Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models

A class of exact solutions of the gravitational field equations in the vacuum on the brane are obtained by assuming the existence of a conformal Killing vector field, with non-static and non-central symmetry. In this case, the general solution of the field equations can be obtained in a parametric form in terms of the Bessel functions. The behavior of the basic physical parameters describing the non-local effects generated by the gravitational field of the bulk (dark radiation and dark pressure) is also considered in detail, and the equation of state satisfied at infinity by these quantities is derived. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity of the particle is a monotonically increasing function of the radial distance and, in the limit of large values of the radial coordinate, tends to a constant value, which is independent on the parameters describing the model. Therefore, a brane geometry admitting a one-parameter group of conformal motions may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter.     

Orbital Precession Effect in the Reissner-Nordström Field with a Global Monopole

Using an elegant mathematical method advanced by us, we calculate the orbital precession effect in the gravitational field of the centre mass with electric charge and a global monopole. Analysing the results, we obtain that the orbital precession effect increases on account of the global symmetry breaking, but the orbital precession effect aroused by the electric charge of the field source reduces the orbital precession effect aroused by the mass of the field source. Generalizing the effect in the Schwarzschild field, we obtain interesting results by discussing the parameters of the celestial body, which provide a feasible experimental verification of the general relativity.     

Potential symmetry and invariant solutions of Fokker-Planck equation in cylindrical coordinates related to magnetic field diffusion in magnetohydrodynamics including the Hall current

Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some simplifications allow to obtain a Fokker-Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flow and the Hall-current. Some interesting side results of this approach are new exact solutions that do not seem to have been reported in the literature.     

Spatially resolved ultrasonic attenuation in resistance spot welds: implications for nondestructive testing

Spatial variation of ultrasonic attenuation and velocity has been measured in plane parallel specimens extracted from resistance spot welds. In a strong weld, attenuation is larger in the nugget than in the parent material, and the region of increased attenuation is surrounded by a ring of decreased attenuation. In the center of a stick weld, attenuation is even larger than in a strong weld, and the low-attenuation ring is absent. These spatial variations are interpreted in terms of differences in grain size and martensite formation. Measured frequency dependences indicate the presence of an additional attenuation mechanism besides grain scattering. The observed attenuations do not vary as commonly presumed with weld quality, suggesting that the common practice of using ultrasonic attenuation to indicate weld quality is not a reliable methodology.     

On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow

While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.     

Role of nonequilibrium entropy in Einstein’s theory of gravitation

We employ the covariant version of a systematic framework of nonequilibrium thermodynamics to clarify the role of entropy in the classical theory of gravitation. An expression for the global entropy is identified naturally from the covariant formulation, and a dual role of the Einstein equation as a fundamental evolution equation and as a thermodynamic equation of state follows immediately. The covariant time integral of the entropy is a more fundamental quantity than the entropy itself. In the absence of matter, the gravitational entropy alone cannot generate any irreversible processes. Some implications for the structure of a quantum theory of gravity are discussed.     

Superluminality and parelectricity: The ammonia maser revisited

It is well known that the inversion of populations in the ammonia maser leads to stimulated emission, and hence amplification, of microwaves. However, it is not well known that an inverted medium also leads to the superluminal propagation of off-resonance, finite-band-width wave packets, whose phase, group, energy, and signal velocities, as defined by Sommerfeld and Brillouin, all exceed the vacuum speed of lightc. Einstein causality is not violated, since the front velocity isc. The inversion of populations also implies a parelectric medium with negative electric susceptibility. (Parelectric media should not be confused withparaelectric media, which are ferroelectrics just above their Curie points.) The existence of a parelectric medium implies the possibility of the levitation of an electrical charge in the vacuum above this medium, as well as stable electrostatic configurations of charges placed inside an evacuated cavity surrounded by this medium. The apparent violation of Earn-shaw's theorem will be discussed. Numerical estimates for a proposed experiment to observe parelectricity will be given.Dedicated to Walther on the ocassion of his 60 birthday     

Ultraviolet photoelectron spectroscopy of Si 4 - to Si 1000 -

Using a new experimental setup we have measured UV (h ν = 6.4 eV) photoelectron spectra of cold silicon cluster anions Si _n ^- in a very broad size range. For sizes up to n = 46 the spectra exhibit rich structures. For larger sizes only smooth spectra have been obtained. No trace of a bandgap has been found even for clusters with more than 1000 atoms. Received 30 November 2000