Analysis of the performance of caissons with a yard and cylindrical geometry as a breakwater. Apollonius caisson

En el presente trabajo se analiza el cajón Apolonio como diseño conceptual para controlar la reflexión en monolitos de gravedad sometidos a esfuerzos dinámicos de oleaje.

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

The calibration coefficients of two commercial anemometers equipped with different rotors were studied. The rotor cups had the same conical shape, while the size and distance to the rotation axis varied.The analysis was based on the 2-cup positions analytical model, derived using perturbation methods to include second-order effects such as pressure distribution along the rotating cups and friction.Thecomparison with the experimental data indicates a nonuniformdistribution of aerodynamic forces on the rotating cups, with higher forces closer to the rotating axis. The 2-cup analytical model is proven to be accurate enough to study the effect of complex forces on cup anemometer performance.

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

In different problems of Elasticity the definition of the optimal gcometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

NURBS-Based Geometry Parameterization for Aerodynamic Shape Optimization

La motivación de esta tesis es el desarrollo de una herramienta de optimización automática para la mejora del rendimiento de formas aerodinámicas enfocado en la industria aeronáutica. Este trabajo cubre varios aspectos esenciales, desde el empleo de Non-Uniform Rational B-Splines (NURBS), al cálculo de gradientes utilizando la metodología del adjunto continuo, el uso de b-splines volumétricas como parámetros de diseño, el tratamiento de la malla en las intersecciones, y no menos importante, la adaptación de los algoritmos de la dinámica de fluidos computacional (CFD) en arquitecturas hardware de alto paralelismo, como las tarjetas gráficas, para acelerar el proceso de optimización. La metodología adjunta ha posibilitado que los métodos de optimización basados en gradientes sean una alternativa prometedora para la mejora de la eficiencia aerodinámica de los aviones. La formulación del adjunto permite calcular los gradientes de una función de coste, como la resistencia aerodinámica o la sustentación, independientemente del número de variables de diseño, a un coste computacional equivalente a una simulación CFD. Sin embargo, existen problemas prácticos que han imposibilitado su aplicación en la industria, que se pueden resumir en: integrabilidad, rendimiento computacional y robustez de la solución adjunta. Este trabajo aborda estas contrariedades y las analiza en casos prácticos. Como resumen, las contribuciones de esta tesis son: • El uso de NURBS como variables de diseño en un bucle de automático de optimización, aplicado a la mejora del rendimiento aerodinámico de alas en régimen transónico. • El desarrollo de algoritmos de inversión de punto, para calcular las coordenadas paramétricas de las coordenadas espaciales, para ligar los vértices de malla a las NURBS. • El uso y validación de la formulación adjunta para el calculo de los gradientes, a partir de las sensibilidades de la solución adjunta, comparado con diferencias finitas. • Se ofrece una estrategia para utilizar la geometría CAD, en forma de parches NURBS, para tratar las intersecciones, como el ala-fuselaje. • No existen muchas alternativas de librerías NURBS viables. En este trabajo se ha desarrollado una librería, DOMINO NURBS, y se ofrece a la comunidad como código libre y abierto. • También se ha implementado un código CFD en tarjeta gráfica, para realizar una valoración