Counting results for sparse pseudorandom hypergraphs I

We establish a so-called counting lemma that allows embeddings of certain linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a result for graphs [Embedding graphs with bounded degree in sparse pseudorandom graphs, Israel J. Math. 139 (2004), 93-137]. Applications of our result are presented in the companion paper [Counting results for sparse pseudorandom hypergraphs II]

On the Magnitude of Dark Energy Voids and Overdensities

We investigate the clustering of dark energy within matter overdensities and voids. In particular, we derive an analytical expression for the dark energy density perturbations, which is valid both in the linear, quasi-linear and fully non-linear regime of structure formation. We also investigate the possibility of detecting such dark energy clustering through the ISW effect. In the case of uncoupled quintessence models, if the mass of the field is of order the Hubble scale today or smaller, dark energy fluctuations are always small compared to the matter density contrast. Even when the matter perturbations enter the non-linear regime, the dark energy perturbations remain linear. We find that virialised clusters and voids correspond to local overdensities in dark energy, with \delta_{\phi}/(1+w) \sim \Oo(10^{-5}) for voids, \delta_{\phi}/(1+w) \sim \Oo(10^{-4}) for super-voids and \delta_{\phi}/(1+w) \sim \Oo(10^{-5}) for a typical virialised cluster. If voids with radii of $100-300 {\rm Mpc}$ exist within the visible Universe then $\delta_{\phi}$ may be as large as $10^{-3}(1+w)$. Linear overdensities of matter and super-clusters generally correspond to local voids in dark energy; for a typical super-cluster: \delta_{\phi}/(1+w) \sim \Oo(-10^{-5}). The approach taken in this work could be straightforwardly extended to study the clustering of more general dark energy models.Comment: 20 pages, 14 figures. Accepted by the Astrophys.

An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution

We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model is designed so that it predicts a relation between the peculiar velocity and density contrast that agrees with the results of N-body simulations in the region where such a comparison can sensibly be made. Prior to turnaround, when the unmodified spherical collapse model is expect to be a good approximation, the predictions of the two models coincide almost exactly. The effects of a late time dominating dark energy component are also taken into account. The improved spherical collapse model is a useful tool when one requires a good approximation not just to the evolution of the density contrast but also its trajectory. Moreover, the analytical fitting formulae presented is simple enough to be used anywhere where the standard spherical collapse might be used but with the advantage that it includes a realistic model of the effects of virialisation.Comment: 6 pages, 3 figures. Matches the version in print at Astrophys.

Universe acceleration and fine structure constant variation in BSBM theory

In this work we investigate the utility of using SNe Ia observations in constraining the cosmological parameters in BSBM theory where a scalar field is responsible for both fine structure constant variation and late time universe acceleration. The model is discussed in the presence of an exponential self potential for the scalar field. Stability and phase space analysis of the solutions are studied. The model is tested against observational data for Hubble parameter and quasar absorption spectra. With the best fitted model parameters, the theory predicts a good match with the experimental results and exhibits fine structure constant variation. The analysis also shows that for the equation of state parameter, recent universe acceleration and possible phantom crossing in future is forecasted.Comment: 14 pages, 10 figures, final version with minor modification accepted to be published in JCA

Innovative board game design in an academic environment during the Covid-19 pandemic

Leisure or entertainment, like other everyday needs, are fundamental activities for human well-being. The creation of activities that lead to moments of satisfaction and relaxation are also a focus of attention and one of the areas of intervention where design can contribute solutions. This project challenged a group of students on a degree course in product design to develop modern, alternative board games, centred on users and on situations and environments of use, in order to exercise the practice of product design and seek to present innovative solutions. The challenge came through a local Cultural Association, with a tradition in promoting this type of game. The project followed a design project methodology that led students through a first phase of immersion in the theme, mechanics and strategies of games and their variety, going through the generation of ideas, models, evaluation tests, to the production of prototypes. The project was subject to the constraints of the Covid-19 pandemic, which forced students and teachers to work at home. To improve teaching and learning experiences, the project involved specialists and professionals who shared their knowledge and experience in developing this type of product. This gave rise to a great diversity of solutions, resulting from the use of an adequate methodology, making it possible to design new board games in which the mechanics, when articulated with a theme of interest to the target audience, can result in a proposal for an appealing and unique game.101E-1BBD-F278 | Jo?o Carlos Monteiro Martinsinfo:eu-repo/semantics/publishedVersio