Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

Effects of residues on the degradation of PHA produced from mixed microbial cultures and processed in extrusion

Thermal degradation upon melting is one of the major drawbacks reported for polyhydroxyalkanoates (PHA). However, the role of residues originating from the fermentation and the extraction steps on the thermal stability of this class of biopolymers still needs to be clarified. In the particular case of PHA produced from mixed microbial cultures (MMC), this topic is even less documented in the literature. Here, two polyhydroxy(butyrate-co-valerate) (PHBV) produced from MMC enriched in PHA accumulating organisms and fed with cheese whey were studied. A micro extrusion line is used to produce filaments and assess the processability and the degradation of processed PHBV. The prototype micro extrusion line allows for studying grams of materials. The two PHBV contain 18 mol% HV. PHBV was recovered with 11 wt% residues, and further submitted to a purification procedure resulting in a second biopolyester containing less than 2 wt% impurities. The thermorheological characterization of the two PHBV is first presented, together with their semicrystalline properties. Then the processing windows of the two biopolyesters are presented. Finally, the properties of extruded filaments are reported and the thermomechanical degradation of PHBV is extensively studied. The structure was assessed by wide angle X-ray diffraction, mechanical and rheological properties are reported, thermal properties are studied with differential scanning calorimetry and thermogravimetric analysis, whereas Fourier Transform Infrared spectroscopy was used to assess the impact of the extrusion on PHBV chemical structure. All results obtained with the two PHBV are compared to assess the effects of residues on both PHBV processability and degradation.

A new empirical system for rock slope stability analysis in exploitation stage

An empirical system was developed to obtain a quality index for rock slopes in road infrastructures, named Slope Quality Index (SQI), and it was applied to a set of real slopes.The SQI is supported in nine factors affecting slope stability that contemplate the evaluation of different parameters. Consequently, each factor is classified by the degree of importance and influence by assigned weights. These weights were established through a statistical analysis of replies to a survey that was distributed to several experienced professionals in the field. The proposed SQI varies between1 and 5, corresponding to slopes in very good and very bad condition state, respectively. Besides the advantage linked to a quantitative and qualitative evaluation of slopes, theSQI also allows identifying the most critical factors on the slope stability, which is a fundamental issue for an efficient management of the slope network in the road infrastructure, namely in the planning of conservation and maintenance operations.

Evolution of the functional properties of titanium–silver thin films for biomedical applications: Influence of in-vacuum annealing

In this work, the thermal stability of TiAgx thin films, deposited by magnetron sputtering, was evaluated, envisaging their application in biomedical devices, namely as electrodes for biosignal acquisition. Based on the composition and microstructural characterization, a set of four representative TiAgx thin films was selected in order to infer whether they are thermally stable in terms of functional properties. In order to achieve this purpose, the structural and morphological evolution of the films with annealing temperature was correlated with their electrical, mechanical and thermal properties. Two distinct zones were identified and two samples from each zone were extensively analysed. In the first zone (zone I), Ti was the main component (Ti-rich zone) while in the second, zone II, the Ag content was more significant. The selected samples were annealed in vacuum at four different temperatures up to 500 oC. For the samples produced within zone I, small microstructural changes were observed due to the recrystallization of the Ti structure and grain size increment. Also, no significant changes were observed with annealing temperature regarding the f l ’ functional properties, being thermally stable up to 500 oC. For higher Ag contents (zone II) the energy supplied by thermal treatments was sufficient to activate the crystallization of Ti-Ag intermetallic phases. A strong increase of the grain size of these phases was also reported. The structural and morphological organization proved to be determinant for the physical responses of the TiAgx system. The hardness and Y g’s modulus were significantly improved with the formation of the intermetallic phases. The silver addition and annealing treatments also played an important role in the electrical conductivity of the films, which was once again improved by the formation of Ti-Ag phases. The thermal diffusivity of the films was practically unchanged with the heat-treatment. This set of results shows that this intermetallic-like thin film system has good thermal stability up to high temperatures (as high as 500 oC), which in case of the highest Ag content zone is particularly evident for electrical and mechanical properties, showing an important improvement. Hardness increases about three times, while resistivity values become half of those from the lowest Ag contents zone. These set of characteristics are consistent with the targeted applications, namely in terms of biomedical sensing devices.

Kinematic constraint equations

This chapter presents a general methodology for the formulation of the kinematic constraint equations at position, velocity and acceleration levels. Also a brief characterization of the different type of constraints is offered, namely the holonomic and nonholonomic constraints. The kinematic constraints described here are formulated using generalized coordinates. The chapter ends with a general approach to deal with the kinematic analysis of multibody systems.

Equations of motion for constrained systems

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"

Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\'enyi relative entropy formula.