Fluoropolymer piezoelectrets with tubular channels: resonance behavior controlled by channel geometry

Ferro- or piezoelectrets are dielectric materials with two elastically very different macroscopic phases and electrically charged interfaces between them. One of the newer piezoelectret variants is a system of two fluoroethylenepropylene (FEP) films that are first laminated around a polytetrafluoroethylene (PTFE) template. Then, by removing the PTFE template, a two-layer FEP structure with open tubular channels is obtained. After electrical charging, the channels form easily deformable macroscopic electric dipoles whose changes under mechanical or electrical stress lead to significant direct or inverse piezoelectricity, respectively. Here, different PTFE templates are employed to generate channel geometries that vary in height or width. It is shown that the control of the channel geometry allows a direct adjustment of the resonance frequencies in the tubular-channel piezoelectrets. By combining several different channel widths in a single ferroelectret, it is possible to obtain multiple resonance peaks that may lead to a rather flat frequency-response region of the transducer material. A phenomenological relation between the resonance frequency and the geometrical parameters of a tubular channel is also presented. This relation may help to design piezoelectrets with a specific frequency response.

Effects of specimen geometry and loading mode on crack growth resistance curves of a high-strength pipeline girth weld

This work presents an investigation of the ductile tearing properties for a girth weld made of an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves. Use of these materials is motivated by the increasing demand in the number of applications for manufacturing high strength pipes for the oil and gas industry including marine applications and steel catenary risers. Testing of the pipeline girth welds employed side-grooved, clamped SE(T) specimens and shallow crack bend SE(B) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance (UC) method using the single specimen technique. Recently developed compliance functions and η-factors applicable for SE(T) and SE(B) fracture specimens with homogeneous material and overmatched welds are introduced to determine crack growth resistance data from laboratory measurements of load-displacement records.

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.

A variational approach to 3D cylindrical geometry reconstruction from multiple views

[EN] In this paper we present a variational technique for the reconstruction of 3D cylindrical surfaces. Roughly speaking by a cylindrical surface we mean a surface that can be parameterized using the projection on a cylinder in terms of two coordinates, representing the displacement and angle in a cylindrical coordinate system respectively. The starting point for our method is a set of different views of a cylindrical surface, as well as a precomputed disparity map estimation between pair of images. The proposed variational technique is based on an energy minimization where we balance on the one hand the regularity of the cylindrical function given by the distance of the surface points to cylinder axis, and on the other hand, the distance between the projection of the surface points on the images and the expected location following the precomputed disparity map estimation between pair of images. One interesting advantage of this approach is that we regularize the 3D surface by means of a bi-dimensio al minimization problem. We show some experimental results for large stereo sequences.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

People semantic description and re-identification from point cloud geometry

The automatic extraction of biometric descriptors of anonymous people is a challenging scenario in camera networks. This task is typically accomplished making use of visual information. Calibrated RGBD sensors make possible the extraction of point cloud information. We present a novel approach for people semantic description and re-identification using the individual point cloud information. The proposal combines the use of simple geometric features with point cloud features based on surface normals.

Influence of reservoir geometry and conditions on the seismic response of arch dams

[EN]An analysis of the influence that reservoir levels and bottom sediment properties (especially on the degree of saturation) have on the dynamic response of arch dams is caried out. For this purpose, a Boundary Element Model developed by the authors that allows the direct dynamic study of problems that incorporate scalar, viscoelastic and poroelastic media is used.

Aspetti innovativi per la valutazione e la misura della porosità nei materiali dell'edilizia antica e moderna. La geometria frattale della porosità

New concepts on porosity appraisal in ancient and modern construction materials. The role of Fractal Geometry on porosity characterization and transport phenomena. This work studied the potential of Fractal Geometry to the characterization of porous materials. Besides the descriptive aspects of the pore size distribution, the fractal dimensions have led to the development of rational relations for the prediction of permeability coefficients to fluid and heat transfer. The research considered natural materials used in historical buildings (rock and earth) as well as currently employed materials as hydraulic cement and technologically advanced materials such as silicon carbide or YSZ ceramics. The experimental results of porosity derived from the techniques of mercury intrusion and from the image analysis. Data elaboration was carried out according to established procedures of Fractal Geometry. It was found that certain classes of materials are clearly fractal and respond to simple patterns such as Sierpinski and Menger models. In several cases, however, the fractal character is not recognised because the microstructure of the material is based on different phases at different dimensional scales, and in consequence the “fractal dimensions” calculated from porosimetric data do not come within the standard range (less than 3). Using different type and numbers of fractal units is possible, however, to obtain “virtual” microstructures that have the fraction of voids and pore size distribution equivalent with the experimental ones for almost any material. Thus it was possible to take the expressions for the permeability and the thermal conduction which does not require empirical “constants”, these expressions have also provided values that are generally in agreement with the experimental available data. More problematic has been the fractal discussion of the geometry of the rupture of the material subjected to mechanical stress both external and internal applied. The results achieved on these issues are qualitative and prone to future studies. Keywords: Materials, Microstructure, Porosity, Fractal Geometry, Permeability, Thermal conduction, Mechanical strength.