de cómo se puede adaptar un código sobre malla no estructurada a arquitecturas paralelas. • Finalmente, se propone una metodología, basada en la función de Green, como una forma eficiente de paralelizar simulaciones numéricas. Esta tesis ha sido apoyada por las actividades realizadas por el Área de Dinámica da Fluidos del Instituto Nacional de Técnica Aeroespacial (INTA), a través de numerosos proyectos de financiación nacional: DOMINO, SIMUMAT, y CORESFMULAERO. También ha estado en consonancia con las actividades realizadas por el departamento de Métodos y Herramientas de Airbus España y con el grupo Investigación y Tecnología Aeronáutica Europeo (GARTEUR), AG/52. ABSTRACT The motivation of this work is the development of an automatic optimization strategy for large scale shape optimization problems that arise in the aeronautics industry to improve the aerodynamic performance; covering several aspects from the use of Non-Uniform Rational B-Splines (NURBS), the calculation of the gradients with the continuous adjoint formulation, the development of volumetric b-splines parameterization, mesh adaptation and intersection handling, to the adaptation of Computational Fluid Dynamics (CFD) algorithms to take advantage of highly parallel architectures in order to speed up the optimization process. With the development of the adjoint formulation, gradient-based methods for aerodynamic optimization become a promising approach to improve the aerodynamic performance of aircraft designs. The adjoint methodology allows the evaluation the gradients to all design variables of a cost function, such as drag or lift, at the equivalent cost of more or less one CFD simulation. However, some practical problems have been delaying its full implementation to the industry, which can be summarized as: integrability, computer performance, and adjoint robustness. This work tackles some of these issues and analyse them in well-known test cases. As summary, the contributions comprises: • The employment of NURBS as design variables in an automatic optimization loop for the improvement of the aerodynamic performance of aircraft wings in transonic regimen. • The development of point inversion algorithms to calculate the NURBS parametric coordinates from the space coordinates, to link with the computational grid vertex. • The use and validation of the adjoint formulation to calculate the gradients from the surface sensitivities in an automatic optimization loop and evaluate its reliability, compared with finite differences. • This work proposes some algorithms that take advantage of the underlying CAD geometry description, in the form of NURBS patches, to handle intersections and mesh adaptations. • There are not many usable libraries for NURBS available. In this work an open source library DOMINO NURBS has been developed and is offered to the community as free, open source code. • The implementation of a transonic CFD solver from scratch in a graphic card, for an assessment of the implementability of conventional CFD solvers for unstructured grids to highly parallel architectures. • Finally, this research proposes the use of the Green's function as an efficient paralellization scheme of numerical solvers. The presented work has been supported by the activities carried out at the Fluid Dynamics branch of the National Institute for Aerospace Technology (INTA) through national founding research projects: DOMINO, SIMUMAT, and CORESIMULAERO; in line with the activities carried out by the Methods and Tools and Flight Physics department at Airbus and the Group for Aeronautical Research and Technology in Europe (GARTEUR) action group AG/52.

