On the Jacobi-Metric Stability Criterion

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure

Geodesics in a quasispherical spacetime: A case of gravitational repulsion

Geodesics are studied in one of the Weyl metrics, referred to as the M--Q solution. First, arguments are provided, supporting our belief that this space--time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi--spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the $r=2M$ surface, and related to the quadrupole moment of the source.Comment: 30 pages late

The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy

We calculate the instantaneous proper radial acceleration of test particles (as measured by a locally defined Lorentzian observer) in a Weyl spacetime, close to the horizon. As expected from the Israel theorem, there appear some bifurcations with respect to the spherically symmetric case (Schwarzschild), which are explained in terms of the behaviour of the superenergy, bringing out the physical relevance of this quantity in the study of general relativistic systems.Comment: 14 pages, Latex. 4 figures. New references added. Typos corrected. To appear in Int. J. Theor. Phy

Thermal Conduction in Systems out of Hydrostatic Equilibrium

We analyse the effects of thermal conduction in a relativistic fluid, just after its departure from hydrostatic equilibrium, on a time scale of the order of thermal relaxation time. It is obtained that the resulting evolution will critically depend on a parameter defined in terms of thermodynamic variables, which is constrained by causality requirements.Comment: 16 pages, emTex (LaTex 2.09). To appear in Classical and Quantum Gravit

Simple solution of DC-offset rejection based phase-locked loop for single-phase grid-connected converters

Distributed Generators (DG) systems based on Renewable Energy Sources (RES) such as hydro, wind, and solar power plants have been spread widely due to their lower cost and the advanced capability of connecting them with the grid. The power generated from the DG must be shaped to be interfaced with the grid employing power electronics converters. The grid-connected power electronics converters must be synchronized with the grid (i.e., the same fundamental component of the grid frequency, phase, amplitude, and sequence). Synchronization techniques are employed to achieve accurate and fast grid synchronization between the converter and the grid. The existence of (DC-offset) in the input of Phase Locked Loop (PLL) caused synchronization problems as it causes oscillations in the estimated fundamental grid phase, frequency, and amplitude. In addition, the closed-loop system stability can be affected. This work proposes a simple technique for grid synchronization based on PLL with a phase angle correction. The proposed method was developed using Transfer Delay (TD) and Delay Signal Cancelation (DSC) operators; then, the small single model and stability analysis was employed. Several scenarios were developed to compare the proposed method with previous methods using MATLAB/Simulink tool. The scenarios involve introducing phase jumps, DC offsets, and amplitude changes to the grid voltage. Additionally, the grid frequency was also changed. The results show that the proposed PLL can solved the DC-offset problem using any delay time and fully synchronized with the grid. Moreover, the proposed PLL has the fastest dynamic response and shortest synchronization time over the other methods from literature

How can exact and approximate solutions of Einstein's field equations be compared?

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate solution whose form on the symmetry axis is subsequently used for the identification of the exact solution possessing the same multipole structure, and (ii) the generation of approximate solutions from exact ones by expanding the latter in series of powers of a small parameter. The central result of our paper is the derivation of the correct approximate analogues of the double-Kerr solution possessing the physically meaningful equilibrium configurations. We also show that the interpretation of an approximate solution originally attributed to it on the basis of some general physical suppositions may not coincide with its true nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure