Analytical solution for transient one-dimensional couette flow considering constant and time-dependent pressure gradients

This paperaims to determine the velocity profile, in transient state, for a parallel incompressible flow known as Couette flow. The Navier-Stokes equations were applied upon this flow. Analytical solutions, based in Fourier series and integral transforms, were obtained for the one-dimensional transient Couette flow, taking into account constant and time-dependent pressure gradients acting on the fluid since the same instant when the plate starts it´s movement. Taking advantage of the orthogonality and superposition properties solutions were foundfor both considered cases. Considering a time-dependent pressure gradient, it was found a general solution for the Couette flow for a particular time function. It was found that the solution for a time-dependent pressure gradient includes the solutions for a zero pressure gradient and for a constant pressure gradient.

Modelagem Matemática e Análise de Modelos Matemáticos na Educação Matemática

In this paper we present two studies, the first one completed and the second one in development, which are based in teaching approaches that propose the qualitative study of mathematical models as a strategy for the teaching and learning of mathematical concepts. These teaching approaches focus on subjects from Higher Education such as Introduction to Ordinary Differential Equations and Topics of Differential and Integral Calculus. We denominate this common aspect of the teaching approaches as Model Analysis and in a preliminary level we relate it with Mathematical Modeling. Furthermore, we discuss some questions related with the choice of the theme and the role of Digital Technologies when Model Analysis is applied.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Quadraturformeln für das Qualokationsverfahren

Im Mittelpunkt dieser Arbeit steht Beweis der Existenz- und Eindeutigkeit von Quadraturformeln, die für das Qualokationsverfahren geeignet sind. Letzteres ist ein von Sloan, Wendland und Chandler entwickeltes Verfahren zur numerischen Behandlung von Randintegralgleichungen auf glatten Kurven (allgemeiner: periodische Pseudodifferentialgleichungen). Es erreicht die gleichen Konvergenzordnungen wie das Petrov-Galerkin-Verfahren, wenn man durch den Operator bestimmte Quadraturformeln verwendet. Zunächst werden die hier behandelten Pseudodifferentialoperatoren und das Qualokationsverfahren vorgestellt. Anschließend wird eine Theorie zur Existenz und Eindeutigkeit von Quadraturformeln entwickelt. Ein wesentliches Hilfsmittel hierzu ist die hier bewiesene Verallgemeinerung eines Satzes von Nürnberger über die Existenz und Eindeutigkeit von Quadraturformeln mit positiven Gewichten, die exakt für Tschebyscheff-Räume sind. Es wird schließlich gezeigt, dass es stets eindeutig bestimmte Quadraturformeln gibt, welche die in den Arbeiten von Sloan und Wendland formulierten Bedingungen erfüllen. Desweiteren werden 2-Punkt-Quadraturformeln für so genannte einfache Operatoren bestimmt, mit welchen das Qualokationsverfahren mit einem Testraum von stückweise konstanten Funktionen eine höhere Konvergenzordnung hat. Außerdem wird gezeigt, dass es für nicht-einfache Operatoren im Allgemeinen keine Quadraturformel gibt, mit der die Konvergenzordnung höher als beim Petrov-Galerkin-Verfahren ist. Das letzte Kapitel beinhaltet schließlich numerische Tests mit Operatoren mit konstanten und variablen Koeffizienten, welche die theoretischen Ergebnisse der vorangehenden Kapitel bestätigen.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

We Did It Our Way: Motivations, Satisfactions, and Accomplishments of Senior Academic Women

In a survey of senior academic women whose careers began around 1970, over half of the 98 respondents cited the desire to serve or make a difference and sought personal fulfillment in their work. Most saw men’s motivations as dissimilar, typically as more self-interested and competitive. Despite generally high satisfaction, dissatisfaction with time pressure/workload and with support was common. Satisfactions and accomplishments overlapped. Frequently mentioned were teaching, scholarship, and their discipline, especially by faculty, and programmatic accomplishments, especially by administrators. Many respondents mentioned helping women; many mentioned a collaborative, nurturing style as integral to their success and as different from their typical male colleagues. Context is provided by the metaphor of immigration (Martin, 1997, 2000), the concept of ambivalent sexism (Krefting, 2003; Glick & Fiske, 1999), and recent work on women and leadership by Eagly and colleagues (e.g., Eagly, 2005; Eagly & Carli, 2007).

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u (*)/u (*R) , where u (*) is the friction velocity and u (*R) is the friction velocity from the uniform building height case, is expressed well as an algebraic function of lambda and sigma (h) /h (m) , where lambda is the frontal area index, sigma (h) is the standard deviation of the building height, and h (m) is the mean building height. The simulations also resulted in a simple algebraic relation for z (0)/z (0R) as a function of lambda and sigma (h) /h (m) , where z (0) is the aerodynamic roughness length and z (0R) is z (0) found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.

