Orientador: José Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T18:40:32Z (GMT). No. of bitstreams: 1 Oliveira_AndreaGenovesede_M.pdf: 1278255 bytes, checksum: f16ace92e18ff9cf5e8a4f8a66829f47 (MD5) Previous issue date: 2012 / Resumo: Analisamos um sistema não linear parabólico de reação-difusão com duas equações definidas em ]0,T[x'ômega', (0 < T < 'infinito' e Q 'pertence' R³ limitado) e condições de fronteira do tipo Neumann. Tal sistema foi proposto para modelar o movimento de uma população de amebas unicelulares e tem como base o processo de locomoção chamado quimiotaxia positiva, na qual as amebas se movimentam em direção à região de alta concentração de uma certa substância química, que, neste caso, é produzida pelas próprias amebas. Embora adicionando os detalhes técnicos, este trabalho seguiu livremente o método de resolução proposto no artigo de A. Boy, Analysis for a System of Coupled Reaction-Diffusion Parabolic Equations Arising in Biology, Computers Math. Applic. Vol. 32, No. 4, páginas 15-21, 1996 / Abstract: We will be analyzing a nonlinear parabolic reaction diffusion system with two equations, defined in ]0,T[x'omega', (0 < T < 'infinite' and Q 'belongs' R³) with Neumann boundary conditions. This system was proposed in order to model the movement of a population of single-cell amoebae and is based on the process of movement called chemotaxis, in which the amoebae move in the direction of the region of high concentration of a certain chemical substance, which, in this case, is produced by the amoebae themselves.While adding the technical details, this dissertation followed freely the solution method proposed in the paper: A. Boy, Analysis for a System of Coupled Reaction-Diffusion Parabolic Equations Arising in Biology, Computers Math. Applic. Vol. 32, No. 4, pages 15-21, 1996 / Mestrado / Matematica / Mestre em Matemática

L’objectif de cette thèse est d’ouvrir la voie à la démonstration de l’amplification parabolique à 2 μm en format tout fibré. La théorie sur l’amplification d’impulsions auto-similaires est d’abord présentée. Il en découle que le meilleur amplificateur tout fibré à 2 μm devra s’appuyer sur une fibre dopée aux ions Tm3+ présentant à la fois une forte dispersion normale et une grand aire effective. L’amplification parabolique ne peut pas être réalisée dans des fibres monomodes à base de silice à 2 μm du fait de la forte dispersion anormale présentée par le matériau. Afin de surmonter cette limitation, une fibre dont le mode LP02 présente à la fois une forte dispersion normale et une grande aire effective à 2 μm a été conçue et réalisée. Un convertisseur spatial de lumière dédié à la génération du mode LP02 a également été conçu et réalisé. La pureté d’excitation par ce convertisseur du mode LP02 de la fibre passive a été évaluée à 99,9% par la technique interférométrique d’imagerie spatialement et spectralement résolue. Une source d’impulsions ultrabrèves (100 fs) et accordable en longueur d’onde de 1,6 μm à 2 μm a été créée pour générer le signal de l’amplificateur. Cette source a en outre permis de mesurer la dispersion du mode LP02 de la fibre passive à la longueur d’onde de 1,95 μm, celle-ci vaut -106 ps/(nm.km) en excellent accord quantitatif avec les résultats numériques. Des modélisations numériques de l’amplificateur nonlinéaire basé sur la version active de cette fibre indiquent que des impulsions présentant une puissance crête de l’ordre du MW à 1,9 μm sont envisageables en sortie de l’amplificateur parabolique. / The goal of this PhD thesis is to pave the way towards the demonstration of parabolic amplification at 2 μm in an all-fiber format. The physical theory on self-similar pulse amplification is first presented. The best all-fiber amplifier at 2 μm would need a special Tm-doped fiber with both high normal dispersion and large effective area. Parabolic amplification is however prohibited in silica based singlemode fiber working at 2 μm due to the large anomalous dispersion of silica. To overcome this limitation, a four-mode fiber in which the LP02 mode exhibits high normal dispersion combined with large effective area at 2 μm was designed and manufactured. A dedicated mode converter has also been designed and manufactured. Using the spatially- and spectrally-resolved imaging technique the purity of excitation of the LP02 mode in the passive fiber was evaluated to 99.9%. An ultrashort pulse (100 fs) source tunable from 1.6 μm to 2 μm was implemented to seed the amplifier. This source allowed to measure the LP02 mode dispersion of the passive fiber at the wavelength of 1.95 μm: D = -106 ps/(nm.km) in excellent quantitative agreement with the simulations. Numerical modeling of a nonlinear amplifier based on the realized active fiber shows that MW peak power class pulses centered at 1.9 μm can be obtained at the output of the parabolic amplifier.

