Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the $L_\infty$ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an $L_q$ norm with $q<\infty$ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis.Comment: 24 page

Formation of X-ray emitting stationary shocks in magnetized protostellar jets

X-ray observations of protostellar jets show evidence of strong shocks heating the plasma up to temperatures of a few million degrees. In some cases, the shocked features appear to be stationary. They are interpreted as shock diamonds. We aim at investigating the physics that guides the formation of X-ray emitting stationary shocks in protostellar jets, the role of the magnetic field in determining the location, stability, and detectability in X-rays of these shocks, and the physical properties of the shocked plasma. We performed a set of 2.5-dimensional magnetohydrodynamic numerical simulations modelling supersonic jets ramming into a magnetized medium and explored different configurations of the magnetic field. The model takes into account the most relevant physical effects, namely thermal conduction and radiative losses. We compared the model results with observations, via the emission measure and the X-ray luminosity synthesized from the simulations. Our model explains the formation of X-ray emitting stationary shocks in a natural way. The magnetic field collimates the plasma at the base of the jet and forms there a magnetic nozzle. After an initial transient, the nozzle leads to the formation of a shock diamond at its exit which is stationary over the time covered by the simulations (~ 40 - 60 yr; comparable with time scales of the observations). The shock generates a point-like X-ray source located close to the base of the jet with luminosity comparable with that inferred from X-ray observations of protostellar jets. For the range of parameters explored, the evolution of the post-shock plasma is dominated by the radiative cooling, whereas the thermal conduction slightly affects the structure of the shock.Comment: Accepted for publication in Astronomy and Astrophysic

Pathway Weathering in Granitoid Rocks from Central Region of Angola: Geochemical and Mineralogical Data

The Central Region of Angola is characterized by the abundance of granitoid rocks, whose weathering “in situ” originated the so-called residual soils. The textural, geochemical and mineralogical properties of these soils depend not only on the chemical composition of parent rock, but mainly on the local climatic and geomorphological characteristics. In the study area, sampling sites were selected, which extend from the region of Kwanza- Norte (Kassenda, Dondo) through Kwanza-Sul (Cangulo, Quibala and Waco Kungo) until the plateau of Huambo, where samples of fresh rock, weathered rock and its residual soil were collected along each weathering profile. Chemical analytical data were determined using X-ray fluorescence (XRF) analysis of the major and minor elements, whereas mineralogical data were determined using X-ray diffraction (XRD), on the samples of rock and on the respective residual soil. The results obtained and their comparative analysis between the sampling sites, as well as along each weathering profile is presented. This paper allows contributing to the knowledge of the geochemical weathering in tropical areas, as is the case of Angola

Quality of board members’ training and bank financial performance : evidence from Portugal

This study examines the impact of the quality of board members’ training on the financial performance of Portuguese banks. The study employs a sample of 276 board members. Financial ratios such as return on average assets (ROAA) and return on average equity (ROAE) are used as measures for gauging banks’ financial performance. Three indexes are used as proxies for board members’ educational qualifications, specifically: Eduindex, for all academic qualifications obtained in areas such as business or economics; EduindexDP, for all qualifications obtained in prestigious domestic business schools; and EduindexFP, for all qualifications obtained in prestigious foreign business schools. The study findings have important policy implications, specifically a positive and significant impact on the bank’s financial performance from having board members holding degrees from prestigious foreign business schools. In particular, the findings suggest that the prudential supervision developed by Banco de Portugal in cooperation with the European Central Bank should include a more rigorous process in the selection of board members. The present study is one of the first attempts in the literature emphasizing all these aspects simultaneously, that is, the banking sector, quality of board members’ training, and Eduniversal Rankings, in the context in which all the banks of a specific country are analysed.peer-reviewe

Quality of board members’ training and bank financial performance: evidence from Portugal

This study examines the impact of the quality of board members’ training on the financial performance of Portuguese banks. The study employs a sample of 276 board members. Financial ratios such as return on average assets (ROAA) and return on average equity (ROAE) are used as measures for gauging banks’ financial performance. Three indexes are used as proxies for board members’ educational qualifications, specifically: Eduindex, for all academic qualifications obtained in areas such as business or economics; EduindexDP, for all qualifications obtained in prestigious domestic business schools; and EduindexFP, for all qualifications obtained in prestigious foreign business schools. The study findings have important policy implications, specifically a positive and significant impact on the bank’s financial performance from having board members holding degrees from prestigious foreign business schools. In particular, the findings suggest that the prudential supervision developed by Banco de Portugal in cooperation with the European Central Bank should include a more rigorous process in the selection of board members. The present study is one of the first attempts in the literature emphasizing all these aspects simultaneously, that is, the banking sector, quality of board members’ training, and Eduniversal Rankings, in the context in which all the banks of a specific country are analysed. © 2018 International Strategic Management Association.info:eu-repo/semantics/publishedVersio