Natural patterns and anthropogenic disturbance in north Adriatic marine benthic assemblages: descriptive and methodological studies

Marine soft bottom systems show a high variability across multiple spatial and temporal scales. Both natural and anthropogenic sources of disturbance act together in affecting benthic sedimentary characteristics and species distribution. The description of such spatial variability is required to understand the ecological processes behind them. However, in order to have a better estimate of spatial patterns, methods that take into account the complexity of the sedimentary system are required. This PhD thesis aims to give a significant contribution both in improving the methodological approaches to the study of biological variability in soft bottom habitats and in increasing the knowledge of the effect that different process (both natural and anthropogenic) could have on the benthic communities of a large area in the North Adriatic Sea. Beta diversity is a measure of the variability in species composition, and Whittaker’s index has become the most widely used measure of beta-diversity. However, application of the Whittaker index to soft bottom assemblages of the Adriatic Sea highlighted its sensitivity to rare species (species recorded in a single sample). This over-weighting of rare species induces biased estimates of the heterogeneity, thus it becomes difficult to compare assemblages containing a high proportion of rare species. In benthic communities, the unusual large number of rare species is frequently attributed to a combination of sampling errors and insufficient sampling effort. In order to reduce the influence of rare species on the measure of beta diversity, I have developed an alternative index based on simple probabilistic considerations. It turns out that this probability index is an ordinary Michaelis-Menten transformation of Whittaker's index but behaves more favourably when species heterogeneity increases. The suggested index therefore seems appropriate when comparing patterns of complexity in marine benthic assemblages. Although the new index makes an important contribution to the study of biodiversity in sedimentary environment, it remains to be seen which processes, and at what scales, influence benthic patterns. The ability to predict the effects of ecological phenomena on benthic fauna highly depends on both spatial and temporal scales of variation. Once defined, implicitly or explicitly, these scales influence the questions asked, the methodological approaches and the interpretation of results. Problem often arise when representative samples are not taken and results are over-generalized, as can happen when results from small-scale experiments are used for resource planning and management. Such issues, although globally recognized, are far from been resolved in the North Adriatic Sea. This area is potentially affected by both natural (e.g. river inflow, eutrophication) and anthropogenic (e.g. gas extraction, fish-trawling) sources of disturbance. Although few studies in this area aimed at understanding which of these processes mainly affect macrobenthos, these have been conducted at a small spatial scale, as they were designated to examine local changes in benthic communities or particular species. However, in order to better describe all the putative processes occurring in the entire area, a high sampling effort performed at a large spatial scale is required. The sedimentary environment of the western part of the Adriatic Sea was extensively studied in this thesis. I have described, in detail, spatial patterns both in terms of sedimentary characteristics and macrobenthic organisms and have suggested putative processes (natural or of human origin) that might affect the benthic environment of the entire area. In particular I have examined the effect of off shore gas platforms on benthic diversity and tested their effect over a background of natural spatial variability. The results obtained suggest that natural processes in the North Adriatic such as river outflow and euthrophication show an inter-annual variability that might have important consequences on benthic assemblages, affecting for example their spatial pattern moving away from the coast and along a North to South gradient. Depth-related factors, such as food supply, light, temperature and salinity play an important role in explaining large scale benthic spatial variability (i.e., affecting both the abundance patterns and beta diversity). Nonetheless, more locally, effects probably related to an organic enrichment or pollution from Po river input has been observed. All these processes, together with few human-induced sources of variability (e.g. fishing disturbance), have a higher effect on macrofauna distribution than any effect related to the presence of gas platforms. The main effect of gas platforms is restricted mainly to small spatial scales and related to a change in habitat complexity due to a natural dislodgement or structure cleaning of mussels that colonize their legs. The accumulation of mussels on the sediment reasonably affects benthic infauna composition. All the components of the study presented in this thesis highlight the need to carefully consider methodological aspects related to the study of sedimentary habitats. With particular regards to the North Adriatic Sea, a multi-scale analysis along natural and anthopogenic gradients was useful for detecting the influence of all the processes affecting the sedimentary environment. In the future, applying a similar approach may lead to an unambiguous assessment of the state of the benthic community in the North Adriatic Sea. Such assessment may be useful in understanding if any anthropogenic source of disturbance has a negative effect on the marine environment, and if so, planning sustainable strategies for a proper management of the affected area.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Friedrich Riesz' Beiträge zur Herausbildung des modernen mathematischen Konzepts abstrakter Räume

