Friedmann branes with variable tension

We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by E\"otv\"os. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a Friedmann brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter space-time.Comment: 12 pages, to appear in Phys. Rev.

Study on the leaching of phthalates from polyethylene terephthalate bottles into mineral water

Carbonated and non-carbonated mineral water samples bottled in 0.5-L, 1.5-L and 2.0-L polyethylene terephthalate (PET) containers belonging to three different water brands commercialized in Hungary were studied in order to determine their phthalate content by gas chromatography - mass spectrometry. Among the six investigated phthalates, diisobutyl phthalate, di-n-butyl-phthalate, benzyl-butyl phthalate and di(2-ethyl-hexyl) phthalate (DEHP) were determined in non-carbonated samples as follows: <3.0 ng L-1 - 0.2 μg L-1, <6.6 ng L-1 - 0.8 μg L-1, <6.0 ng L-1 - 0.1 μg L-1 and <16.0 ng L-1 - 1.7 μg L-1, respectively. Any of the above-mentioned phthalate esters could not be detected in carbonated mineral water samples. DEHP was the most abundant phthalate in the investigated samples. It could be detected after 44 days of storage at 22 ºC and its leaching was the most pronounced when samples were stored over 1200 days. Mineral water in PET bottles of 0.5 L had the highest phthalate concentrations compared to those obtained for waters of the identical brand bottled in 1.5-L or 2.0-L PET containers due to the higher surface/volume ratio. No clear trend could be established for phthalate leaching when water samples were kept at higher temperatures (max. 60 ºC) showing improper storage conditions. Phthalate determination by pyrolysis - gas chromatography/ mass spectroctrometric measurements in the plastic material as well as in the aqueous phase proved the importance of the quality of PET raw material used for the production of the pre-form (virgin vs. polymer containing recycled PET)

The Kepler equation for inspiralling compact binaries

Compact binaries consisting of neutron stars / black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments of the binary components. The post-Newtonian motion of such systems decouples into radial and angular parts. We present here for the first time the radial motion of such a binary encoded in a generalized Kepler equation, with the inclusion of all above-mentioned contributions, up to linear order in the perturbations. Together with suitably introduced parametrizations, the radial motion is solved completely

Distribution and Intracellular Localization of Titanium in Plants After Titanium Treatment

The physiological role of titanium in plants has not been elucidated yet, but a higher rate of growth , greater chlorophyll content and higher productivity, among others , may be attributed to this element. We have investigated the distribution of titanium in wheat seedlings after Titavit (a Ti ·ascorbate containing plant conditioner) treatment applied either through the leaf or through the root. In field experiments, we also sprayed spinach plants with Titavit. We have found a practically unidirectional tran slocation of Ti from the shoot into the root, and a preferential local ization of Ti in the nuclear cell fraction as seen by JCP-AES (inductively coupled plasma atomic emission spectrometry). Electron microscopic X·ray microanalysis after chemical fixation showed little or no accumulation of Ti in the cells of the treated organs . However, if there was in appreciable Xray emission at 4.5 keV (Ti), it was recorded from the nucleoplasm and nucleolus. The comparison of ICPAES and X-ray analyses leads us to the conclusion that the majority of Ti may be in a diffusible form in the treated cells, except the nuclei, where Ti may be bound firmly

