A measure of the quality of Voronoi tessellations resulting from various mesh generators founded on feature-driven models is introduced in this work. A planar tessellation covers an image with polygons of various shapes and sizes. Tessellations have potential utility due to their geometry and the opportunity to derive useful information from them for object recognition, image processing and classification. Problem domains including images are generally feature-endowed, non-random domains. Generators modeled otherwise may easily guarantee quality of meshes but certainly bear no reference to features of the meshed problem domain. They are therefore unsuitable in point pattern identification, characterization and subsequently the study of meshed regions. We therefore found generators on features of the problem domain. This provides a basis for element quality studies and improvement based on quality criteria. The resulting polygonal meshes tessellating an n-dimensional digital image into convex regions are of varying element qualities. Given several types of mesh generating sets, a measure of overall solution quality is introduced to determine their effectiveness. Given a tessellation of general and mixed shapes, this presents a challenge in quality improvement. The Centroidal Voronoi Tessellation (CVT) technique is developed for quality improvement and guarantees of mixed, general-shaped elements and to preserve the validity of the tessellations. Mesh quality indicators and entropies introduced are useful for pattern studies, analysis, recognition and assessing information. Computed features of tessellated spaces are explored for image information content assessment and cell processing to expose detail using information theoretic methods. Tessellated spaces also furnish information on pattern structure and organization through their quality distributions. Mathematical and theoretical results obtained from these spaces help in understanding Voronoi diagrams as well as for their successful applications. Voronoi diagrams expose neighbourhood relations between pattern units. Given this realization, the foundation of near sets is developed for further applications. / February 2017

Massive multiple input multiple output - MIMO systems are a reality and modern communication systems rely upon this technology to cope with the increasing need for capacity and network usage. Antenna arrays are at the heart of the of the massive-MIMO system and are the enabling technology. The defining cost of such a system is the number of transmit receive ports TRx as they dictate the number of control points and the associated digital control computational capacity. Typically users are spread along the azimuth and there is limited angular user spread along elevation. This enables us to group the elements in elevation which of course limits the elevation scanning performance. The element grouping result in grating lobes when we do elevation scanning. In the newly introduced frequency range 3 - FR3 in the envisioned 6G communication systems that is from 6-20 GHz it will not be allowed to transmit power above the horizon and the resulting grating lobes from the standard grouping should be mitigated. This project is structured into two parts. In the first part a grating lobe mitigation technique based on irregular subarray grouping utilizing the wellknown Penrose irregular tessellation is developed. This tessellation is based into two geometrical shapes where when put together they can fully tile the space aperiodically. Introducing this apperiodicity the grating or quantization lobes of the array are mitigated. In addition, in the first part a beam forming algorithm is developed based on particle swarm optimization that is able to produce the optimal weights for the array steering as well as optimize some of the embedded patterns of the irregular grouping. The last optimization step of the irregular subarray patterns is utilized only when the grouping results in a narrow pattern in azimuth and as a result we have static single port beamforming networks. This of course is a trade off between the broadside gain and the azimuth steerability of the array. In the second part of this thesis two low loss band pass filters have been developed with a PCB integrated suspended stripline techology. The filters were optimised for the frequencies within FR3. The resulted filtering structures can further be integrated at the input port of the proposed feeding network with the same technology. The two parts of this thesis target to introduce on one hand a antenna array architecture with subarray groupings that produce no grating lobes and on the other hand the proposed filtering structures have small enough dimensions to fit within the subarray footprint. / Dagens moderna kommunikationssystem använder sig av Massive multiple input multiple output (m-MIMO) för att kunna möta det allt större kraven på kapacitet och nätverksanvändning. Gruppantenner är den mest fundamentala delen av massive-MIMO system och möjliggör dess funktion. För ett sådant system (m-MIMO-system), så kommer den största kostnaden från antalet sändare/mottagare (TRx) -portar som används. Antalet portar i ett massiveMIMO system bestämmer vilken kapacitet systemet har till hands när det gäller lobformning. Vanligtvis är användare utspridda i det horisontella planet, samtidigt som de är begränsade i sin spridning i höjdled. Detta möjliggör användandet av en gruppantenn som grupperar sina antennelement i höjdled, vilket såklart begränsar gruppantennens lobformning i höjdled. Grupperandet av antennelement skapar sidlober när gruppantennen lobformar i höjdled. I det nya frekvensbandet, 3 - FR3 i det föreställda 6G kommunikationssystemet som opererar mellan 6-20 GHz, så kommer det inte att vara tillåtet att sända ut effekt över horisonten, samtidigt som de sidlober som kommer från standardgruppering måste begränsas. Detta projekt är strukturerat i två delar. I första delen så presenteras ett sätt att lindra sidlober, som baseras på irreguljära gruppantenner via Penrose tessellation. Denna tessellation är indelad i två geometriska former sådan att när vi sätter ihop dem så kan de framgångsrikt täcka vår geometri icke-periodvist. Genom att introducera denna icke-periodicitet så kan sidloberna från gruppanetnnen lindras. Utöver detta så är också så är en lobformningsalgoritm skapad som baseras på particle swarm optimization (PSO), som kan skapa de optimala vikterna för lobformning och lobstyrning. Det sista optimiseringssteget av de irreguljära gruppantennmönstret används bara när gruppering av antennelement resulterar i ett snävt mönster i azimut-riktning. Därför använder vi ett statiskt enportsmatningsnätverk. Detta är såklart en vägning mellan bredsideförstärkning och förmågan att kunna lobforma i det horisontella planet. I den andra delen så har två låg förlust bandpassfilter utvecklats med en PCB-integrerad suspended sripline teknik. Filtrerna optimerades för frekvenser inom FR3. De resulterande filterstrukturerna kan integreras längs input-porten av det föreslagna matningsnätverket som använder sig av den samma teknik. De två delarna i denna uppsats presenterar dels en gruppantenn med irreguljär antennelementsindelning som lindrar sidlober, samt dels filterstrukturer som kan användas tillsammans med gruppantennen.

