Our analysis is based on the boundary dynamics of a six-dimensional model in the presence of an induced gravity term on the brane and a Gauss-Bonnet term in the bulk. With the assumption that the bulk contains only a cosmological constant Lambda_B, we find that the isotropic evolution of the brane-universe imposes a tuned relation between the energy density and the brane equation of state. The evolution of the system has fixed points (attractors), which correspond to a final state of radiation for Lambda_B=0 and to de Sitter state for Lambda_B>0. Furthermore, considering anisotropic matter on the brane, the tuning of the parameters is lifted, and new regions of the parametric space are available for the cosmological evolution of the brane-universe. The analysis of the dynamics of the system shows that, the isotropic fixed points remain attractors of the system, and for values of Lambda_B which give acceptable cosmological evolution of the equation of state, the line of isotropic tuning is a very weak attractor. The initial conditions, in this case, need to be fine tuned to have an evolution with acceptably small anisotropy.Comment: 20 pages, 4 figures, typo correcte

Problems of the gauge theory of weak, electromagnetic and strong interactions

The aim of this thesis is to present and discuss some mathematical and physical problems in the theory of weak, electromagnetic and strong interactions. Our main concern is a parallel development of mathematical and physical concepts and when it is possible, an attempt to bridge the abstract mathematical formulations with physical ideas. A central role in this thesis is played by a general construction scheme, which enables us to calculate explicitly all the mathematical quantities like matrix elements, Clebsch-Gordan series, Clebsch-Gordan coefficients which are necessary for a Grand Unification model construction. In this content, we have followed two basic principles: simplicity and applicability. To meet the first principle, all the construction methods developed are based on first principles and basic concepts of the Lie algebras and its representation theory, like roots and weights. Moreover, the requirement of applicability is met with the implementation of all the algorithms into computer programs. In the physical area, we have concentrated on the problem of mass. The lepton mass spectrum us studied in a theory of weak and electromagnetic interactions, while the mass problem of the SO(10) Grand Unified theory is analysed as a direct application of our Lie group construction scheme

Stability Analysis of a 70m-High Cut at an Ancient Landslide Area in Patras, Greece

A 70m-high slope is currently under construction near the entrance of a cut-and-cover tunnel in the inner loop highway of City of Patras – a seismically active area in Western Greece (PGA = 0.24g). The slope consists of marl layers dipping inwards and exhibiting distinct sets of joints. The landscape provides evidence that the site has been subjected to a major landslide at an unknown time in the past. Geotechnical investigation detected a sheared zone at about 15m below ground surface, and a water table a few meters below the planned toe of the slope. The angle and position of the slope surface together with the estimated position of the sheared zone provide a chair-like potentially unstable volume with convex plan view. In addition to the general stability problem, surface instabilities due to the aforementioned sets of joints create the potential of smaller wedge-type failures near the surface of the slope. Following a detailed geotechnical investigation, nonlinear stress finite-element analyses considering both gravitational and earthquake loads were performed. The analyses encompassed a number of different assumptions about: (a) depth to water table, (b) soil strength and (c) geometry of slope and soil layer interfaces. Results show that adequate safety can be achieved using a combination of piles and passive anchors. The effects of various factors/assumptions on the safety of the slope are discussed

Cosmological Evolution in a Type-0 String Theory

We study the cosmological evolution of a type-0 string theory by employing non-criticality, which may be induced by fluctuations of the D3 brane worlds. We check the consistency of the approach to O(alpha ') in the corresponding sigma-model. The ten-dimensional theory is reduced to an effective four-dimensional model, with only time dependent fields. We show that the four-dimensional universe has an inflationary phase and graceful exit from it, while the other extra dimensions are stabilized to a constant value, with the fifth dimension much larger than the others. We pay particular attention to demonstrating the role of tachyonic matter in inducing these features. The Universe asymptotes, for large times, to a non-accelerating linearly-expanding Universe with a time-dependent dilaton and a relaxing to zero vacuum energy a la quintessence.Comment: 33 pages LATEX, seven eps figures incorporate

AdS/CFT Correspondence and the Reheating of the Brane-Universe

We present a mechanism for exit from inflation and reheating using the AdS/CFT correspondence. A cosmological evolution is induced on a probe D3-brane as it moves in a black D-brane background of type-0 string theory. If the tachyon field is non zero, inflation is induced on the brane-universe, with the equation of state parameter in the range -1<w<-1/3 depending on the position of the probe brane in the bulk. As the probe brane approaches the horizon of the background black hole, the inflation rate decreases and the value of w gets larger. At some critical distance away from the horizon, inflation ends. When the brane-universe reaches the horizon, the conformal invariance is restored, the background geometry becomes AdS{5}X S{5}, and the brane-universe feels the CFT thermal radiation and reheats.Comment: LaTex file, 18 pages, 2 figures, accepted for publication in JHE

Acceleration of the Universe in Type-0 Non-Critical Strings

Presently there is preliminary observational evidence that the cosmological constant might be non zero, and hence that our Universe is eternally accelerating (de Sitter). This poses fundamental problems for string theory, since a scattering matrix is not well defined in such Universes. In a previous paper we have presented a model, based on (non-equilibrium) non-critical strings, which is characterized by eventual ``graceful'' exit from a de Sitter phase. The model is based on a type-0 string theory, involving D3 brane worlds, whose initial quantum fluctuations induce the non criticality. We argue in this article that this model is compatible with the current observations. A crucial r\^ole for the correct ``phenomenology'' of the model is played by the relative magnitude of the flux of the five form of the type 0 string to the size of five of the extra dimensions, transverse to the direction of the flux-field. We do not claim, at this stage at least, that this model is a realistic physical model for the Universe, but we find it interesting that the model cannot be ruled out immediately, at least on phenomenological grounds

QCD uncertainties at the LHC and the implications of HERA

Strong interaction physics will be ubiquitous at the Large Hadron Collider since the colliding beams consist of confined quarks and gluons. Although the main purpose of the LHC is to study the mechanism of electroweak symmetry breaking and to search for physics beyond the Standard Model, to maximise the precision and sensitivity of such anaylses it is necessary to understand in detail various perturbative, semi-perturbative and non-perturbative QCD effects. Many of these effects have been extensively studied at HERA and will be studied further at HERA II. We discuss the impact of the knowledge thus gained on physics at the LHC.Comment: Contributed to the Proceedings of DIS04, Strbske Pleso, Slovaki