High-Temperature Activated AB2 Nanopowders for Metal Hydride Hydrogen Compression

A reliable process for compressing hydrogen and for removing all contaminants is that of the metal hydride thermal compression. The use of metal hydride technology in hydrogen compression applications though, requires thorough structural characterization of the alloys and investigation of their sorption properties. The samples have been synthesized by induction - levitation melting and characterized by Rietveld analysis of the X-Ray diffraction (XRD) patterns. Volumetric PCI (Pressure-Composition Isotherm) measurements have been conducted at 20, 60 and 90 oC, in order to investigate the maximum pressure that can be reached from the selected alloys using water of 90oC. Experimental evidence shows that the maximum hydrogen uptake is low since all the alloys are consisted of Laves phases, but it is of minor importance if they have fast kinetics, given a constant volumetric hydrogen flow. Hysteresis is almost absent while all the alloys release nearly all the absorbed hydrogen during desorption. Due to hardware restrictions, the maximum hydrogen pressure for the measurements was limited at 100 bars. Practically, the maximum pressure that can be reached from the last alloy is more than 150 bars.Comment: 9 figures. arXiv admin note: text overlap with arXiv:1207.354

The formation of black holes in spherically symmetric gravitational collapse

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines $r=c\in [0,2M]$ are incomplete, and for r>2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We also give examples of such initial data with the additional property that the solutions exist for all $r\geq 0$ and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modification

Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$ with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with $n=5$ and $n \ge 6$. There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of $n=5$ must be naked. In the minus-branch solution, naked singularities are massless for $n \ge 6$, while massive naked singularities are possible for $n=5$. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for $n \ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge 10$ and for $n=9$ depending on the parameters in the initial data, while a naked singularity is always formed for $5 \le n \le 8$. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.Comment: 23 pages, 1 figure, final version to appear in Physical Review

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

On Linear Congestion Games with Altruistic Social Context

We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a framework, given a real matrix $\Gamma=(\gamma_{ij})$ specifying a particular social context, each player $i$ aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player $j$, the multiplicative coefficient is given by the value $\gamma_{ij}$. We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature

Self-Similar Collapse of Conformally Coupled Scalar Fields

A massless scalar field minimally coupled to the gravitational field in a simplified spherical symmetry is discussed. It is shown that, in this case, the solution found by Roberts, describing a scalar field collapse, is in fact the most general one. Taking that solution as departure point, a study of the gravitational collapse for the self-similar conformal case is presented.Comment: 9 pages, accepted for publication, Classical and Quantum Gravity. Available at http://dft.if.uerj.br/preprint/e-17.tex or at ftp://dft.if.uerj.br/preprint/e-17.tex . Figures can be obtained on request at [email protected]

Mathematical modelling of water absorption and evaporation in a pharmaceutical tablet during film coating

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature

Designing cost-sharing methods for Bayesian games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players

Mathematical Modeling of Spray Impingement and Film Formation on Pharmaceutical Tablets during Coating

The application of coating films is an important step in the manufacture of pharmaceutical tablets. Understanding the phenomena taking place during coating spray application provides important information that can be used to reduce the number of defective tablets and select the optimal conditions for the coating process. In this work, we investigate spray impact and film spreading on a tablet while this passes through the spray-zone in a rotating coating drum. To simulate spray impingement, we developed an one-dimensional (1D) spreading model that is based on the mechanical energy equation. We assumed the spray to be uniform and we divided it into arrays of droplets that impinge successively on the substrate orthogonally to its surface. In the mechanical energy equation that describes the coating spreading, we accounted for the rate of work done on the surface of the liquid coating film by the impinging droplets that leads to volume change (film spreading and thickness increase). The novel model we propose in this work can calculate the coating spreading rate and thickness. We implemented the mathematical model employing the gPROMS Modelbuilder platform. To study the effect of coating properties and process parameters on the film spreading rate and on the final liquid film thickness, we performed variance-based sensitivity analysis. The model predictions are in good agreement with experimental data found in the literature