Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.

Detector de contorns basat en el domini transformat

RESUM En aquest document es presenta un detector de contorns d’imatges basat en el domini transformat. A partir de la interpretació de la transformada de Fourier de la imatge i la seva formulació matricial en termes dels diferents modes, es realitza una selecció de les components passa baixes a partir de les quals es reconstrueix la component de baixa freqüència que es resta de la imatge original per tal d’obtenir el detector. Aquest detector de contorns no és esbiaixat. L’algorisme pot ser aplicat utilitzant diferents mides del bloc de processament, que pot anar de la imatge sencera a blocs de reduïdes dimensions: 36X36, 16x16 o 8x8, per fer un seguiment de les propietats locals de la imatge quan aquesta és presenta característiques espacials poc uniformes.

Expectations, Learning and Monetary Policy: An Overview of Recent Research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents’ learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

On the characterisation and measurement of the welfare effects of income mobility from an ex-ante perspective

The paper employs a rank-dependent formulation of the social welfare function with time-separable utilities to evaluate the economic consequences of income mobility from an ex-ante perspective. The resultant class of measures can be decomposed not only in terms of structural and exchange mobility but also in terms of vertical and horizontal mobility, thereby encompassing two of the main approaches in the literature. We illustrate our measurement framework by comparing mobility in the USA and Germany using data from the Cross-National Equivalent File 1980-2005. We find that the pattern of income mobility in the USA was both less pro-poor and more horizontally inequitable than in Germany, but that the latter did not translate into higher levels of exchange mobility given higher levels of absolute inequality and the vertical stance of the growth process.

Two different 3D biogeochemical models for the NW mediterranean sea: validation with Meris data and intercomparison

Report for the scientific sojourn carried out at the University of New South Wales from February to June the 2007. Two different biogeochemical models are coupled to a three dimensional configuration of the Princeton Ocean Model (POM) for the Northwestern Mediterranean Sea (Ahumada and Cruzado, 2007). The first biogeochemical model (BLANES) is the three-dimensional version of the model described by Bahamon and Cruzado (2003) and computes the nitrogen fluxes through six compartments using semi-empirical descriptions of biological processes. The second biogeochemical model (BIOMEC) is the biomechanical NPZD model described in Baird et al. (2004), which uses a combination of physiological and physical descriptions to quantify the rates of planktonic interactions. Physical descriptions include, for example, the diffusion of nutrients to phytoplankton cells and the encounter rate of predators and prey. The link between physical and biogeochemical processes in both models is expressed by the advection-diffusion of the non-conservative tracers. The similarities in the mathematical formulation of the biogeochemical processes in the two models are exploited to determine the parameter set for the biomechanical model that best fits the parameter set used in the first model. Three years of integration have been carried out for each model to reach the so called perpetual year run for biogeochemical conditions. Outputs from both models are averaged monthly and then compared to remote sensing images obtained from sensor MERIS for chlorophyll.

A Salience Theory of Choice Errors

We study a psychologically based foundation for choice errors. The decision maker applies a preference ranking after forming a 'consideration set' prior to choosing an alternative. Membership of the consideration set is determined both by the alternative specific salience and by the rationality of the agent (his general propensity to consider all alternatives). The model turns out to include a logit formulation as a special case. In general, it has a rich set of implications both for exogenous parameters and for a situation in which alternatives can a¤ect their own salience (salience games). Such implications are relevant to assess the link between 'revealed' preferences and 'true' preferences: for example, less rational agents may paradoxically express their preference through choice more truthfully than more rational agents.

Notes on Agents’ Behavioral Rules Under Adaptive Learning and Studies of Monetary Policy

These notes try to clarify some discussions on the formulation of individual intertemporal behavior under adaptive learning in representative agent models. First, we discuss two suggested approaches and related issues in the context of a simple consumption-saving model. Second, we show that the analysis of learning in the NewKeynesian monetary policy model based on “Euler equations” provides a consistent and valid approach.

