Teleparallel Energy-Momentum Distribution of Static Axially Symmetric Spacetimes

This paper is devoted to discuss the energy-momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau-Lifshitz, Bergmann and M$\ddot{o}$ller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of General Relativity. It is mentioned here that M$\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $\lambda$. Finally, we calculate energy-momentum distribution for the Curzon metric, a special case of the above mentioned spacetime.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.

Relativistic Static Thin Disks: The Counter-Rotating Model

A detailed study of the Counter-Rotating Model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, there is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities and stable against radial perturbations. The CRM obtained are in agree with the strong energy condition, but there are regions of the disks with negative energy density, in violation of the weak energy condition.Comment: 19 pages, 6 figures. Submitted to Physical Review

Relativistic Static Thin Disks with Radial Stress Suport

New solutions for static non-rotating thin disks of finite radius with nonzero radial stress are studied. A method to introduce either radial pressure or radial tension is presented. The method is based on the use of conformal transformations.Comment: 19 pages, LaTeX, 7 figures, submitted to Class. Quan. Gra

The song of the dunes as a self-synchronized instrument

Since Marco Polo (1) it has been known that some sand dunes have the peculiar ability of emitting a loud sound with a well defined frequency, sometimes for several minutes. The origin of this sustained sound has remained mysterious, partly because of its rarity in nature (2). It has been recognized that the sound is not due to the air flow around the dunes but to the motion of an avalanche (3), and not to an acoustic excitation of the grains but to their relative motion (4-7). By comparing several singing dunes and two controlled experiments, one in the laboratory and one in the field, we here demonstrate that the frequency of the sound is the frequency of the relative motion of the sand grains. The sound is produced because some moving grains synchronize their motions. The existence of a velocity threshold in both experiments further shows that this synchronization comes from an acoustic resonance within the flowing layer: if the layer is large enough it creates a resonance cavity in which grains self-synchronize.Comment: minor changes, essentially more references

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.Comment: More comments for the quantitative estimation of chaos are added, and some inappropriate terms are changed. This will appear on Class. Quant. Gra

Performance of discrete heat engines and heat pumps in finite time

The performance in finite time of a discrete heat engine with internal friction is analyzed. The working fluid of the engine is composed of an ensemble of noninteracting two level systems. External work is applied by changing the external field and thus the internal energy levels. The friction induces a minimal cycle time. The power output of the engine is optimized with respect to time allocation between the contact time with the hot and cold baths as well as the adiabats. The engine's performance is also optimized with respect to the external fields. By reversing the cycle of operation a heat pump is constructed. The performance of the engine as a heat pump is also optimized. By varying the time allocation between the adiabats and the contact time with the reservoir a universal behavior can be identified. The optimal performance of the engine when the cold bath is approaching absolute zero is studied. It is found that the optimal cooling rate converges linearly to zero when the temperature approaches absolute zero.Comment: 45 pages LaTeX, 25 eps figure

Energy Distribution associated with Static Axisymmetric Solutions

This paper has been addressed to a very old but burning problem of energy in General Relativity. We evaluate energy and momentum densities for the static and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen and the gamma metrics, belonging to the Weyl class. We apply four well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and M$\ddot{o}$ller to compute energy-momentum density components. We obtain that these prescriptions do not provide similar energy density, however momentum becomes constant in each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc

Superposition of Weyl solutions: The equilibrium forces

Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detailComment: 31 pages, 7 figures, psbox macro. Submitted to Classical and Quantum Gravit

Exact General Relativistic Thick Disks

A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a ``displace, cut, {\it fill} and reflect'' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have non trivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR

Optimization of the deposition conditions and structural characterization of Y1Ba2Cu3O(7-x) thin superconducting films

Two series of Y1Ba2Cu3O(z) thin films deposited on (001) LaAl03 single crystals by excimer laser ablation under two different protocols have been investigated. The research has yielded well defined deposition conditions in terms of oxygen partial pressure p(O2) and substrate temperature of the deposition process Th, for the growth of high quality epitaxial films of YBCO. The films grown under conditions close to optimal for both j(sub c) and T(sub c) exhibited T(sub c) greater than or equal to 91 K and j(sub c) greater than or equal to 4 x 106 A/sq cm, at 77 K. Close correlations between the structural quality of the film, the growth parameters (p(O2), T(sub h)) and j(sub c) and T(sub c) have been found