E\"otv\"os branes

The high value of brane tension has a crucial role in recovering Einstein's general relativity at low energies. In the framework of a recently developed formalism with variable brane tension one can pose the question, whether it was always that high? In analogy with fluid membranes, in this paper we allow for temperature dependent brane tension, according to the corresponding law established by E\"otv\"os. For cosmological branes this assumption leads to several immediate consequences: (a) The brane Universe was created at a finite temperature $T_{c}$ and scale factor $a_{\min}$. (b) Both the brane tension and the 4-dimensional gravitational coupling 'constant' increase with the scale factor from zero to asymptotic values. (c) The 4-dimensional cosmological 'constant' evolves with $a$, starting with a huge negative value, passing through zero, finally reaching a small positive value. Such a scale-factor dependent cosmological constant is able to generate a surplus of attraction at small $a$ (as dark matter does) and a late-time repulsion at large $a$ (dark energy). In the particular toy model discussed here the evolution of the brane tension is compensated by energy interchange between the brane and the fifth dimension, such that the continuity equation holds for the cosmological fluid. The resulting cosmology closely mimics the standard model at late times, a decelerated phase being followed by an accelerated expansion. The energy absorption of the brane drives the 5D space-time towards maximal symmetry, becoming Anti de Sitter.Comment: v2: 6 pages, 4 figures; expanded introduction and bibliography; published versio

Semi-transparent brane-worlds

We study the evolution of a closed Friedmann brane perturbed by the Hawking radiation escaping a bulk black hole. The semi-transparent brane absorbes some of the infalling radiation, the rest being transmitted across the brane to the other bulk region. We characterize the cosmological evolution in terms of the transmission rate $\epsilon$. For small values of $\epsilon$ a critical-like behaviour could be observed, when the acceleration due to radiation pressure and the deceleration induced by the increasing self-gravity of the brane roughly compensate each other, and cosmological evolution is approximately the same as without radiation. Lighter (heavier) branes than those with the critical energy density will recollapse slower (faster). This feature is obstructed at high values of $\epsilon$, where the overall effect of the radiation is to speed-up the recollapse. We determine the maximal value of the transmission rate for which the critical-like behaviour is observed. We also study the effect of transmission on the evolution of different source terms of the Friedmann equation. We conclude that among all semi-transparent branes the slowest recollapse occurs for light branes with total absorption.Comment: 15 pages, 8 figure

Galactic rotation curves in brane world models

In the braneworld scenario the four dimensional effective Einstein equation has extra source terms, which arise from the embedding of the 3-brane in the bulk. These non-local effects, generated by the free gravitational field of the bulk, 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. In the present paper we consider the asymptotic behavior of the galactic rotation curves in the brane world models, and we compare the theoretical results with observations of both High Surface Brightness and Low Surface Brightness galaxies. For the chosen sample of galaxies we determine first the baryonic parameters by fitting the photometric data to the adopted galaxy model; then we test the hypothesis of the Weyl fluid acting as dark matter on the chosen sample of spiral galaxies by fitting the tangential velocity equation of the combined baryonic-Weyl model to the rotation curves. We give an analytical expression for the rotational velocity of a test particle on a stable circular orbit in the exterior region to a galaxy, with Weyl fluid contributions included. The model parameter ranges for which the $\chi^2$ test provides agreement (within 1$\sigma$ confidence level) with observations on the velocity fields of the chosen galaxy sample are then determined. There is a good agreement between the theoretical predictions and observations, showing that extra-dimensional models can be effectively used as a viable alternative to the standard dark matter paradigm.Comment: to be published in MNRAS, 17 pages, 31 figures, version including corrections on the proo

The paradox of soft singularity crossing and its resolution by distributional cosmological quantitities

A cosmological model of a flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dust-like matter exhibits a future soft singularity, where the pressure of the anti-Chaplygin gas diverges (while its energy density is finite). Despite infinite tidal forces the geodesics pass through the singularity. Due to the dust component, the Hubble parameter has a non-zero value at the encounter with the singularity, therefore the dust implies further expansion. With continued expansion however, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined, hence from the point of view of the anti-Chaplygin gas only a contraction is allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. This obviosly could not happen. We solve the paradox by redefining the anti-Chaplygin gas in a distributional sense. Then a contraction could follow the expansion phase at the singularity at the price of a jump in the Hubble parameter. Although such an abrupt change is not common in any cosmological evolution, we explicitly show that the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity. We also prove that the Israel junction conditions are obeyed through the singular spatial hypersurface. In particular we enounce and prove a more general form of the Lanczos equation.Comment: 12 pages; to be published in Phys.Rev.