Does a dynamical system lose energy by emitting gravitational waves?

We note that Eddington's radiation damping calculation of a spinning rod fails to account for the complete mass integral as given by Tolman. The missing stress contributions precisely cancel the standard rate given by the 'quadrupole formula'. This indicates that while the usual 'kinetic' term can properly account for dynamical changes in the source, the actual mass is conserved. Hence gravity waves are not carriers of energy in vacuum. This supports the hypothesis that energy including the gravitational contribution is confined to regions of non-vanishing energy-momentum tensor $T_{ik}$. PACS numbers: 04.20.Cv, 04.30.-wComment: Published in Modern Physics Letters A vol 14, no 23, 1531, 1999 Full text available in the journa

Repeated Relativistic Ejections in GRS 1915+105

In 1994 February-August we observed with the VLA four ejection events of radio emitting clouds from the high energy source GRS 1915+105. These events are all consistent with anti-parallel ejections of twin pairs of clouds moving away from the compact source at $\sim$ 0.92 of the speed of light and angles of $\sim$ 70$^{\circ}$ with respect to the line of sight. The flux ratios and time evolution of the expelled clouds are consistent with actual motions of the radiating matter rather than with the simple propagation of pulses in a medium moving at slower velocities. The large kinetic power of the sudden, short, and rather discontinuous ejections exceeds by more than an order of magnitude the maximum steady photon luminosity of the source, suggesting that in GRS 1915+105 a radiation acceleration mechanism of the ejecta is unlikely. As in other galactic and extragalactic radio sources, the decrease in flux density as a function of angular separation from the central source shows a steepening with distance. Additional ejection events have been observed in 1995 and 1997 and we compare them with the 1994 events.Comment: 20 pages, 7 figures. To appear in The Astrophysical Journal, January 10, 1999 issu

Stability of Gravitational and Electromagnetic Geons

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the period of the comprising waves. This contradicts the requirement of slow evolution. Thus not all of the requirements for the existence of electromagnetic or gravitational geons are met though perturbation theory. From this result it cannot be concluded that an electromagnetic or a gravitational geon is a viable entity. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.Comment: 40 pages, 5 EPS figures, uses overcite.st

Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity

Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order $\epsilon^2$ in general magnetic geometry. Here $\epsilon$ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present article, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order $\epsilon^2$. These higher-order pieces contain both neoclassical and turbulent contributions, and constitute one of the necessary ingredients (the other is given by the short-wavelength components up to second order) that will eventually enter a complete model for the radial transport of toroidal angular momentum in a tokamak in the low flow ordering. Finally, we provide an explicit and detailed proof that the system consisting of second-order gyrokinetic Fokker-Planck and quasineutrality equations leaves the long-wavelength radial electric field undetermined; that is, the turbulent tokamak is intrinsically ambipolar.Comment: 70 pages. Typos in equations (63), (90), (91), (92) and (129) correcte

The fundamental group and torsion group of Beauville surfaces

We give a survey on the fundamental group of surfaces isogenous to a higher product. If the surfaces are regular, e.g. if they are Beauville surfaces, the first homology group is a finite group. We present a MAGMA script which calculates the first homology groups of regular surfaces isogenous to a product.Comment: 14 pages; MAGMA script included; v2: minor corrections, final version to appear in the Proceedings of the Conference "Beauville Surfaces and Groups", Newcastle University (UK), 7-9th June 201

Tree-level unitarity constraints in the most general 2HDM

We obtain tree-level unitarity constraints for the most general Two Higgs Doublet Model (2HDM) with explicit CP-violation. We briefly discuss correspondence between possible violation of tree level unitarity limitation and physical content of the theory.Comment: 6 pages, no figure

Estimation of household demand systems with theoretically compatible Engel curves and unit value specifications

We develop a method for estimation of price reactions using unit value data which exploits the implicit links between quantity and unit value choices. This allows us to combine appealing Engel curve specifications with a model of unit value determination in a way which is consistent with demand theory, unlike methods hitherto prominent in the literature. The method is applied to Czech data