Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4771591]

Tsunamigenic earthquakes in the Gulf of Cadiz: fault model and recurrence

The Gulf of Cadiz, as part of the Azores-Gibraltar plate boundary, is recognized as a potential source of big earthquakes and tsunamis that may affect the bordering countries, as occurred on 1 November 1755. Preparing for the future, Portugal is establishing a national tsunami warning system in which the threat caused by any large-magnitude earthquake in the area is estimated from a comprehensive database of scenarios. In this paper we summarize the knowledge about the active tectonics in the Gulf of Cadiz and integrate the available seismological information in order to propose the generation model of destructive tsunamis to be applied in tsunami warnings. The fault model derived is then used to estimate the recurrence of large earthquakes using the fault slip rates obtained by Cunha et al. (2012) from thin-sheet neotectonic modelling. Finally we evaluate the consistency of seismicity rates derived from historical and instrumental catalogues with the convergence rates between Eurasia and Nubia given by plate kinematic models.

A produção de educação nos Açores: a nota de matemática

Tese de Doutoramento, Ciências Económicas e Empresariais (Desenvolvimento Económico e Social e Economia Pública), 16 de Janeiro de 2014, Universidade dos Açores.

Entrepreneurship Strategies in a Portuguese and in a Polish Region

In the present paper we will consider strategies of innovation, risk and proactivity as entre/ intrapreneurship strategies. This study was done in a Portuguese and in a Polish region. In Portugal the region was Vale do Sousa, located in the northern Portugal. The Polish region was Lublin Voivodeship and it is situated in the south-eastern part of the country. The study focused on Industrial and Construction sectors. In order to get a valid sample, a group of 251 firms were analysed in Portugal, and 215 in Poland. However, the minimum sample size in Poland should be 323. Since this is a work in progress, we are aiming for this number of questionnaires. Each strategy was analysed individually for both regions and the results pointed to a lack of culture of entrepreneurship in firms’ management. Only Proactivity presented a positive result in firms’ management. Polish firms tend to be more innovative and more risk takers, while in proactivity Portuguese ones present a slightly higher result. Combining the strategy results, it was possible to identify that 61.2% of Portuguese firms present a low level of entrepreneurship, while 60% of Polish firms present a moderate level. Considering intrapreneurship good levels, while Portugal account for 5.2% this figure is 19.1% in Poland.

Planning, Cooperation and Competition: A case study in industry and construction in a Portuguese Region

In the present paper we analyzed the behavior of firms in the construction and manufacturing sectors, located in the region of Vale do Sousa, in the north of Portugal. From the literature, even existing some disagreements, it is possible to conclude that planning is crucial for firms survival and growth. Cooperation is another aspect that the literature presents as an important factor for firms sustainability. It also plays a major role in competition, since firms are adopting coopetition strategies. By studying a sample of 251 firms, it was possible to realize, that the majority started their business without a formal planning, and they keep going without using it. In cooperation aspects, there is a lack of cooperation. It was possible to verify, that existing cooperation has some evidence but at a vertical level. These vertical relations were also identified in stakeholder’s involvement.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Models with three Higgs doublets in the triplet representations of A(4) or S-4

We consider the quark sector of theories containing three scalar SU(2)(L) doublets in the triplet representation of A(4) (or S-4) and three generations of quarks in arbitrary A(4) (or S-4) representations. We show that for all possible choices of quark field representations and for all possible alignments of the Higgs vacuum expectation values that can constitute global minima of the scalar potential, it is not possible to obtain simultaneously nonvanishing quark masses and a nonvanishing CP-violating phase in the Cabibbo-Kobayashi-Maskawa quark mixing matrix. As a result, in this minimal form, models with three scalar fields in the triplet representation of A(4) or S-4 cannot be extended to the quark sector in a way consistent with experiment. DOI: 10.1103/PhysRevD.87.055010.

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).

Neutrino masses and mixing in A(4) models with three Higgs doublets

We study neutrino masses and mixing in the context of flavor models with A(4) symmetry, three scalar doublets in the triplet representation, and three lepton families. We show that there is no representation assignment that yields a dimension-5 mass operator consistent with experiment. We then consider a type-I seesaw with three heavy right-handed neutrinos, explaining in detail why it fails, and allowing us to show that agreement with the present neutrino oscillation data can be recovered with the inclusion of dimension-3 heavy neutrino mass terms that break softly the A(4) symmetry.

Interpretation of gravity data to delineate structural features connected to low-temperature geothermal resources at Northeastern Portugal

A great number of low-temperature geothermal fields occur in Northern-Portugal related to fractured rocks. The most important superficial manifestations of these hydrothermal systems appear in pull-apart tectonic basins and are strongly conditioned by the orientation of the main fault systems in the region. This work presents the interpretation of gravity gradient maps and 3D inversion model produced from a regional gravity survey. The horizontal gradients reveal a complex fault system. The obtained 3D model of density contrast puts into evidence the main fault zone in the region and the depth distribution of the granitic bodies. Their relationship with the hydrothermal systems supports the conceptual models elaborated from hydrochemical and isotopic water analyses. This work emphasizes the importance of the role of the gravity method and analysis to better understand the connection between hydrothermal systems and the fractured rock pattern and surrounding geology. (c) 2013 Elsevier B.V. All rights reserved.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Geographical, temporal and environmental determinants of bryophyte species richness in the Macaronesian Islands

Copyright: © 2014 Aranda et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Assesing multileaf collimator effect on the build-up region using Monte Carlo method

Previous Monte Carlo studies have investigated the multileaf collimator (MLC) contribution to the build-up region for fields in which the MLC leaves were fully blocking the openings defined by the collimation jaws. In the present work, we investigate the same effect but for symmetric and asymmetric MLC defined field sizes (2×2, 4×4, 10×10 and 3×7 cm2). A Varian 2100C/D accelerator with 120-leaf MLC is accurately modeled fora6MVphoton beam using the BEAMnrc/EGSnrc code. Our results indicate that particles scattered from accelerator head and MLC are responsible for the increase of about 7% on the surface dose when comparing 2×2 and 10×10 cm2 fields. We found that the MLC contribution to the total build-up dose is about 2% for the 2×2 cm2 field and less than 1% for the largest fields.

Comportamento das famílias em relação ao consumo de eletricidade: o caso dos Açores

Dissertação de Mestrado em Ciências Económicas e Empresariais