Dans le cadre du déploiement de nouveaux systèmes de transmission basés sur les technologies xDSL (x Digital Subscriber Loop) et PLC (PowerLine Communication). Ces techniques, mises en oeuvre sur l'infrastructure existante (réseau téléphonique ou électrique) afin de transmettre des données haut débit, et offrent de nouveaux services avec un accès à l'information qui devient illimité. Cependant, cette augmentation des débits sur des voies de transmission de plus en plus variées, et l'utilisation de fréquences élevées exigent de sévères contraintes de compatibilité électromagnétique. Ces fréquences susceptibles d'engendrer des phénomènes d'interférences électromagnétiques associés aux caractéristiques des équipements déployés et des liens physiques utilisés. Il convient donc de prendre en compte ces problèmes d'émission électromagnétique lors du déploiement des services haut débit afin d'éviter d'éventuelles conséquences sur les systèmes radioélectriques, ou entre systèmes filaires hauts débits occupant les mêmes bandes de fréquences. Ce travail de thèse s'inscrit dans ce cadre général et est orienté vers le développement de méthodes prédictives en vue de les appliquer à des systèmes de transmission haut débit rencontrés dans le réseau d'accès. Il s'agit de sélectionner une théorie efficace, permettant de déterminer le rayonnement trouvé à proximité de lignes de télécommunications ou électriques, parcourues par des signaux de hautes fréquences. Le second axe de ce travail est consacré à la recherche de méthodes permettant de diminuer les émissions électromagnétiques de ces nouveaux services

Lying between the microwave and far infrared (IR) regions, the "terahertz gap" is a relatively unexplored frequency band in the electromagnetic spectrum that exhibits a unique combination of properties from its neighbors. Like in IR, many materials have characteristic absorption spectra in the terahertz (THz) band, facilitating the spectroscopic "fingerprinting" of compounds such as drugs and explosives. In addition, non-polar dielectric materials such as clothing, paper, and plastic are transparent to THz, just as they are to microwaves and millimeter waves. These factors, combined with sub-millimeter wavelengths and non-ionizing energy levels, makes sensing in the THz band uniquely suited for many NDE applications. In a typical nondestructive test, the objective is to detect a feature of interest within the object and provide an accurate estimate of some geometrical property of the feature. Notable examples include the thickness of a pharmaceutical tablet coating layer or the 3D location, size, and shape of a flaw or defect in an integrated circuit. While the material properties of the object under test are often tightly controlled and are generally known a priori, many objects of interest exhibit irregular surface topographies such as varying degrees of curvature over the extent of their surfaces. Common THz pulsed imaging (TPI) methods originally developed for objects with planar surfaces have been adapted for objects with curved surfaces through use of mechanical scanning procedures in which measurements are taken at normal incidence over the extent of the surface. While effective, these methods often require expensive robotic arm assemblies, the cost and complexity of which would likely be prohibitive should a large volume of tests be needed to be carried out on a production line. This work presents a robust and efficient physics-based image processing approach based on the mature field of parabolic equation methods, common to undersea acoustics, seismology, and other areas of science and engineering. The method allows the generation of accurate 3D THz tomographic images of objects with irregular, non-planar surfaces using a simple planar scan geometry, thereby facilitating the integration of 3D THz imaging into mainstream NDE use.

The experimental studies of this work were done using a microwave cavity spectrometer, Escherichia coli (E-coli) bacteria, and other peripheral equipment. The experiment consists of two steps. First, a general survey of frequencies from 8 GHz to 12 GHz was made. Second, a detailed experiment for specific frequencies selected from the first survey were further studied. Interesting frequency dependent results, such as unusually higher growing or killing rates of E-coli at some frequencies, were found. It is also concluded that some results are genetic, that is, the 2nd, and 3rd subcultures showed the same growing status as the 1st cultures.

Hybrid energy harvesting is a concept applied for improving the performance of the conventional stand-alone energy harvesters. The thesis presents the analytical formulations and characterization of a hybrid energy harvester that incorporates photovoltaic, piezoelectric, electromagnetic, and electrostatic mechanisms. The initial voltage required for electrostatic mechanism is obtained by the photovoltaic technique. Other mechanisms are embedded into a bimorph piezoelectric cantilever beam having a tip magnet and two sets of comb electrodes on two sides of its substructure. All the segments are interconnected by an electric circuit to generate combined output when subjected to vibration and solar illumination. Results for power output have been obtained at resonance frequency using an optimum load resistance. As the power transduced by each of the mechanisms is combined, more power is generated than those obtained by stand-alone mechanisms. The synergistic feature of this research is further promoted by adding fatigue analysis using finite element method.

