Regge calculus in teleparallel gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller and smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths l between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two-dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.

What do very nearly flat detectable cosmic topologies Rook like?

Recent studies of the delectability of the cosmic topology of nearly flat universes have often concentrated on the range of values of Omega(0) given by current observations. Here we study the consequences of taking a range of bounds satisfying \Omega(0) - 1\ much less than 1, which include those expected from future observations such as the Planck mission, as well as those predicted by inflationary models. We show that in this limit, a generic detectable non-flat manifold is locally indistinguishable from either a cylindrical (R-2 X S) or toroidal (R x T-2) manifold, irrespective of its global shape, with the former being more likely. Importantly, this is compatible with some recent indications of the alignment of the quadrupole and octupole moments, based on the analysis of the first year WMAP data. It also implies that in this limit an observer would not be able to distinguish topologically whether the universe is spherical, hyperbolic or flat. By severely restricting the expected topological signatures of detectable isometries, our results provide an effective theoretical framework for interpreting cosmological observations, and can be used to confine the parameter spaces which realistic search strategies, such as the 'circles in the sky' method, need to concentrate on.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Quantum states, thermodynamic limits, and entropy in M theory

We discuss the matching of the BPS part of the spectrum for a (super) membrane, which gives the possibility of getting the membrane's results via string calculations. In the small coupling limit of M theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at a large coupling constant is computed by considering M theory on a manifold with a topology T-2 x R-9. We argue that the finite temperature partition functions (brane Laurent series for p not equal 1) associated with the BPS p-brane spectrum can be analytically continued to well-defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit p --> 0 (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.

Entropy and thermodynamic limits in M-theory

The matching of the BPS part of the (super) membrane's spectrum enables one to obtain membrane's results via string calculations. We compute the thermodynamic behavior at large coupling constant by considering M-theory on a manifold with topology T-2 X R-9. In the small coupling limit of M-theory the entropy coincides with the standard entropy of type IIB strings. We claim that the finite temperature partition functions associated with BPS p-brane spectrum can be analytically continued to well-defined functionals. This means that finite temperature can be introduced in brane theory. For the point particle limit (p --> 0) the entropy has the standard behavior of thermodynamic quantities.

Interacting spin 0 fields with torsion via Duffin-Kemmer-Petiau theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KO field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenbock manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.

Metric-affine approach to teleparallel gravity

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. on the other hand, geometrically, the Weitzenbock spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to teleparallelism. We present a systematic treatment of teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

Braneworld remarks in Riemann-Cartan manifolds

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On the dynamics of free and excited oscillations of a simple portal frame foundation

In this paper we search for the dynamics of a simple portal structure in the free and in the periodic excitation cases. By using the Center Manifold approach and Averaging Method, we obtain results on both stability and bifurcation of equilibrium points and periodic orbits. (C) 2005 Elsevier Ltd. All rights reserved.

On the appearance of a Hopf bifurcation in a non-ideal mechanical problem

In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. (C) 2003 Elsevier Ltd. All rights reserved.

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent 1 is observed. (C) 2011 Elsevier B.V. All rights reserved.

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Immersions in the metastable dimension range via the normal bordism approach

Let f : M --> N be a continuous map between two closed n-manifolds such that f(*): H-*(M, Z(2)) --> H-* (N, Z(2)) is an isomorphism. Suppose that M immerses in Rn+k for 5 less than or equal to n < 2k. Then N also immerses in Rn+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homolog condition by the corresponding one in homotopy. (C) 2001 Elsevier B.V. B.V. All rights reserved.

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.