Der ungarische Mathematiker Friedrich Riesz studierte und forschte in den mathematischen Milieus von Budapest, Göttingen und Paris. Die vorliegende Arbeit möchte zeigen, daß die Beiträge von Riesz zur Herausbildung eines abstrakten Raumbegriffs durch eine Verknüpfung von Entwicklungen aus allen drei mathematischen Kulturen ermöglicht wurden, in denen er sich bewegt hat. Die Arbeit konzentriert sich dabei auf den von Riesz 1906 veröffentlichten Text „Die Genesis des Raumbegriffs". Sowohl für seine Fragestellungen als auch für seinen methodischen Zugang fand Riesz vor allem in Frankreich und Göttingen Anregungen: Henri Poincarés Beiträge zur Raumdiskussion, Maurice Fréchets Ansätze einer abstrakten Punktmengenlehre, David Hilberts Charakterisierung der Stetigkeit des geometrischen Raumes. Diese Impulse aufgreifend suchte Riesz ein Konzept zu schaffen, das die Forderungen von Poincaré, Hilbert und Fréchet gleichermaßen erfüllte. So schlug Riesz einen allgemeinen Begriff des mathematischen Kontinuums vor, dem sich Fréchets Konzept der L-Klasse, Hilberts Mannigfaltigkeitsbegriff und Poincarés erfahrungsgemäße Vorstellung der Stetigkeit des ‚wirklichen' Raumes unterordnen ließen. Für die Durchführung seines Projekts wandte Riesz mengentheoretische und axiomatische Methoden an, die er der Analysis in Frankreich und der Geometrie bei Hilbert entnommen hatte. Riesz' aufnahmebereite Haltung spielte dabei eine zentrale Rolle. Diese Haltung kann wiederum als ein Element der ungarischen mathematischen Kultur gedeutet werden, welche sich damals ihrerseits stark an den Entwicklungen in Frankreich und Deutschland orientierte. Darüber hinaus enthält Riesz’ Arbeit Ansätze einer konstruktiven Mengenlehre, die auf René Baire zurückzuführen sind. Aus diesen unerwarteten Ergebnissen ergibt sich die Aufgabe, den Bezug von Riesz’ und Baires Ideen zur späteren intuitionistischen Mengenlehre von L.E.J. Brouwer und Hermann Weyl weiter zu erforschen.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

A LES study of a modified Ahmed body geometry

A numerical study using Large Eddy Simulation Coherent Structure Model (LES-CSM), of the flow around a simplified Ahmed body, has been done in this work of thesis. The models used are two salient geometries from the experimental investigation performed in [1], and consist, in particular, in two notch-back body geometries. Six simulation are carried out in total, changing Reynolds number and back-light angle of the model’s rear part. The Reynolds numbers used, based on the height of the models and the free stream velocity, are Re = 10000, Re = 30000 and Re = 50000. The back-light angles of the slanted surface with respect to the horizontal roof surface, that characterizes the vehicle, are taken as B = 31.8◦ and B = 42◦ respectively. The experimental results in [1] have shown that, depending on the parameter B, asymmetric and symmetric averaged flow over the back-light and in the wake for a symmetric geometry can be observed. The aims of the present work of master thesis are principally two. The first aim is to investigate and confirm the influence of the parameter B on the presence of the asymmetry of the averaged flow, and confirm the features described in the experimental results. The second important aspect is to investigate and observe the influence of the second variable, the Reynolds number, in the developing of the asymmetric flow itself. The results have shown the presence of the mentioned asymmetry as well as an influence of the Reynolds number on it.