Este trabalho propõe uma solução inovadora para o amortecimento de vibrações laterais indesejadas em máquinas rotativas através da conversão de energia cinética em energia elétrica por meio de um dispositivo eletromagnético passivo de colheita de energia, com o mínimo de geração de torque reativo. Para atingir estes objetivos, foram descritas e avaliadas as três principais técnicas de coleta de energia vibratória (piezelétrica, eletrostática e eletromagnética) juntamente com análises qualitativas das equações de eletromagnetismo e pelo Método dos Elementos Finitos. Um protótipo que consiste em um conjunto de ímãs permanentes anexos ao rotor e um conjunto de bobinas no estator demonstrou experimentalmente uma diminuição da amplitude de vibração em até 6,8%, na região de velocidades críticas, com geração não significativa de torque. Estes resultados foram obtidos experimentalmente mantendo-se os enrolamentos independentes entre si. / In this work, it is proposed a novel damping solution for undesired lateral vibrations in rotating machines by converting kinetic energy into electrical energy through a passive electromagnetic energy harvesting device, with minimal generation of reactive torque. In order to achieve these goals, it is described and evaluated the three main vibration energy harvesting techniques (piezoelectric, electrostatic and electromagnetic) along with qualitative analysis of electromagnetic equations and nite element analysis (FEA). Furthermore, a prototype consisting of a set of permanent magnets attached to the rotor and a set of coils attached to the stator showed a decrease in the amplitude of vibration up to 6,8% in the range of critical velocities, with non-signicant torque generation. Such results were obtained experimentally with independent-circuit coils.

O presente trabalho propõe a utilização do método de otimização baseado no paradigma de enxame de partículas no projeto de um dispositivo eletromagnético, modelado analiticamente. A otimização baseada em enxames de partículas pertence à classe dos algoritmos evolutivos e é baseada no algoritmo de simulação do movimento de pássaros na busca por comida. O trabalho será focado na resolução de problemas de otimização multiobjetivo e apenas alguns casos de otimização mono-objetivo serão resolvidos para demonstrar a funcionalidade do método de otimização. Dois métodos de otimização multiobjetivo são propostos: um é baseado num algoritmo de otimização multiobjetivo que utiliza o paradigma de enxames em conjunto com soluções adotadas pelo algoritmo genético multiobjetivo denominado Nondominated Sorting Genetic Algorithm-II (NSGA-II) e o outro é baseado também no paradigma de enxames utilizando elementos do algoritmo de otimização multiobjetivo intitulado Strength Pareto Evolutionary Algorithm (SPEA). Ambos algoritmos são validados em um problema de otimização baseado no projeto de um motor de corrente contínua sem escovas, um benchmark de otimização. / This work proposes the use of the optimization method based on the particle swarm paradigm in the design of electromagnetic device, analytically modeled. Particle swarm optimization belongs to the class of evolutionary algorithms and is based on the movement simulation of birds searching for food. This work will be focused on solving multi-criteria optimization problems and some cases of single-objective optimization problems will be solved only to demonstrate the functionality of optimization method. Two multi-criteria optimization methods are proposed: one based on an optimization algorithm that uses the multiobjective particle swarm paradigm and some concepts extracted from the multiobjective genetic algorithm called Nondominated Sorting Genetic Algorithm-II (NSGA-II) and the other is based on the particle swarm paradigm by using some elements of another multiobjective optimization algorithm entitled Strength Pareto Evolutionary Algorithm (SPEA). Both methods are applied to an optimization problem related to the design of a brushless direct current motor.