We present an implicit approach for constructing smooth isolated or interconnected 3-D inscribed volumes which can be employed for volumetric modeling of various kinds of spongy or porous structures, such as volcanic rocks, pumice stones, Cancellus bones *, liquid or dry foam, radiolarians, cheese, and other similar materials. The inscribed volumes can be represented in their normal or positive forms to model natural pebbles or pearls, or in their inverted or negative forms to be used in porous structures, but regardless of their types, their smoothness and sizes are controlled by the user without losing the consistency of the shapes. We introduce two techniques for blending and creating interconnections between these inscribed volumes to achieve a great flexibility to adapt our approach to different types of porous structures, whether they are regular or irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us a freedom to exploit volumetric surface combinations and deformations operations effortlessly / Graduate

Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.

Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.

Les dunes marines sont de grandes structures sédimentaires qui, ensemble, couvrent de larges zones appelées champs de dunes. Des dunes ont été découvertes dans tous les océans, de la côte jusqu'aux talus continentaux. Leur forme et mobilité sont des témoins du lien étroit qui existe entre le transport sédimentaire, l'hydrodynamique (courants marins) et la topographie du fond. L'étude des dunes est intéressante scientifiquement parlant, mais elle est également motivée par des enjeux économiques et environnementaux. Les dunes peuvent être étudiées de deux manières : La modélisation et l'analyse de données de terrain (granulométrie, courantométrie, données sismiques, données bathymétriques). Ces deux approches sont très différentes mais complémentaires. Avec l'amélioration des données Sondeur Multi-Faisceaux (SMF), il est maintenant possible de visualiser la morphologie des dunes et de suivre leur évolution de manière plus détaillée. Plusieurs méthodes automatiques d'analyse de la morphologie et de la dynamique des dunes ont été développées pour analyser les Modèles Numériques de Terrain (MNTs) construits à partir de ces données SMF. Pourtant, aucun ne permet d'estimer les valeurs de descripteurs morphologiques et dynamiques pour chaque dune. L'analyse et l'évaluation de ces descripteurs restent régionales avec le découpage des MNTs en régions rectangulaires. Seul un traitement manuel permet d'estimer ces descripteurs pour chaque dune. L'objectif de cette thèse est de développer des algorithmes automatiques permettant de quanti er la morphologie et la dynamique de chaque dune. Pour ce faire, une représentation des données SMF sous forme d'une tessellation triangulaire a été préférée au classique MNT régulier. Tout d'abord, les dunes doivent être extraites de la topographie du fond marin. Un algorithme par accroissement de régions avec adaptation de l'échelle d'analyse, issu de la géomorphométrie est proposé. Les crêtes de dunes sont d'abord extraites en combinant un algorithme de simplification de tessellations avec un algorithme d'extraction de lignes de crête. La résolution de la tessellation est adaptée par l'algorithme de simplification afin de faciliter l'extraction des lignes de crête. Les lignes de crête sont des objets bien définis en géométrie différentielle. Leur extraction s'appuie sur l'interprétation de cette définition appliquée à des modèles discrets du fond (tessellations). Les crêtes servent d'embryons à l'algorithme d'extraction des dunes. L'estimation des paramètres morphologiques des dunes (longueur, largeur, hauteur, etc.) découle de l'extraction automatique des dunes. L'utilisation d'une méthode de recalage non rigide (isométrique) pour la quantification de la dynamique est discutée. Des tessellations représentant la topographie d'un même champ de dunes à différents moments sont analysées par l'algorithme d'extraction des dunes. Ensuite, une dune est associée à une dune d'une autre tessellation qui lui correspond (même dune à un autre instant). La dynamique de chaque dune est quantifiée à partir des résultats de l'algorithme de recalage : les transformations permettant d'aligner différentes représentations d'une dune. / Marine dunes are large sedimentary mounds often organized in dunefields. Theyhave been discovered in oceans all around the globe, from continental rises to nearshore areas. These mobile seafloor structures reflect the unique and complex relationship between the sediment, the seafloor topography and the hydrodynamics (currents). Dunes are not only interesting at a scientific level. In fact, their study is also motivated by economic, safety and environmental reasons. The study of dunes can be divided into two complementary approaches: Modelling and analysis of in situ data (granulometry, current, bathymetric data).The increased quality of MultiBeam EchoSounder (MBES) data allows scientists to monitor and visualize the complexity of, both, dune morphology and dynamics. Au-tomatic methods to characterize dune morphology and dynamics using Digital TerrainModels (DTMs) have already been proposed. But, none does it at the dune scale. Mor-phological and dynamical descriptors are estimated for patches of the dunefield. Today, the evaluation of such descriptors for each dune can only be achieved manually.The objective of this thesis is to design automatic algorithms for the quantification of dune morphology and dynamics. A representation of MBES data as triangular meshes has been preferred to the usual gridded DTMs. The first stage consists of delineating dunes in the seafloor. A scale adaptative, region growing algorithm based on geomorphometry is proposed. The combination of mesh implification and crest extraction algorithms enables to accurately recover dune crest lines. The mesh simplification facilitates the crest extraction by adapting the mesh resolution. Crest extraction is based on the discrete interpretation of the definition of crest lines in differential geometry. The crests are, then, used as seed regions by the dune extraction algorithm.