CARACTERIZAÇÃO GEOLÓGICA E GEOTÉCNICA DE SOLOS RESIDUAIS TROPICAIS DA REGIÃO CENTRAL DE ANGOLA

Poucos são os trabalhos científicos existentes que contemplem a composição química, mineralógica e textural de solos residuais tropicais de Angola, sendo que os mais comuns têm sido focados para a caracterização pedológica, fundamentalmente para fins agrícolas [Castanheira, 1998], ou baseiam-se em classificações cujas realidades não se enquadram com as de Angola, tanto pela ausência de bibliografia, como pela complexidade que os mesmos apresentam. Em resultado disso, a aplicação destes solos para fins de engenharia traz, muitas das vezes, consequências nefastas que podem ser imprevisíveis e irreversíveis, do ponto de vista da funcionalidade e segurança das obras de engenharia. Assim, o presente trabalho tem como objectivo determinar características geológicas e geotécnicas dos solos residuais da Região Central de Angola (Huambo, Kwanza-Sul e Kwanza-Norte), ilustrados na Figura 1, assim como identificar os principais factores que determinam a formação dos mesmos. Dado que a composição mineralógica e textural de um solo residual, é resultado principalmente da história geológica herdada da rocha-mãe, do clima predominante e das condições geomorfológicas, não se pode caracterizar os solos residuais sem antes conhecer a composição química e mineralógica da rocha-mãe em questão [Duarte, 2002]. Sendo assim, a caracterização mineralógica foi efetuada mediante a aplicação das técnicas de análise mineralógica por difracção de raios-X (DRX) e a análise química por espectrometria de fluorescência de raios-X (FRX), a fim de se identificar os principais tipos de minerais, assim como os elementos químicos constituintes tanto da rocha-mãe, como do solo residual resultante. Os resultados de DRX revelam que as de rochas de origem são constituídas por quartzo muito abundante, presença de feldspatos potássicos (microclina e ortose) e plagioclases ricas em sódio (Albite) [Ferreira da Silva, 2009]. As micas estão presentes em todas as rochas, às vezes com a maior preponderância da biotite (amostras A e B), e noutros casos com o maior predomínio da moscovite/ilite (amostras C e F). Noutros casos (e.g. amostra de rocha F), constata-se que os seus minerais constituintes são o quartzo, a albite, a moscovite/ilite, a ortose e a braunite (óxido silicato de manganês). Esta constituição mineralógica é típica de rochas granitóides, precisamente granitos, e é confirmada pelos dados químicos obtidos por FRX que revelam que as rochas são constituídas por SiO2 (71%), Al2O3 (14%), K2O (4%), Fe3O2 (3%), Na2O (3%) e CaO (2%) [Duarte et al, 2013]. Com a atuação dos mecanismos de alteração, os minerais que se cristalizam em primeiro lugar, formados a temperaturas mais altas (e.g. as biotites) são menos estáveis quando submetidos as condições atmosféricas mais rigorosas (e.g. os solos do Huambo) dando lugar aos óxidos de ferro e de alumínio (hematite, goethite e a gibsite). Ao passo que os minerais que se cristalizam em último lugar, formados em temperaturas mais baixas e mais próximas às das condições superficiais (e.g. o quartzo), são mais estáveis. Os resultados da caracterização mineralógica são confirmados pela FRX que nos revelam que as perdas são muito acentuadas em regiões com taxas altas de precipitação, onde os elementos mais móveis (Na, K, Ca, Mg, etc.) quase desapareceram na totalidade, obtendo-se a composição de um solo rico em alumínio e ferro, com algum titânio. Noutras regiões (e.g. Cassenda, com menor taxa de precipitação), os elementos móveis mantém-se parcialmente nas amostras, o que denota menor disponibilidade de água para lixiviar tais elementos. Os dados obtidos a partir das análises mineralógicas e químicas efetuadas, permitem identificar os processos de alteração envolvidos nos solos em causa, e compreender os resultados experimentais relativos às propriedades físicas e mecânicas (composição textural, consistência, porosidade, peso volúmico seco máximo, teor em água ótimo, C.B.R., etc.), cuja determinação pode aferir acerca das áreas da engenharia geotécnica onde estes solos poderão ser aplicados [Duarte et al, 2011]

Assembly of the Auditory Circuitry by a Hox Genetic Network in the Mouse Brainstem

Rhombomeres (r) contribute to brainstem auditory nuclei during development. Hox genes are determinants of rhombomere-derived fate and neuronal connectivity. Little is known about the contribution of individual rhombomeres and their associated Hox codes to auditory sensorimotor circuitry. Here, we show that r4 contributes to functionally linked sensory and motor components, including the ventral nucleus of lateral lemniscus, posterior ventral cochlear nuclei (VCN), and motor olivocochlear neurons. Assembly of the r4-derived auditory components is involved in sound perception and depends on regulatory interactions between Hoxb1 and Hoxb2. Indeed, in Hoxb1 and Hoxb2 mutant mice the transmission of low-level auditory stimuli is lost, resulting in hearing impairments. On the other hand, Hoxa2 regulates the Rig1 axon guidance receptor and controls contralateral projections from the anterior VCN to the medial nucleus of the trapezoid body, a circuit involved in sound localization. Thus, individual rhombomeres and their associated Hox codes control the assembly of distinct functionally segregated sub-circuits in the developing auditory brainstem