Neste trabalho apresentar-se-á um método para a determinação de modelos simplificados de fontes equivalentes de campos elétricos e magnéticos aplicáveis à análise de compatibilidade eletromagnética de sistemas embarcados. Esses modelos são obtidos a partir de medições laboratoriais, com técnicas de cálculos analíticos, numéricos e híbridos. Destacam-se, o fato da utilização do método de medição através de antenas de grandes loops (ou, laços, em português), na determinação de fontes equivalentes de emissão radiada e a aplicação destas na avaliação dos campos eletromagnéticos radiados. A contribuição deste trabalho é a obtenção dessas fontes equivalentes de emissão radiada, que possibilitam a avaliação da contribuição dos campos elétricos e magnéticos em ambientes eletromagnéticos. E também contribui com a aplicação de uma metodologia para a obtenção dos campos elétricos a partir dos campos magnéticos previamente determinados. Em particular, este trabalho pode ser considerado como decorrente da evolução da Dissertação de Mestrado [1]. / It will be shown in this work a method for simplified models determination of equivalent sources for electric and magnetic fields, applicable to embedded systems electromagnetic compatibility analysis. These models are obtained by laboratory tests with analytical calculation techniques associated to numerical and hybrid calculations. This work highlights the application of measurement method by Large Loop Antennas (LLAs) for the creation of radiated emission equivalent sources and the application of a corresponding method for obtaining radiated electromagnetic fields. The contribution of this work is the acquisition of these equivalent sources of radiated emission, which allows the evaluation of the magnetic and electric field contribution in electromagnetic environments. And it also contributes with the application of a methodology to obtain the electric fields from previously determined magnetic fields. In special, this work may be considered as an evolution of the Master\'s Thesis [1]

by Cheng Yat Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 1-6 (2nd gp.)). / Abstracts in English and Chinese. / Acknowledgements / Abstract: / A CD containing the Simulator and Results / List of Figures / List of Tables / Chapter 1. --- Introduction / Introduction --- p.1 / Chapter 2 --- Background Theory / Chapter 2.1 --- Empirical Design Formulas for Some Passive Microwave structures --- p.2 / Chapter 2.2.1 --- Short Dipole and Monopole --- p.4 / Chapter 2.2.2 --- Slot Antenna --- p.6 / Chapter 2.2.3 --- Stripline --- p.8 / Chapter 2.2.4 --- Microstrip --- p.10 / Chapter 2.2 --- Edge Based Finite Element Method and the Generalized Variational Principle --- p.12 / Chapter 2.2.1 --- Vector Finite Element Method for Electromagnetics --- p.14 / Chapter 2.2.1.1 --- Variational Formulation --- p.14 / Chapter 2.2.1.2 --- Advantages in Total Field Formulation --- p.16 / Chapter 2.2.2 --- Formulation by Method of Weighted Residual the Galerkin's Approach --- p.17 / Chapter 2.2.3 --- "the Vector Bases for BRICK, PRISM, TETRA" --- p.21 / Chapter 2.2.3.1 --- BRICK --- p.23 / Chapter 2.2.3.2 --- PRISM --- p.26 / Chapter 2.2.4 --- "Domain Discretization: Mesh Generation Scheme for 3D, 2D, ID Geometrical Entities in the Cartesian Domain" --- p.29 / Chapter 2.3 --- Construction of the Functional with Total Field Formulation --- p.31 / Chapter 2.3.1 --- Vector Wave Equation in the Cartesian Domain --- p.32 / Chapter 2.3.2 --- Boundary Conditions in the Cartesian Domain --- p.33 / Chapter 2.3.2.1 --- Perfect Magnetic Wall (Neumann's Boundary Condition) --- p.34 / Chapter 2.3.2.2 --- Perfect Electric Wall (Dirichlet Boundary Condition) --- p.34 / Chapter 2.3.2.3 --- Anisotropic Perfectly Matched Layer (APML) --- p.35 / Chapter 2.3.2.4 --- 2nd Order Absorbing Boundary Conditions --- p.39 / Chapter 2.3.2.5 --- Plane Wave Incidence (Uinc) --- p.40 / Chapter 2.3.2.6 --- Magnetic Aperture (M) --- p.42 / Chapter 2.3.2.7 --- Passive Lumped Load (ZL1D ) --- p.42 / Chapter 2.3.2.8 --- Current Feed (J) --- p.42 / Chapter 2.3.2.9 --- Voltage Feed (impressed E-field) --- p.43 / Chapter 2.3.2.10 --- Resistive Sheet ( =lst order ABC = standard IBC ) --- p.44 / Chapter 2.4 --- Visualization and Post-Processing of the Solution Field --- p.45 / Chapter 2.4.1 --- Field Pattern Plot --- p.45 / Chapter 2.4.2 --- Impedance at Input Port --- p.45 / Chapter 2.4.3 --- Y-parameter Extraction. --- p.46 / Chapter 3. --- Simulation Results and Discussion; / Chapter 3.1 --- Radiating Structures --- p.48 / Chapter 3.1.1 --- Short Dipole and Monopole --- p.48 / Chapter 3.1.1.1 --- Short Dipole --- p.48 / Chapter 3.1.1.2 --- Equivalent Monopole --- p.50 / Chapter 3.1.2 --- Slot Antenna --- p.52 / Chapter 3.1.2.1 --- Slot Antenna excited by the equivalent magnetic aperture --- p.52 / Chapter 3.1.2.3 --- Slot Antenna Excited by Unit Current Feed with Plane Wave Incidence ( Uinc) --- p.54 / Chapter 3.2 --- Striplines --- p.57 / Chapter 3.2.1 --- A Straight 50Ω Stripline --- p.57 / Chapter 3.2.1.1 --- Optimizing the Thickness and Number of Layer of PML --- p.58 / Chapter 3.2.1.2 --- Different Combination of BRICK and PRISM Mesh --- p.60 / Chapter 3.2.2 --- A Cross Junction --- p.63 / Chapter 3.2.3 --- A Squared 90° Corner --- p.69 / Chapter 3.2.4 --- A Champfered 90° Corner --- p.73 / Chapter 3.2.5 --- A Pair of Slot-Coupled Stripline Each Terminated with Open Circuit at Slot + λ/2 --- p.75 / Chapter 3.2.6 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.78 / Chapter 3.2.7 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and Shorted through the Slot --- p.80 / Chapter 3.2.8 --- A Pair of Slot-Coupled Striplines Each Terminated with Short Circuit at Slot + λ/4 and has 50Ω Load through the Slot --- p.83 / Chapter 3.3 --- Calculating the Input Impedance ( Vport / Iport ) / Chapter 3.3.1 --- A Pair of Slot-Coupled Stripline Each Terminated with Short Circuit at Slot + λ/4 --- p.85 / Chapter 4 --- Conclusion / Chapter 4.1 --- Conclusion --- p.88 / Chapter 4.2 --- Minor Problems Encountered --- p.89 / Chapter 4.2 --- To Probe Further --- p.90 / Chapter Appendex: --- Implementation of the Edge-Based Finite Element Method / Chapter A.1 --- Mesh Generation Scheme --- p.92 / Chapter A.1.1 --- "Global Node, Edge and Primitive Assignment" --- p.93 / Chapter A.1.2 --- Property Assignment Local to Every Basis and Primitive --- p.94 / Chapter A.2 --- Assembly the Global System of Equations from the Element Stamps of all Primitives wrt. Global Edge Numbering --- p.95 / Chapter A.2.1 --- Setting up the Volumetric Integral for the Vector Wave Equation --- p.95 / Chapter A.2.1.1 --- Volume Integration of Constant Tangential Brick Elements --- p.96 / Chapter A.2.1.2 --- Volume Integration of Constant Tangential Pyramidal Elements --- p.98 / Chapter A.2.2 --- Incorporation of Boundary Conditions --- p.100 / Chapter A.2.2.1 --- Surface Integration of Constant Tangential Brick Elements --- p.100 / Chapter A.2.2.2 --- Surface Integration of Constant Tangential Pyramidal Elements --- p.105 / Chapter A.3 --- Solution to the Final System --- p.110 / Chapter A.3.1 --- Solving a System of Linear Equations by Diagonalization & Blockwise Partitioning --- p.111 / Chapter A.3.2 --- Direct Solution Method for Complex-valued System --- p.114 / Chapter A.4 --- Visualization and Post-Processing of the Solution Field --- p.115 / Chapter A.4.1 --- Field Pattern Visualization --- p.115 / Chapter A.4.2 --- Input Impedance Definition ( Vport /Iport). --- p.115 / Chapter A.4.3 --- Y-parameter Extraction. --- p.115 / Chapter A.4.3.1 --- Surface Integration of Brick Elements --- p.115 / Chapter A.4.3.2 --- Surface Integration of Pyramidal Elements --- p.117 / Chapter A.5 --- Simulation Setup with BRICK+PRISM+higher order TETRA --- p.119 / References / Books: / Journals and Papers: / for Hierarchal Edge Bases and FEM Formulations: / for ABC and PML: / for Mesh Generation: / for Free FEM Source Code Matrix Solver: / Miscellaneous:

Les suies et leur caractérisation constituent des sujets de recherche très actuels dans divers domaines tels que le diagnostic de la combustion, la combustion numérique, l’optique atmosphérique, l'environnement et les applications de santé. Notre étude se concentre sur les propriétés radiatives des agrégats de suie issus de flammes de combustion ; notre objectif est de déterminer l’effet de la présence de suies sur le transfert de chaleur par rayonnement pour la simulation d'applications industrielles à haute température impliquant la combustion de gaz. Les études actuelles de modélisation du transfert de chaleur par rayonnement à travers les mélanges gazeux chargés de suies ne considèrent que