Bulk metallic glasses represent a newly developed class of materials. Some metallic glasses possess combinations of very good or even excellent mechanical, chemical and/or magnetic properties uncovering a broad range of both industrial and vital applications. Besides all advantages metallic glasses have also significant drawbacks, which have to be overcome for commercial application. Apart from low critical thicknesses, brittleness and chemical inhomogeneity one important problem of metallic glasses is the lack of an appropriate theory describing their structure. Therefore, the search for new glass forming compositions as well as the improving of existing ones occurs at present by means of trial-and-error methods and a number of empirical rules. Empirical rules for good glass-forming ability of bulk metallic glasses have been established in recent years by Inoue and Egami. Two of these rules, (i) Preference of more than 3 elements and (ii) Need of more than 12 % radii difference of base elements, seem to be closely related to topological (geometrical) criteria. From this point of view topological parameters contribute essentially to the glass-forming ability. The third rule (iii) demands a negative mixing enthalpy of base elements and refers to the chemical interaction of the atoms. The generalized Bernal’s model (hard-sphere approximation) was used for the simulation of monatomic, binary and multi-component structures. Excluding chemical interaction, this method allows the investigation of topological criteria of the glass-forming ability. Bernal’s hard-sphere model was shown to be a good approximation for bulk metallic glasses and metallic liquids and yields good coincidence of experimental and theoretical results. • The Laguerre (weighted Voronoi) tessellation technique was used as the main tool for the structural analysis. Due to very complex structures it is impossible to determine the structure of bulk metallic glasses by means of standard crystallographic methods. • Density, radial distribution function, coordination number and Laguerre polyhedra analysis confirm amorphism of the simulated structures and are in a good agreement with available experimental results. • The ratio of the fractions of non-crystalline to crystalline Laguerre polyhedra faces was introduced as a new parameter . This parameter reflects the total non-crystallinity of a structure and the amount of atomic rearrangements necessary for crystallization. Thus, the parameter is related to the glass-forming ability. It depends strongly on composition and atomic size ratio and indicates a region of enhanced glass-forming ability in binary mixtures at 80 % of small atoms and atomic size ratio of 1.3. All found maxima of parameter for ternary mixtures have compositions and size ratios which are nearly the same as for the binary mixture with the maximum value of . • A new method of multiple-compression was introduces in order to test the tendency towards densification and/or crystallization of the simulated mixtures. The results of the multiple-compression of monatomic mixtures indicate a limiting value of about 0.6464 for the density of the amorphous state. Further densification is necessarily connected to formation and growth of nano-crystalline regions. • The results of the multiple-compression for binary mixtures shows a new maximum of the density at the size ratio of 1.3 and 30 % to 90 % of small atoms. This maximum indicates a local island of stability of the amorphous state. The maximal receivable density without crystallization in this region is enhanced compared to neighbouring regions. • The comparison of the parameter and the density to the distribution of known binary bulk metallic (metal-metal) glasses clearly shows that both parameters play a significant role in the glass-forming ability. • The polyhedra analysis shows regions with enhanced fraction of the icosahedral short-range order (polyhedron (0, 0, 12)) in the binary systems with the maximum at 80 % of small atoms and size ratio of 1.3. Comparison of the distribution of the (0, 0, 12) polyhedra to the distribution of known binary metallic (metal-metal) glasses and to the parameter shows that icosahedral short-range order is not related to the glass-forming ability and is a consequence of the high non-crystallinity (high values of ) of the mixtures and non vice versa. Results for the ternary mixtures confirm this observation. • A new approach for the calculation of the mixing enthalpy is proposed. The new method is based on the combination of Miedema’s semi-empirical model and Laguerre tessellation technique. The new method as well as 6 other methods including the original Miedema’s model were tested for more than 1400 ternary and quaternary alloys. The results show a better agreement with experimental values of the mixing enthalpy for the new model compared to all other methods. The new model takes into account the local structure at atom site and can be applied to all metallic alloys without additional extrapolations if the atomic structure of the considered alloy is known from a suitable atomistic structure model.

