On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Complex variable positive definite functions

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

Invariant integrals applied to nematic liquid crystals with small Ericksen number and topological defects

Invariant integrals are derived for nematic liquid crystals and applied to materials with small Ericksen number and topological defects. The nematic material is confined between two infinite plates located at y = -h and y = h (h is an element of R+) with a semi-infinite plate at y = 0 and x < 0. Planar and homeotropic strong anchoring boundary conditions to the director field are assumed at these two infinite and semi-infinite plates, respectively. Thus, a line disclination appears in the system which coincides with the z-axis. Analytical solutions to the director field in the neighbourhood of the singularity are obtained. However, these solutions depend on an arbitrary parameter. The nematic elastic force is thus evaluated from an invariant integral of the energy-momentum tensor around a closed surface which does not contain the singularity. This allows one to determine this parameter which is a function of the nematic cell thickness and the strength of the disclination. Analytical solutions are also deduced for the director field in the whole region using the conformal mapping method. (C) 2013 Elsevier Ltd. All rights reserved.

Five models for lepton mixing

We produce five flavour models for the lepton sector. All five models fit perfectly well - at the 1 sigma level - the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type I seesaw mechanism, on a Z(2) symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange - or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for the phase delta in lepton mixing; the fifth model also predicts a correlation between the lepton mixing angles theta(12) and theta(23).

SCANNERS: constraining the phase diagram of a complex scalar singlet at the LHC

We present the first version of a new tool to scan the parameter space of generic scalar potentials, SCANNERS (Coimbra et al., SCANNERS project., 2013). The main goal of SCANNERS is to help distinguish between different patterns of symmetry breaking for each scalar potential. In this work we use it to investigate the possibility of excluding regions of the phase diagram of several versions of a complex singlet extension of the Standard Model, with future LHC results. We find that if another scalar is found, one can exclude a phase with a dark matter candidate in definite regions of the parameter space, while predicting whether a third scalar to be found must be lighter or heavier. The first version of the code is publicly available and contains various generic core routines for tree level vacuum stability analysis, as well as implementations of collider bounds, dark matter constraints, electroweak precision constraints and tree level unitarity.

Controlo da qualidade dosimétrico no serviço de radioterapia do Hospital CUF Descobertas (HCD): importância do controlo da qualidade do sector da física e resultados da auditoria ESTRO-EQUAL

A calibração e o controlo da qualidade de um acelerador linear são passos muito importantes num serviço de Radioterapia, para garantir a qualidade dos tratamentos prestados. O sector da Física da Unidade de Radioterapia do Hospital Cuf Descobertas implementou um rigoroso Programa de controlo de qualidade ao equipamento produtor de radiação e aos equipamentos medidores de radiação, de acordo com o Dec-Lei 180/2002 e com os protocolos internacionais. Para tal, foram implementados procedimentos, criadas folhas de cálculo, instruções de trabalho e impressos. Foram ainda implementados testes aos equipamentos com periodicidade definida: controlo de qualidade diário e controlo de qualidade após intervenções (manutenções preventivas e correctivas). No decorrer do ano de 2005, o sector da Física colaborou activamente com toda a equipa da Radioterapia na implementação da Norma ISO 9001:2000 no serviço, contribuindo com o seu know how na implementação desta, numa área tão importante como a da garantia da qualidade dos feixes de radiação e das respectivas calibrações em dose. Numa procura de melhoria contínua da qualidade dos serviços prestados aos pacientes, decorre ainda uma auditoria externa da EQUAL-ESTRO*, intercomparação postal com dosímetros termoluminescentes. A qualidade dos feixes de energias utilizados diariamente é analisada, tanto ao nível das calibrações absolutas de cada um dos feixes de fotões e de electrões, como ao nível dos cálculos de dose obtidos com o sistema de planimetria XiO da CMS. Os resultados das duas primeiras fases da intercomparação, relativa aos dois feixes de fotões de 6 MV e 15 MV e feixes de electrões de 4 MeV, 8 MeV e 12 MeV, foram considerados pela EQUAL-ESTRO num nível óptimo (desvio máximo na dose medida em relação à dose de referência |d| ≤ 3%).

Experimental signatures of fermiophobic Higgs bosons

The most general Two Higgs Doublet Model potential without explicit CP violation depends on 10 real independent parameters. Excluding spontaneous CP violation results in two 7 parameter models. Although both models give rise to 5 scalar particles and 2 mixing angles, the resulting phenomenology of the scalar sectors is different. If flavour changing neutral currents at tree level are to be avoided, one has, in both cases, four alternative ways of introducing the fermion couplings. In one of these models the mixing angle of the CP even sector can be chosen in such a way that the fermion couplings to the lightest scalar Higgs boson vanishes. At the same time it is possible to suppress the fermion couplings to the charged and pseudo-scalar Higgs bosons by appropriately choosing the mixing angle of the CP odd sector. We investigate the phenomenology of both models in the fermiophobic limit and present the different branching ratios for the decays of the scalar particles. We use the present experimental results from the LEP collider to constrain the models.

Estudo comparativo da estrutura de betão armado de um edifício dimensionada segunda a actual regulamentação nacional e os eurocódigos estruturais

Dissertação para obtenção do grau de Mestre em Engenharia Civil - Ramo de Estruturas

Metop-A generator for single top production via FCNC interactions

We present a generator for single top-quark production via flavour-changing neutral currents. The MEtop event generator allows for Next-to-Leading-Order direct top production pp -> t and Leading-Order production of several other single top processes. A few packages with definite sets of dimension six operators are available. We discuss how to improve the bounds on the effective operators and how well new physics can be probed with each set of independent dimension six operators.