Evaluation of different Cypermethrin formulations and concentrations in the control of Musca domestica

Cypermethrin (4 g/l, 5 g/l wettable powder and 7 ml/l, 10 ml/l emulsifiable concentrate) was tested, under laboratory conditions, against the adult Musca domestica. As a standard for comparison, a 6 ml/l concentrate suspension formulation of deltamethrin was used. One and twenty-four hours after application, mortality counts showed that the substances under test killed, respectively, more than 80% and 85% of the exposed insects. Under the conditions of the test, cypermethrin was considered effective in the control of the house fly.

Cost-effectiveness analysis in Chagas' disease vectors control interventions

After a large scale field trial performed in central Brazil envisaging the control of Chagas' disease vectors in an endemic area colonized by Triatoma infestans and T. sordida the cost-effectiveness analysis for each insecticide/formulation was performed. It considered the operational costs and the prices of insecticides and formulations, related to the activity and persistence of each one. The end point was considered to be less than 90% of domicilliary unitis (house + annexes) free of infestation. The results showed good cost-effectiveness for a slow-release emulsifiable suspension (SRES) based on PVA and containing malathion as active ingredient, as well as for the pyrethroids tested in this assay-cyfluthrin, cypermethrin, deltamethrin and permethrin.

Study on thermostabilizers for trivalent oral poliomyelitis vaccine

Different formulations of trivalent oral poliomyelitis vaccine were tested, in order to obtain better thermostability, reduce corrosion of machinery and improve production costs. Magnesium chloride, sucrose, arginine and 199-Hank's medium were used in the formulations. The most appropriate formulation was a mixture of MgCl2 and arginine, which was highly thermostable, and had low production costs. The low corrosive formulation was rejected, due to low thermostability on storage.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Particulate formulations for the delivery of poly(I:C) as vaccine adjuvant.

Current research and development of antigens for vaccination often center on purified recombinant proteins, viral subunits, synthetic oligopeptides or oligosaccharides, most of them suffering from being poorly immunogenic and subject to degradation. Hence, they call for efficient delivery systems and potent immunostimulants, jointly denoted as adjuvants. Particulate delivery systems like emulsions, liposomes, nanoparticles and microspheres may provide protection from degradation and facilitate the co-formulation of both the antigen and the immunostimulant. Synthetic double-stranded (ds) RNA, such as polyriboinosinic acid-polyribocytidylic acid, poly(I:C), is a mimic of viral dsRNA and, as such, a promising immunostimulant candidate for vaccines directed against intracellular pathogens. Poly(I:C) signaling is primarily dependent on Toll-like receptor 3 (TLR3), and on melanoma differentiation-associated gene-5 (MDA-5), and strongly drives cell-mediated immunity and a potent type I interferon response. However, stability and toxicity issues so far prevented the clinical application of dsRNAs as they undergo rapid enzymatic degradation and bear the potential to trigger undue immune stimulation as well as autoimmune disorders. This review addresses these concerns and suggests strategies to improve the safety and efficacy of immunostimulatory dsRNA formulations. The focus is on technological means required to lower the necessary dosage of poly(I:C), to target surface-modified microspheres passively or actively to antigen-presenting cells (APCs), to control their interaction with non-professional phagocytes and to modulate the resulting cytokine secretion profile.

Agapornis: relació entre fertilitat i neixements en els Agapornis lilianae i negrigenis

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. A partir d’ous exemplars de dues espècies d’agapornis -nigrigenis i lilianae-, es pretén realitzar un estudi comparatiu d’ambdues, tant pel que fa a l’etologia com a la reproducció, als hàbits alimentaris, etc. La idea inicial parteix de la possibilitat d’intercanviar alguns ous de cada espècie per mirar d’esbrinar si els ocells reproductors s’adonen de tal canvi. La hipòtesi inicial del treball considera que els ocells els criaran de la mateixa forma que si es tractés dels seus propis pollets. Les conclusions, però, han anat més enllà de la formulació de la hipòtesi inicial, de tal manera que, al final, i en forma de diagrama, s’ha pogut parlar de l’eclosió o manca d’eclosió dels ous d’aquesta espècie, tot relacionant temes diversos que van des de la fertilitat a les diferents mides dels ous. A més, l’autor també ha pogut concloure que els Agapornis lilianae són capaços de criar ocells d’una altra espècie (en aquest cas d Agapornis roseicollis) amb tota normalitat.