Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Critical magnetic elds in superconducting systems with semi-metallic bands

In this work, we study the Zeeman splitting effects in the parallel magnetic field versus temperature phase diagram of two-dimensional superconductors with one graphene-like band and the orbital effects of perpendicular magnetic fields in isotropic two-dimensional semi-metallic superconductors. We show that when parallel magnetic fields are applied to graphene and as the intraband interaction decreases to a critical value, the width of the metastability region present in the phase diagram decreases, vanishing completely at that critical value. In the case of two-band superconductors with one graphene-like band, a new critical interaction, associated primarily with the graphene-like band, is required in order for a second metastability region to be present in the phase diagram. For intermediate values of this interaction, a low-temperature first-order transition line bifurcates at an intermediate temperature into a first-order transition between superconducting phases and a second-order transition line between the normal and the superconducting states. In our study on the upper critical fields in generic semi-metallic superconductors, we find that the pair propagator decays faster than that of a superconductor with a metallic band. As result, the zero field band gap equation does not have solution for weak intraband interactions, meaning that there is a critical intraband interaction value in order for a superconducting phase to be present in semi-metallic superconductors. Finally, we show that the out-of-plane critical magnetic field versus temperature phase diagram displays a positive curvature, contrasting with the parabolic-like behaviour typical of metallic superconductors.

Desenho do real : análise, representação e consciência crítica

O presente relatório reflete sobre o processo de representação pelo desenho de uma forma tridimensional num suporte bidimensional. A intenção deste relatório é analisar e compreender a relação entre o que é analisado pelo cérebro, o que é representado no papel e a consciência crítica do erro praticado no desenho de observação, bem como conhecer como poderá ser desenvolvida esta triangulação (análise, representação e consciência crítica do erro) de modo a melhorar a qualidade da representação do real. A investigação empírica foi realizada na disciplina de Desenho A, no ano letivo de 2012/2013, com duas turmas do 11º ano do Curso de Design de Produto na Escola Artística Soares dos Reis, no Porto. Os resultados obtidos sugerem que a perspetiva, enquanto estratégia, poderá melhorar significativamente a qualidade da representação do real. Todavia, relativamente ao estímulo da consciência crítica do erro através das estratégias abordadas dentro de sala de aula, não ficou comprovada relevância na qualidade das representações.