Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.

Blue-enhanced thin-film photodiode for dual-screen x-ray imaging

This article reports on a-Si:H-based low-leakage blue-enhanced photodiodes for dual-screen x-ray imaging detectors. Doped nanocrystalline silicon was incorporated in both the n- and p-type regions to reduce absorption losses for light incoming from the top and bottom screens. The photodiode exhibits a dark current density of 900 pA/cm(2) and an external quantum efficiency up to 90% at a reverse bias of 5 V. In the case of illumination through the tailored p-layer, the quantum efficiency of 60% at a 400 nm wavelength is almost double that for the conventional a-Si:H n-i-p photodiode.

Imposto pessoal sobre o rendimento: compatibilidade com um modelo dual de tributação

De entre os impostos que integram o nosso sistema fiscal, o imposto sobre o rendimento das pessoas singulares, ocupa um lugar de destaque na arrecadação de receitas. A sua im-portância coloca este imposto sobre pressão, pondo em confronto a tributação dos rendi-mentos de capitais e a tributação dos rendimentos do trabalho. O modelo de base compreensiva em que assenta o imposto pessoal está semi dualizado, dado tributar de forma diferente os rendimentos com origem em investimentos financeiros, subtraindo-os ao englobamento com os restantes rendimentos. Com a presente dissertação, pretende-se averiguar se o imposto pessoal, face ao recorte constitucional, pode adoptar um modelo de base semi-dual. Esta configuração permitiria simplificar o imposto, assumir duas bases e coloca-lo em linha com os modelos de tributação pessoal adoptados em alguns países europeus. O estudo realizado permitiu concluir que é possível a adopção de um modelo de base semi-dual, desde que se mantenha, por opção do contribuinte, o regime do englobamento com os restantes rendimentos. A dúvida que manifestamos relaciona-se com a oportuni-dade da concretização da reforma. O momento delicado de finanças públicas que o nosso país atravessa, traz tarefas acrescidas aos políticos, fruto dos compromissos internacionais assumidos, o que pode obstar ao agendamento da reforma do imposto pessoal que muitos reclamam. Daí que o caminho a seguir seria o do aperfeiçoamento do actual modelo.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.