Feo, inútil, inestable: pensamiento crítico contemporáneo y procesos proyectivos en arquitectura = Ugly, useless, unstable: contemporary critical thought and projective processes in architecture

La presente tesis doctoral persigue dos objetivos simultáneos: Determinar el alcance de los criterios clásicos para la evaluación de arquitectura y poner en crisis la prevalencia de esos mismos criterios dentro del marco crítico y productivo actual. En concreto, esta tesis se interroga sobre la posible contribución de determinadas corrientes del pensamiento post-estructuralista y neo-materialista a las tareas de expansión y transformación de los criterios clásicos antes mencionados. Asimismo, se plantea la oportunidad de formalizar estas incorporaciones conceptuales como metodologías para el proyectar arquitectónico. La tesis emplea un análisis pormenorizado de las cualidades implícitas en la triada Firmitas, Utilitas, Venustas elaborada por Vitruvio como vehículo para calibrar la influencia de los paradigmas de pensamiento clásico en nuestras posiciones críticas contemporáneas. Como reacción al carácter dominante de dichos paradigmas, y con la ayuda de una compilación selectiva de ejemplos procedentes de los campos artístico y arquitectónico, la presente tesis procede a examinar y clasificar diversas estrategias arquitectónicas basadas en la no conformidad con los criterios clásicos de evaluación de la disciplina. A la hora de realizar esta tarea, y con el objetivo de superar el dualismo trascendental que caracteriza la gran mayoría de dichos criterios clásicos, se propone un modelo analítico y multidimensional que formula las instancias arquitectónicas como posibles posiciones dentro de un extenso continuo combinatorio de cualidades formales, estructurales y organizativas. Este modelo conceptual permite replantear el aparente antagonismo entre los principios de Vitruvio y sus opuestos, estableciendo en su lugar un dominio operativo continuo de producción arquitectónica. Esta operación abre una ventana de oportunidad para expandir los límites del marco crítico actual más allá de las fronteras establecidas por nuestra herencia clásica. En consecuencia con esta voluntad, la presente tesis pretende habilitar un ámbito para el análisis crítico de las estrategias que caracterizan ciertas corrientes del proyectar contemporáneo, pero también contribuir a informar nuevas aproximaciones metodológicas al proceso de proyecto, desplazando progresivamente su foco desde lo descriptivo hacia lo proyectivo. ABSTRACT This doctoral thesis attempts to simultaneously determine the scope of the classical criteria for the evaluation of architecture and challenge their prevalence within the current framework of architectural production and criticism. It examines how specific strands of post-structuralism and neo-materialism may contribute to both the expansion and the transformation of these criteria and, in doing so, sets itself the goal of mobilising these conceptual incorporations as explicit design methodologies. A detailed analysis of the formal, structural and organisational qualities implicit in Vitruvius’ triad Firmitas, Utilitas, Venustas is used as a starting point to determine the influence of classical paradigms in our current critical positions. As a reaction to this critical pervasiveness, and supported by a curated collection of artistic and architectural works, diverse approaches to non-compliance with the classical criteria of assessment are examined and classified. In order to facilitate this endeavour -and to overcome the transcendental dualism of most classical critical approaches in architecture- this thesis puts forward an analytical, multidimensional model that formulates architectural instances as possible positions within a larger combinatory continuum of formal, structural and organisational qualities. Using this conceptual model, the apparent antagonism between Vitruvius’ principles and its non-compliant opposites is reframed as a continuous operative domain of architectural production, which in turn opens up a window of opportunity to expand the limits of our critical framework beyond the boundaries of classical paradigms. In doing so, this thesis attempts not only to foster a better understanding of some of the strategic approaches that characterise contemporary systems of architectural production, but also to inform future methodological approaches to architectural design, hence situating itself beyond the domain of the descriptive and moving towards the projective.

Tridimensional simulation of the speed, pressure and turbulence fields of the air flow on the geometry of a freight truck inside a wind tunnel

This study shows the air flow behavior through the geometry of a freight truck inside a AF6109 wind tunnel with the purpose to predict the speed, pressure and turbulence fields made by the air flow, to decrease the aerodynamic resistance, to calculate the dragging coefficient, to evaluate the aerodynamics of the geometry of the prototype using the CFD technique and to compare the results of the simulation with the results obtained experimentally with the “PETER 739 HAULER” scaled freight truck model located on the floor of the test chamber. The Geometry went through a numerical simulation process using the CFX 5,7. The obtained results showed the behavior of the air flow through the test chamber, and also it showed the variations of speed and pressure at the exit of the chamber and the calculations of the coefficient and the dragging force on the geometry of the freight truck. The evaluation of the aerodynamics showed that the aerodynamic deflector is a device that helped the reduction the dragging produced in a significant way by the air. Furthermore, the dragging coefficient and force on the prototype freight truck could be estimated establishing an incomplete similarity.

Calibración geométrica de cámaras no métricas. Estudio de metodologías y modelos matemáticos de distorsión

