Spherically symmetric models: separating expansion from contraction in models with anisotropic pressures

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We find that the dividing shell is defined by a relation between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharpe mass inside the separating shell and by the pressure fluxes. This balance is a generalization of the Tolman-Oppenheimer- Volkoff equilibrium condition which defines a local equilibrium condition, but conveys also a non- local character given the definition of the Misner-Sharpe mass. We present a particular solution with dust and radiation that provides an illustration of our results.Comment: 4pp Towards New Paradigms: Proceeding Of The Spanish Relativity Meeting 2011. AIP Conference Proceedings, Volume 1458, pp. 487-490 (2012). Published in AIP Conf.Proc. 1458 (2011) 487-49

Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure

From stellar to planetary composition: Galactic chemical evolution of Mg/Si mineralogical ratio

The main goal of this work is to study element ratios that are important for the formation of planets of different masses. We study potential correlations between the existence of planetary companions and the relative elemental abundances of their host stars. We use a large sample of FGK-type dwarf stars for which precise Mg, Si, and Fe abundances have been derived using HARPS high-resolution and high-quality data. A first analysis of the data suggests that low-mass planet host stars show higher [Mg/Si] ratios, while giant planet hosts present [Mg/Si] that is lower than field stars. However, we found that the [Mg/Si] ratio significantly depends on metallicity through Galactic chemical evolution. After removing the Galactic evolution trend only the difference in the [Mg/Si] elemental ratio between low-mass planet hosts and non-hosts was present in a significant way. These results suggests that low-mass planets are more prevalent around stars with high [Mg/Si]. Our results demonstrate the importance of Galactic chemical evolution and indicate that it may play an important role in the planetary internal structure and composition.Comment: Accepted by A&A (Letter to the Editor

Brane Isotropisation in Extra-Dimensional Tolman-Bondi Universe

We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special role. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann-Lemaitre 4d space-time. For instance, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann-Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.Comment: 16 pages, 8 figures, one reference adde

The role of shell crossing on the existence and stability of trapped matter shells in spherical inhomogeneous \Lambda-CDM models

We analyse the dynamics of trapped matter shells in spherically symmetric inhomogeneous \Lambda-CDM models. The investigation uses a Generalised Lema\^itre-Tolman-Bondi description with initial conditions subject to the constraints of having spatially asymptotic cosmological expansion, initial Hubble-type flow and a regular initial density distribution. We discuss the effects of shell crossing and use a qualitative description of the local trapped matter shells to explore global properties of the models. Once shell crossing occurs, we find a splitting of the global shells separating expansion from collapse into, at most, two global shells: an inner and an outer limit trapped matter shell. In the case of expanding models, the outer limit trapped matter shell necessarily exists. We also study the role of shear in this process, compare our analysis with the Newtonian framework and give concrete examples using density profile models of structure formation in cosmology.Comment: 17pp 12fig

Measurement of gas phase characteristics using amonofibre optical probe in a three-phase flow

The study of gas–liquid–solid systems structure requires reliable measurement tools. In this paper, preliminary results on the potential use of a monofibre optical probe to investigate such flow are presented. This probe, manufactured at LEGI, allows the simultaneous measurement of the gas phase residence time and gas phase velocity. This specificity makes this probe more interesting than classical single tip probes (which measure only the gas residence time) or double tip probes (which are more intrusive). Although extensively used in two-phase gas–liquid, this probe was never used in gas–liquid–solid systems. First, the probe signal response is studied for three-phase flow conditions in the presence of solids. Results show that for soft solids, the probe tips can be contaminated when the probe pierces the solid. The signal processing procedure was modified accordingly to take into account these events. Second, the probe results are validated by comparing global results (global void fraction, gas flowrate) deduced from profile measurements with measurements performed by independent means. Lastly, void fraction profiles and interfacial area are studied more in detail. Depending on the solid loading, these profiles exhibit different behaviours. These features are associated to characteristics of the flow such as the transition from an homogeneous regime to an heterogenous regime, and are consistent with global observation performed by independent means. This demonstrates the ability of the probe to connect local information to the global behaviour and structure of the flow.Fundação para a Ciência e a Tecnologia (FCT

Effect of viscosity on homogeneous–heterogeneous flow regime transition in bubble columns

Experiments were performed in a cylindrical 0.14m diameter bubble column with a metal perforated plate. Air and aqueous solutions of glycerol with viscosity 1–22mPa s were the phases. Gas holdup was measured and plotted against the gas flow rate. The critical point where the homogeneous–heterogeneous regime transition begins was determined by the drift-flux plot of the primary data. The homogeneous regime stability was expressed by the critical values of the gas holdup and gas flow rate. The results show that moderate viscosity (3–22 mPa s) destabilizes the homogeneous regime and advance the transition. The results indicate that low viscosity (1–3 mPa s) could stabilize the homogeneous regime. The destabilizing effect of the column height proved previously for air–water system applies also to viscous batches.Comissão Europeia (CE) - Marie Curie Training Site Fellowship Contract Number HPMT-CT-2000-00074.Grantová agentura České republiky (GA CR) - Grant No. 104/01/0547

Strong curvature singularities in quasispherical asymptotically de Sitter dust collapse

We study the occurrence, visibility, and curvature strength of singularities in dust-containing Szekeres spacetimes (which possess no Killing vectors) with a positive cosmological constant. We find that such singularities can be locally naked, Tipler strong, and develop from a non-zero-measure set of regular initial data. When examined along timelike geodesics, the singularity's curvature strength is found to be independent of the initial data.Comment: 16 pages, LaTeX, uses IOP package, 2 eps figures; accepted for publication in Class. Quantum Gra