l'absorption comme phénomène d'interaction rayonnement-matière. Des corrélations généralisées sont utilisées pour déterminer les propriétés radiatives des suies, soit sur la base de morphologies générées numériquement, soit plus simplement à partir de la taille moyenne des suies, de leur dimension fractale et de leur fraction volumique. Cependant, lorsque la taille de l'objet atteint l'ordre de grandeur des longueurs d'onde du rayonnement incident, l'interaction matière-rayonnement est susceptible d’être plus complexe du fait du phénomène de diffusion au niveau de l’agrégation qui ne peut plus être ignoré.Dans notre travail, nous établissons une méthodologie complète assortie d’une chaîne de calcul allant de la définition d'une morphologie de suie réaliste jusqu'au calcul du transfert de chaleur par rayonnement. À cette fin, des observations de suies émises par des flammes propane / air, méthane / air et méthane / oxygène sont effectuées par Microscopie Electronique à Balayage (MEB). La tomographie MEB est appliquée pour la première fois sur une suie issue d’une flamme propane / air, en combinaison avec la Microscopie Electronique en Transmission (MET) pour les observations. Des techniques d'analyse fractale 2D et 3D sont utilisées pour étudier les propriétés fractales d’agrégats de suie virtuels (générés numériquement) et de l'objet obtenu par la tomographie. Les propriétés radiatives des suies sont ensuite calculées en utilisant notre propre code d’Approximation Dipolaire Discrète (ADD – Discrete Dipole Approximation, ou DDA, en anglais). Une attention particulière est accordée à la modélisation ADD des suies en raison de l’indice optique complexe élevé de leur matériau constitutif, et aux méthodes numériques d’intégration directionnelle car les moyennes directionnelles des propriétés radiatives sont nécessaires pour les simulations ultérieures de transfert radiatif. La morphologie et les propriétés radiatives de l’agrégat de suie réaliste (tomographié) sont comparées à celles d'agrégats de suie numériques représentatifs, générés par un algorithme d’agrégation amas-amas limitée par la diffusion (Diffusion Limited Cluster-Cluster Aggregation, ou DLCCA, en anglais). Les compatibilités et les écarts entre les propriétés radiatives sont examinés, et les différences entre agrégats numériques représentatifs d’une part et agrégat réaliste d’autre part en termes de propriétés radiatives sont soulignées. Enfin, l'effet de la présence et de la morphologie des suies sur le transfert de chaleur par rayonnement est étudié par la résolution de l'équation du transfert radiatif en utilisant la méthode des ordonnées discrètes (Discrete Ordinates Method, ou DOM, en anglais) dans un mélange gazeux chargé de suies et dans une configuration académique 1D de plaques parallèles isothermes. / Soot and its characterization are of interest to researchers from various domains such as combustion diagnostics, numerical combustion, atmospheric optics, environmental and health applications. In this study, the main interest is on the radiative properties of soot aggregates issued directly from combustion flames in order to determine the effect of the presence of soot on the radiative heat transfer in the simulation of high temperature industrial applications involving gas combustion. Current studies modeling the radiative heat transfer through sooty gaseous media consider only the absorption as the main phenomenon of material-radiation interaction. Generalized correlations are used to determine the radiative properties of soot: these radiative properties are either computed over numerically generated aggregate morphologies or simply as a function of the soot average size, the fractal dimension and the volume fraction. However, the material-radiation interaction is susceptible to be more complex and morphology dependent at the aggregate level because of multiple scattering when the size of the object reaches the order of magnitude of the incident radiation wavelengths.In our work, we investigate the possibility to establish a computational methodology and workflow, starting from the definition of a realistic soot morphology up to the computation of the radiative heat transfer. To that end, observations of soot issued from propane/air, methane/air and methane/oxygen flames are performed using Scanning Electron Microscopy (SEM). SEM tomography is applied for the first time on soot issued from a propane/air flame, combined with Transmission Electron Microscopy (TEM) observations. 