Bulk metallic glasses represent a newly developed class of materials. Some metallic glasses possess combinations of very good or even excellent mechanical, chemical and/or magnetic properties uncovering a broad range of both industrial and vital applications. Besides all advantages metallic glasses have also significant drawbacks, which have to be overcome for commercial application. Apart from low critical thicknesses, brittleness and chemical inhomogeneity one important problem of metallic glasses is the lack of an appropriate theory describing their structure. Therefore, the search for new glass forming compositions as well as the improving of existing ones occurs at present by means of trial-and-error methods and a number of empirical rules. Empirical rules for good glass-forming ability of bulk metallic glasses have been established in recent years by Inoue and Egami. Two of these rules, (i) Preference of more than 3 elements and (ii) Need of more than 12 % radii difference of base elements, seem to be closely related to topological (geometrical) criteria. From this point of view topological parameters contribute essentially to the glass-forming ability. The third rule (iii) demands a negative mixing enthalpy of base elements and refers to the chemical interaction of the atoms. The generalized Bernal’s model (hard-sphere approximation) was used for the simulation of monatomic, binary and multi-component structures. Excluding chemical interaction, this method allows the investigation of topological criteria of the glass-forming ability. Bernal’s hard-sphere model was shown to be a good approximation for bulk metallic glasses and metallic liquids and yields good coincidence of experimental and theoretical results. • The Laguerre (weighted Voronoi) tessellation technique was used as the main tool for the structural analysis. Due to very complex structures it is impossible to determine the structure of bulk metallic glasses by means of standard crystallographic methods. • Density, radial distribution function, coordination number and Laguerre polyhedra analysis confirm amorphism of the simulated structures and are in a good agreement with available experimental results. • The ratio of the fractions of non-crystalline to crystalline Laguerre polyhedra faces was introduced as a new parameter . This parameter reflects the total non-crystallinity of a structure and the amount of atomic rearrangements necessary for crystallization. Thus, the parameter is related to the glass-forming ability. It depends strongly on composition and atomic size ratio and indicates a region of enhanced glass-forming ability in binary mixtures at 80 % of small atoms and atomic size ratio of 1.3. All found maxima of parameter for ternary mixtures have compositions and size ratios which are nearly the same as for the binary mixture with the maximum value of . • A new method of multiple-compression was introduces in order to test the tendency towards densification and/or crystallization of the simulated mixtures. The results of the multiple-compression of monatomic mixtures indicate a limiting value of about 0.6464 for the density of the amorphous state. Further densification is necessarily connected to formation and growth of nano-crystalline regions. • The results of the multiple-compression for binary mixtures shows a new maximum of the density at the size ratio of 1.3 and 30 % to 90 % of small atoms. This maximum indicates a local island of stability of the amorphous state. The maximal receivable density without crystallization in this region is enhanced compared to neighbouring regions. • The comparison of the parameter and the density to the distribution of known binary bulk metallic (metal-metal) glasses clearly shows that both parameters play a significant role in the glass-forming ability. • The polyhedra analysis shows regions with enhanced fraction of the icosahedral short-range order (polyhedron (0, 0, 12)) in the binary systems with the maximum at 80 % of small atoms and size ratio of 1.3. Comparison of the distribution of the (0, 0, 12) polyhedra to the distribution of known binary metallic (metal-metal) glasses and to the parameter shows that icosahedral short-range order is not related to the glass-forming ability and is a consequence of the high non-crystallinity (high values of ) of the mixtures and non vice versa. Results for the ternary mixtures confirm this observation. • A new approach for the calculation of the mixing enthalpy is proposed. The new method is based on the combination of Miedema’s semi-empirical model and Laguerre tessellation technique. The new method as well as 6 other methods including the original Miedema’s model were tested for more than 1400 ternary and quaternary alloys. The results show a better agreement with experimental values of the mixing enthalpy for the new model compared to all other methods. The new model takes into account the local structure at atom site and can be applied to all metallic alloys without additional extrapolations if the atomic structure of the considered alloy is known from a suitable atomistic structure model.

