Carbon and titanium diboride (TiB2) multilayer coatings.

Titanium Diboride, (TiB2) is a metal-based refractory ceramic material that has been investigated in industrial applications ranging from, cutting tools to wear parts and for use in the aerospace industry. The unique properties which make this material so fascinating are, its high hardness, high melting point and its corrosion resistance. TiB2 is prevented from wider mainstream use because of its inherent brittle nature. With a view to overcome this in coating form and with the aim of providing in addition inherent lubricity, in this study 50 layer TiB2/C multilayer stacks have been fabricated, with varying volume fractions of ceramic, whereby the interfaces of the layers limit crack propagation in the TiB2 ceramic. TiB2 has been multilayered with carbon, to make use of the unique and hybrid nature of the bonding in carbon coatings. DC magnetron sputtering with substrate bias was the preferred route for the fabrication of these coatings. AISI tool steel has been used as the substrate material. By varying the amount of TiB2 ceramic from 50% to 95%, the Hardness of the coating is seen to increase from 5 GPa to 17GPa. The Hardness is observed to decrease as a function of increasing carbon content, agreeing with other studies that the carbon layers are not load-bearing. The graphitic nature of the sp2 bond, however, acts as a lubricant layer

Geodesic Structure of Lifshitz Black Holes in 2+1 Dimensions

We present a study of the geodesic equations of a black hole space-time which is a solution of the three-dimensional NMG theory and is asymptotically Lifshitz with $z=3$ and $d=1$ as found in [Ayon-Beato E., Garbarz A., Giribet G. and Hassaine M., Phys. Rev. {\bf D} 80, 104029 (2009)]. By means of the corresponding effective potentials for massive particles and photons we find the allowed motions by the energy levels. Exact solutions for radial and non-radial geodesics are given in terms of the Weierstrass elliptic $\wp$, $\sigma$, and $\zeta$ functions.Comment: 10 pages, 6 figures, accepted for publication in Eur. Phys. J.

The golden ratio in Schwarzschild-Kottler black holes

In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio $\Phi = (\sqrt{5}-1)/2$. This is a general result which is independent of the value and sign of the cosmological constant $\Lambda$

On the normalization of Killing vectors and energy conservation in two-dimensional gravity

We explicitly show that, in the context of a recently proposed 2D dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature $T_H$ is then calculated according to this prescription.Comment: 7 pages, Latex, no figure

Testing a dissipative kinetic k-essence model

In this work, we present a study of a purely kinetic k-essence model, characterized basically by a parameter $\alpha$ in presence of a bulk dissipative term, whose relationship between viscous pressure $\Pi$ and energy density $\rho$ of the background follows a polytropic type law $\Pi \propto \rho^{\lambda+1/2}$, where $\lambda$, in principle, is a parameter without restrictions. Analytical solutions for the energy density of the k-essence field are found in two specific cases: $\lambda=1/2$ and $\lambda=(1-\alpha)/2\alpha$, and then we show that these solutions posses the same functional form than the non-viscous counterpart. Finally, both approach are contrasted with observational data from type Ia supernova, and the most recent Hubble parameter measurements, and therefore, the best values for the parameters of the theory are founds.Comment: 9 pages, 5 figures, accepted in EPJ