2D and 3D fractal analysis techniques are used to investigate the fractal properties of virtual (numerically generated) soot clusters and also of the tomography reconstructed objects. The radiative properties of soot are then computed using our in-house developed DDA (Discrete Dipole Approximation) code. Special attention is paid to the DDA modeling of soot because of the high complex extinction index of the material, and to the directional integration numerical methods because direction-averaged radiative properties are required for the subsequent radiative heat transfer simulations. The morphology and the radiative properties of the realistic morphology are compared to the ones of representative soot aggregates numerically generated by a DLCCA (Diffusion Limited Cluster-Cluster Aggregation) algorithm. The similarities and discrepancies on the radiative properties are investigated, and the differences between representative virtual aggregates on the one hand and the tomography reconstructed object on the other hand in terms of radiative properties are highlighted. Finally the effect of the presence and of the morphology of soot on the radiative heat transfer within a sooty gaseous mixture in a 1D isothermal parallel plate configuration is investigated by the resolution of the radiative transfer equation using DOM (Discrete Ordinates Method).

Une des problématiques qui est souvent associée aux réseaux large bande est l’apparition des lobes de réseaux, liée à la périodicité de l’espacement entre les éléments du réseau. Un autre problème dans les réseaux large bande est la fréquence de fonctionnement de l’élément du réseau. La plus basse fréquence d’opération est généralement liée à la taille de l’élément. Dans cette thèse un réseau d’anneaux concentriques a été développé. Les connections entre les spirales de polarisation opposée diminuent le coefficient de réflexion dans les fréquences basses. La topologie des anneaux concentriques a été optimisée avec des Algorithmes Génétiques pour minimiser le niveau des lobes secondaires relatifs dans les hautes fréquences. L’addition d’une contrainte de taille dans la procédure d’optimisation a assuré que le réseau soit compact. Le réseau optimisé opère entre 1 et 6.9 GHz. Le design a été d’avantage développé avec la technique WAVES avec l’inclusion d’une copie réduite en son centre, ce qu’a permis l’extension de la bande passante jusque 13 GHz. De plus, nous avons proposé un nouveau design pour le réseau de spirales connectés qui consiste en des antennes spirales disposées dans un réseau uniforme avec les bras connectés aux bras des antennes voisines. Les simulations indiquent que le réseau peut avoir une bande passante arbitrairement large selon la finitude du réseau. Un prototype a été construit et mesuré pour valider le concept. / One of the usual problems associated with wideband arrays is having the highest frequency of operation limited by the appearance of grating lobes, associated with the periodicity in the spacing between elements of the array. Another issue is the working frequency of the element of the array. The lowest frequency of operation is in general related to the size of the element. In this thesis a Concentric Ring Array of Connecting Spirals has been developed. The connections between spirals of opposite polarizations reduces the reflection coefficient at lower frequencies. The concentric rings topology had the radius and relative rotations of each ring optimized using Genetic Algorithms to minimize the RSLL at higher frequencies. The addition of a size constraint in the optimization procedure kept the array compact. The optimized array operates from 1 to 6.9 GHz. The design was then updated using the WAVES technique to include a scaled down copy in its center, extending the bandwidth of the array up to 13 GHz. Moreover, we proposed a new design for the array of connected spirals which consists of arranging spirals in a uniform array and connecting the arms of the neighboring spirals. Simulations indicate that the design can have an arbitrarily large bandwidth depending on the finiteness of the array. A prototype has been built and measured to validate the concept.