[pt] A extração e visualização de isosuperfícies de campos escalares são importantes para inspeções e análises de modelos em diversas áreas. Uma isosuperfície é representada por uma malha de triângulos que aproxima um conjunto de nível do volume de dados. O foco deste trabalho é a extração e visualização de isosuperfícies de modelos de reservatório de petróleo, representados por malhas de hexaedros levemente côncavos. Para uma melhor representação das isosuperfícies, optou-se pela substituição de triângulos planares por superfícies curvas. Para assegurar a extração de superfícies contínuas e suaves, este trabalho propõe o uso de envelopes para determinação das normais. A técnica proposta é implementada em GPU com uso de subdivisão adaptativa das superfícies. / [en] The extraction and visualization of isosurfaces of scalar fields are important for inspections and analysis of models in several areas. An isosurface is represented by a mesh of triangles that approximates a level set of a data volume. The main focus of this work is the extraction and visualization of isosurfaces of black oil reservoir models, represented by hexahedral meshes with slightly concave cells. For a better representation of the isosurfaces, we have opted to replace planar triangles for curved patches. To ensure the extraction of continuous and smooth surfaces, this work proposes the use of envelopes to determine normals. The proposed technique is implemented in GPU with the usage of adaptive subdivision of patches.

Die vorliegende Dissertation beschäftigt sich mit der thermo-mechanischen Beschreibung und Bewertung von keramischen Filtern für die Metallschmelze-Filtration mithilfe der Finiten-Elemente-Methode. Infolge des zellularen Aufbaus des Werkstoffs handelt es sich um ein Mehrskalenproblem. Grundlegende Aufgaben der Arbeit waren deshalb die geometrische und mechanische Modellbildung sowie die Untersuchung verschiedener effizienzsteigernder Methoden zur Gewinnung einer akkuraten numerischen Lösung. Dabei wurden sowohl verschiedene Verfahren aus der Fachliteratur implementiert und kritisch bewertet, als auch neue Ansätze verfolgt. Die Untersuchungen konzentrierten sich auf das effektive elastische und elastisch-plastische Verhalten von Kelvin-, Weaire-Phelan- und Voronoi-Strukturen. Insbesondere die entwickelten Methoden und Werkzeuge zur automatisierten Modellbildung gestatten in einfacher Weise die Umsetzung von Parameterstudien und Optimierungsaufgaben. Aus darauf aufbauenden Sensitivitätsstudien wurden Empfehlungen hinsichtlich der geometrischen und mechanischen Modellbildung für zellulare Werkstoffe abgeleitet. Diese betreffen auch vielfach eingesetzte Methoden zur Modellreduktion für diese Werkstoffe und tragen somit zukünftig zu einer effizienteren Bewertung von Filterstrukturen bei.