Towards the entropy of gravity time-dependent models via the Cardy-Verlinde formula

For models with several time-dependent components generalized entropies can be defined. This is shown for the Bianchi type IX model. We first derive the Cardy-Verlinde formula under the assumption that the first law of thermodynamics is valid. This leads to an explicit expression of the total entropy associated with this type of universes. Assuming the validity of the Cardy entropy formula, we obtain expressions for the corresponding Bekenstein, Bekenstein-Hawking and Hubble entropies. We discuss the validity of the Cardy-Verlinde formula and possible extensions of the outlined procedure to other time-dependent models.Comment: 13 page

Geometrothermodynamics

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy

Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

Thermodynamic Geometry Of Charged Rotating BTZ Black Holes

We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invariance imposed on the metric in GTD allows one to describe the CR-BTZ black holes and their limiting cases in a consistent and invariant manner

Spall And Dynamic Yielding Of Aluminum And Aluminum Alloys At Strain Rates Of 3X10(6) S(-1)

We have explored the role that grain size, impurity particles and alloying in aluminum play in dynamic yielding and spall fracture at tensile strain rates of similar to 3x10(6) We achieved these strain rates shocking the aluminum specimens via laser ablation using the Z-Beamlet Laser at Sandia National Laboratories. The high purity aluminum and 1100 series aluminum alloy produced very different spall strengths and nearly the same yield strengths. In contrast, various grain-sized Al + 3 wt. % Mg specimens presented the lowest spall strength, but the greatest dynamic yield strength. Fracture morphology results and particle analysis are presented along with hydrodynamic simulations to put these results in context. Impurity particles appeared to play a vital role in spall fracture at these fast strain rates. Alloying elements such as Mg seem to be the dominant factor in the dynamic yield results.Mechanical Engineerin

Is there life inside black holes?

Bound inside rotating or charged black holes, there are stable periodic planetary orbits, which neither come out nor terminate at the central singularity. Stable periodic orbits inside black holes exist even for photons. These bound orbits may be defined as orbits of the third kind, following the Chandrasekhar classification of particle orbits in the black hole gravitational field. The existence domain for the third kind orbits is rather spacious, and thus there is place for life inside supermassive black holes in the galactic nuclei. Interiors of the supermassive black holes may be inhabited by civilizations, being invisible from the outside. In principle, one can get information from the interiors of black holes by observing their white hole counterparts.Comment: 11 pages, 5 figures; references adde

Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions

A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function $F(\Box)$, which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.Comment: 20 pages, 3 figures, published in the proceedings of the VIII International Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, Russia, July 29 - August 3, 2009, http://theor.jinr.ru/~sqs09

Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric

A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.Comment: 18 pages, 3 figures, a few misprints in Section 5 have been correcte

Validation and reconstruction of flow meter data in the Barcelona water distribution network

12 páginas, 16 figuras, 1 tabla.-- El PDF es la versión pre-print.-- et al.This paper presents a signal analysis methodology to validate (detect) and reconstruct the missing and false data of a large set of flow meters in the telecontrol system of a water distribution network. The proposed methodology is based on two time-scale forecasting models: a daily model based on a ARIMA time series, while the 10-min model is based on distributing the daily flow using a 10-min demand pattern. The demand patterns have been determined using two methods: correlation analysis and an unsupervised fuzzy logic classification, named LAMDA algorithm. Finally, the proposed methodology has been applied to the Barcelona water distribution network, providing very good results.This work is part of a applied research project granted by ADASA and AGBAR companies. The authors also wish to thank the support received by the Research Commission of the Generalitat of Catalunya (Group SAC Ref. 2009 SGR 1491) and by CICYT (Ref. HYFA DPI2008-01996 and WATMAN DPI2009-13744) of Spanish Ministry of Education.Peer reviewe

Validation and reconstruction of flow meter data in the Barcelona water distribution network

This paper presents a signal analysis methodology to validate (detect) and reconstruct the missing and false data of a large set of flow meters in the telecontrol system of a water distribution network. The proposed methodology is based on two time-scale forecasting models: a daily model based on a ARIMA time series, while the 10-min model is based on distributing the daily flow using a 10-min demand pattern. The demand patterns have been determined using two methods: correlation analysis and an unsupervised fuzzy logic classification, named LAMDA algorithm. Finally, the proposed methodology has been applied to the Barcelona water distribution network, providing very good results.Peer ReviewedPostprint (author’s final draft