La Fotogrametría, como ciencia y técnica de obtención de información tridimensional del espacio objeto a partir de imágenes bidimensionales, requiere de medidas de precisión y en ese contexto, la calibración geométrica de cámaras ocupa un lugar importante. El conocimiento de la geometría interna de la cámara es fundamental para lograr mayor precisión en las medidas realizadas. En Fotogrametría Aérea se utilizan cámaras métricas (fabricadas exclusivamente para aplicaciones cartográficas), que incluyen objetivos fotográficos con sistemas de lentes complejos y de alta calidad. Pero en Fotogrametría de Objeto Cercano se está trabajando cada vez con más asiduidad con cámaras no métricas, con ópticas de peor calidad que exigen una calibración geométrica antes o después de cada trabajo. El proceso de calibración encierra tres conceptos fundamentales: modelo de cámara, modelo de distorsión y método de calibración. El modelo de cámara es un modelo matemático que aproxima la transformación proyectiva original a la realidad física de las lentes. Ese modelo matemático incluye una serie de parámetros entre los que se encuentran los correspondientes al modelo de distorsión, que se encarga de corregir los errores sistemáticos de la imagen. Finalmente, el método de calibración propone el método de estimación de los parámetros del modelo matemático y la técnica de optimización a emplear. En esta Tesis se propone la utilización de un patrón de calibración bidimensional que se desplaza en la dirección del eje óptico de la cámara, ofreciendo así tridimensionalidad a la escena fotografiada. El patrón incluye un número elevado de marcas, lo que permite realizar ensayos con distintas configuraciones geométricas. Tomando el modelo de proyección perspectiva (o pinhole) como modelo de cámara, se realizan ensayos con tres modelos de distorsión diferentes, el clásico de distorsión radial y tangencial propuesto por D.C. Brown, una aproximación por polinomios de Legendre y una interpolación bicúbica. De la combinación de diferentes configuraciones geométricas y del modelo de distorsión más adecuado, se llega al establecimiento de una metodología de calibración óptima. Para ayudar a la elección se realiza un estudio de las precisiones obtenidas en los distintos ensayos y un control estereoscópico de un panel test construido al efecto. ABSTRACT Photogrammetry, as science and technique for obtaining three-dimensional information of the space object from two-dimensional images, requires measurements of precision and in that context, the geometric camera calibration occupies an important place. The knowledge of the internal geometry of the camera is fundamental to achieve greater precision in measurements made. Metric cameras (manufactured exclusively for cartographic applications), including photographic lenses with complex lenses and high quality systems are used in Aerial Photogrammetry. But in Close Range Photogrammetry is working increasingly more frequently with non-metric cameras, worst quality optical components which require a geometric calibration before or after each job. The calibration process contains three fundamental concepts: camera model, distortion model and method of calibration. The camera model is a mathematical model that approximates the original projective transformation to the physical reality of the lenses. The mathematical model includes a series of parameters which include the correspondents to the model of distortion, which is in charge of correcting the systematic errors of the image. Finally, the calibration method proposes the method of estimation of the parameters of the mathematical modeling and optimization technique to employ. This Thesis is proposing the use of a pattern of two dimensional calibration that moves in the direction of the optical axis of the camera, thus offering three-dimensionality to the photographed scene. The pattern includes a large number of marks, which allows testing with different geometric configurations. Taking the projection model perspective (or pinhole) as a model of camera, tests are performed with three different models of distortion, the classical of distortion radial and tangential proposed by D.C. Brown, an approximation by Legendre polynomials and bicubic interpolation. From the combination of different geometric configurations and the most suitable distortion model, brings the establishment of a methodology for optimal calibration. To help the election, a study of the information obtained in the various tests and a purpose built test panel stereoscopic control is performed.

Soil aggregate geometry: Measurements and morphology

Aggregates provide physical microenvironments for microorganisms, the vital actors of soil systems, and thus play a major role as both, an arena and a product of soil carbon stabilization and dynamics. The surface of an aggregate is what enables exchange of the materials and air and water fluxes between aggregate exterior and interior regions. We made use of 3D images from X-ray CT of aggregates and mathematical morphology to provide an exhaustive quantitative description of soil aggregate morphology that includes both intra-aggregate pore space structure and aggregate surface features. First, the evolution of Minkowski functionals (i.e. volume, boundary surface, curvature and connectivity) for successive dilations of the solid part of aggregates was investigated to quantify its 3D geometrical features. Second, the inner pore space was considered as the object of interest. We devised procedures (a) to define the ends of the accessible pores that are connected to the aggregate surface and (b) to separate accessible and inaccessible porosity. Geometrical Minkowski functionals of the intra-aggregate pore space provide the exhaustive characterization of the inner structure of the aggregates. Aggregates collected from two different soil treatments were analyzed to explore the utility of these morphological tools in capturing the impact on their morphology of two different soil managements, i.e. conventional tillage management, and native succession vegetation treatment. The quantitative tools of mathematical morphology distinguished differences in patterns of aggregate structure associated to the different soil managements.

