A geometrical non-linear model for cable systems analysis

Cable structures are commonly studied with simplified analytical equations. The evaluation of the accuracy of these equations, in terms of equilibrium geometry configuration and stress distribution was performed for standard cables examples. A three-dimensional finite element analysis (hereafter FEA) procedure based on geometry-dependent stiffness coefficients was developed. The FEA follows a classical procedure in finite element programs, which uses an iterative algorithm, in terms of displacements. The theory is based on a total Lagrange formulation using Green-Lagrange strain. Pure Newton-Raphson procedure was employed to solve the non-linear equations. The results show that the rigid character of the catenary’s analytical equation, introduce errors when compared with the FEA

BPS black holes, the Hesse potential, and the topological string

The Hesse potential is constructed for a class of four-dimensional N=2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N=4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, $g_s$, and its complex conjugate. The terms depending holomorphically on $g_s$ are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of $g_s$ and $\bar g_s$ are in principle present.Comment: 28 pages, LaTeX, added comment

Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are carried by the wave equations at issue. What results is, in effect, that the only interactions which ultimately occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.Comment: Many improvements on the paper have still been made. In particular, its title has been modified so as to conform further to one of its main aim

On Quantum Special Kaehler Geometry

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 2

Stability of naked singularities and algebraically special modes

We show that algebraically special modes lead to the instability of naked singularity spacetimes with negative mass. Four-dimensional negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We briefly discuss the generalization of these results to charged and rotating singularities.Comment: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on boundary conditions. Version to appear in Phys. Rev.