Impact of salt on cardiac differential gene expression and coronary lesion in normotensive mineralocorticoid-treated mice

We previously reported that excess of deoxycorticosterone-acetate (DOCA)/salt-induced cardiac hypertrophy in the absence of hypertension in one-renin gene mice. This model allows us to study molecular mechanisms of high-salt intake in the development of cardiovascular remodeling, independently of blood pressure in a high mineralocorticoid state. In this study, we compared the effect of 5-wk low- and high-salt intake on cardiovascular remodeling and cardiac differential gene expression in mice receiving the same amount of DOCA. Differential gene and protein expression was measured by high-density cDNA microarray assays, real-time PCR and Western blot analysis in DOCA-high salt (HS) vs. DOCA-low salt (LS) mice. DOCA-HS mice developed cardiac hypertrophy, coronary perivascular fibrosis, and left ventricular dysfunction. Differential gene and protein expression demonstrated that high-salt intake upregulated a subset of genes encoding for proteins involved in inflammation and extracellular matrix remodeling (e.g., Col3a1, Col1a2, Hmox1, and Lcn2). A major subset of downregulated genes encoded for transcription factors, including myeloid differentiation primary response (MyD) genes. Our data provide some evidence that vascular remodeling, fibrosis, and inflammation are important consequences of a high-salt intake in DOCA mice. Our study suggests that among the different pathogenic factors of cardiac and vascular remodeling, such as hypertension and mineralocorticoid excess and sodium intake, the latter is critical for the development of the profibrotic and proinflammatory phenotype observed in the heart of normotensive DOCA-treated mice.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

[Oral erythroplakia and erythroleukoplakia: red and red-white dysplastic lesions of the oral mucosa--part 1: epidemiology, etiology, histopathology and differential diagnosis]

Oral erythroplakia (OE) and oral erythroleukoplakia (OEL; synonym: speckled leukoplakia) are working diagnoses for red and red-white lesions of the oral mucosa after exclusion of all other possible diagnoses for lesions with a similar clinical appearance. A good knowledge of oral medicine and possible differential diagnoses of oral mucosal pathologies is mandatory to correctly detect OE and OEL on this exclusion basis. In the present review article in a series of two, epidemiologic data, etiologic factors, possible differential diagnoses, and the histopathologic characteristics of OE and OEL will be presented and discussed regarding the current literature. A thorough histopathologic examination of these epithelial precursor lesions is mandatory to recognise the presence and the severity of epithelial dysplasia, which is a decisive factor for the subsequent treatment planning.

Synthesis of computations and experiments for obtaining pulsatile gas flow rates from dynamic pressure difference measurements across an orifice-plate meter

The use of conventional orifice-plate meter is typically restricted to measurements of steady flows. This study proposes a new and effective computational-experimental approach for measuring the time-varying (but steady-in-the-mean) nature of turbulent pulsatile gas flows. Low Mach number (effectively constant density) steady-in-the-mean gas flows with large amplitude fluctuations (whose highest significant frequency is characterized by the value fF) are termed pulsatile if the fluctuations have a direct correlation with the time-varying signature of the imposed dynamic pressure difference and, furthermore, they have fluctuation amplitudes that are significantly larger than those associated with turbulence or random acoustic wave signatures. The experimental aspect of the proposed calibration approach is based on use of Coriolis-meters (whose oscillating arm frequency fcoriolis >> fF) which are capable of effectively measuring the mean flow rate of the pulsatile flows. Together with the experimental measurements of the mean mass flow rate of these pulsatile flows, the computational approach presented here is shown to be effective in converting the dynamic pressure difference signal into the desired dynamic flow rate signal. The proposed approach is reliable because the time-varying flow rate predictions obtained for two different orifice-plate meters exhibit the approximately same qualitative, dominant features of the pulsatile flow.

Improved dispersive analysis of the scalar form factor of the nucleon

We present a coupled system of integral equations for the pp → ¯NN and ¯K K → ¯N N S-waves derived from Roy–Steiner equations for pion–nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili–Omnès problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including ¯KK intermediate states. In particular, we determine the corrections Ds and DD, which are needed for the extraction of the pion– nucleon s term from pN scattering, and show that the difference DD −Ds = (−1.8±0.2)MeV is insensitive to the input pN parameters.

Apolipoprotein E genotypes and cognitive functions in healthy elderly persons

Objectives- We investigated whether apoE genotypes correlate with cognitive functions in clinically healthy persons. Methods - In 1993 and 1995, we measured information processing speed, delayed free recall and semantic aspects of long-term memory in 227 men and 105 women aged 65 and over, a randomly selected subsample of the prospective Basel Study. Cardiovascular risk factors and education were assessed. Results -E2 were more prevalent in old-old (>75 years, 23.5% vs 15%) compared to E4 than in young-old (<75 years, 19.3% vs 23.5%). Taking into account age and education, subjects with ɛ3/ɛ4 or ɛ4/ɛ4 alleles (E4) performed lowest in all 3 tests compared to those homozygous for ɛ3 (E3) or carriers of one or two ɛ2 alleles (E2) (reaction time P=0.009, free recall P=0.05, WAIS-R vocabulary P<0.05). In old-old there was a significant difference between E2 and E4 for reaction time (P=0.02) and free recall (P<0.02) but not for vocabulary (P=0.086). In all 3 groups there were no significant changes after 2 years. The subgroup with the genotype ɛ2/ɛ4 performed consistently best in the cognitive tests. Cholesterol was significantly increased in the E4 and E3 group compared to the E2 group. Conclusion - ApoE genotype correlates with cognitive performance. The increased prevalence of E2 in the old-old and the significantly lower plasma cholesterol levels suggest differential morbidity and mortality as important factors influencing the prevalence of cognitive disorders in late life.

Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.