The interspecific mass–density relationship and plant geometry

We present an a priori theoretical framework for the interspecific allometric relationship between stand mass and plant population density. Our model predicts a slope of −\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\frac{1}{3}\end{equation*}\end{document} between the logarithm of stand mass and the logarithm of stand density, thus conflicting with a previously assumed slope of −½. Our model rests on a heuristic separation of resource-limited living mass and structural mass in the plant body. We point out that because of similar resource requirements among plants of different sizes, a nonzero plant mass–density slope is primarily defined by structural mass. Specifically, the slope is a result of (i) the physical size-dependent relationship between stem width and height, (ii) foliage-dependent demands of conductance, and (iii) the cumulative nature of structural mass. The data support our model, both when the potential sampling bias of taxonomic relatedness is accounted for and when it is not. Independent contrasts analyses show that observed relationships among variables are not significantly different from the assumptions made to build the model or from its a priori predictions. We note that the dependence of the plant mass–density slope on the functions of structural mass provides a cause for the difference from the zero slope found in the animal population mass–density relationship; for the most part, animals do not have a comparable cumulative tissue type.

The making of the architecture of the plant cell wall: How cells exploit geometry

Cell wall deposition is a key process in the formation, growth, and differentiation of plant cells. The most important structural components of the wall are long cellulose microfibrils, which are synthesized by synthases embedded in the plasma membrane. A fundamental question is how the microfibrils become oriented during deposition at the plasma membrane. The current textbook explanation for the orientation mechanism is a guidance system mediated by cortical microtubules. However, too many contraindications are known in secondary cell walls for this to be a universal mechanism, particularly in the case of helicoidal arrangements, which occur in many situations. An additional construction mechanism involves liquid crystalline self-assembly [A. C. Neville (1993) Biology of Fibrous Composites: Development Beyond the Cell Membrane (Cambridge Univ. Press, Cambridge, U.K.)], but the required amount of bulk material that is able to equilibrate thermally is not normally present at any stage of the wall deposition process. Therefore, we have asked whether the complex ordered texture of helicoidal cell walls can be formed in the absence of direct cellular guidance mechanisms. We propose that they can be formed by a mechanism that is based on geometrical considerations. It explains the genesis of the complicated helicoidal texture and shows that the cell has intrinsic, versatile tools for creating a variety of textures. A compelling feature of the model is that local rules generate global order, a typical phenomenon of life.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Specific atomic groups and RNA helix geometry in acceptor stem recognition by a tRNA synthetase

Oligonucleotides that recapitulate the acceptor stems of tRNAs are substrates for aminoacylation by many tRNA synthetases in vitro, even though these substrates are missing the anticodon trinucleotides of the genetic code. In the case of tRNAAla a single acceptor stem G⋅U base pair at position 3·70 is essential, based on experiments where the wobble pair has been replaced by alternatives such as I⋅U, G⋅C, and A⋅U, among others. These experiments led to the conclusion that the minor-groove free 2-amino group (of guanosine) of the G⋅U wobble pair is essential for charging. Moreover, alanine-inserting tRNAs (amber suppressors) that replace G⋅U with mismatches such as G⋅A and C⋅A are partially active in vivo and can support growth of an Escherichia coli tRNAAla knockout strain, leading to the hypothesis that a helix irregularity and nucleotide functionalities are important for recognition. Herein we investigate the charging in vitro of oligonucleotide and full-length tRNA substrates that contain mismatches at the position of the G⋅U pair. Although most of these substrates have undetectable activity, G⋅A and C⋅A variants retain some activity, which is, nevertheless, reduced by at least 100-fold. Thus, the in vivo assays are much less sensitive to large changes in aminoacylation kinetic efficiency of 3·70 variants than is the in vitro assay system. Although these functional data do not clarify all of the details, it is now clear that specific atomic groups are substantially more important in determining kinetic efficiency than is a helical distortion. By implication, the activity of mutant tRNAs measured in the in vivo assays appears to be more dependent on factors other than aminoacylation kinetic efficiency.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.