Philosophiae Doctor - PhD / In recent years, there has been a great interest towards the higher order numerical methods for singularly perturbed problems. As compared to their lower order counterparts, they provide better accuracy with fewer mesh points. Construction and/or implementation of direct higher order methods is usually very complicated. Thus a natural choice is to use some convergence acceleration techniques, e.g., Richardson extrapolation, defect correction, etc. In this thesis, we will consider various classes of problems described by singularly perturbed ordinary and partial differential equations. For these problems, we design some novel numerical methods and attempt to increase their accuracy as well as the order of convergence. We also do the same for existing numerical methods in some instances. We find that, even though the Richardson extrapolation technique always improves the accuracy, it does not perform equally well when applied to different methods for certain classes of problems. Moreover, while in some cases it improves the order of convergence, in other cases it does not. These issues are discussed in this thesis for linear and nonlinear singularly perturbed ODEs as well as PDEs. Extrapolation techniques are analyzed thoroughly in all the cases, whereas the limitations of the defect correction approach for certain problems is indicated at the end of the thesis. / South Africa

Dans ce travail, on s'intéresse à l'analyse mathématique et au contrôle optimal pour des problèmes de diffusion relevant de certains domaines comme l'écologie ou l'environnement et comportant des termes de pollution inconnus en général. De plus, on souhaite agir sur le système en un seul point du domaine considéré pour des raisons de coût. La modélisation de ces problèmes se traduit généralement par un système de type parabolique avec donnée manquante (initiale ou aux limites) représentant la pollution, et où l'on introduit une fonction de contrôle de ce système. La méthode suivie pour résoudre ces problèmes est celle du contrôle à moindres regrets développée par J.-L. Lions et bien adaptée aux problèmes à données manquantes.Plus précisément, on est concerné par des problèmes de type parabolique qui décrivent la diffusion d'un fluide (eau) contaminé dans un domaine (une lagune ou un estuaire) par une pollution ayant son origine sur une partie du bord. De plus, on considère que la fonction source (le contrôle) est localisée en un point, c'est ce qu'on appelle le contrôle ponctuel. On cherche alors le (ou les) contrôle(s) qui peuvent améliorer la situation au lieu de la laisser à l'abandon (sans contrôle).Les solutions ne sont pas des fonctions régulières et ne peuvent être considérées qu'au sens faible. Deux méthodes sont utilisées: la première est la méthode de transposition de Lions-Magenes, détaillée au chapitre 3 de la thèse, et la deuxième méthode consiste à régulariser la masse de Dirac (le support du contrôle est un point) présentée au chapitre4. Pour les deux méthodes, on montre l'existence d'une solution faible et on établit un système d'optimalité singulier (SOS) du contrôle ponctuel à moindres regrets.Un dernier chapitre est consacré aux schémas numériques associés au problème de contrôle ponctuel à moindres regrets, où l'on obtient des estimations d'erreur par la méthode des éléments finis. / In this thesis, we are interested in mathematical analysis and optimal control of diffusion problems where there are pollution terms. In addition, we want to act on the system in a single point of the domain for cost reasons. The systems being studied are parabolic with missing (initial or boundary) data representing pollution, where we introduce a control function. The method of low-regret control of J.-L. Lions, used here for the first time to the pointwise control, seems to be well suited. We then look for the control which can improve the situation instead of doing nothing (no control).Solutions are not regular functions and can only be considered in the weak sense. Two methods are used here: the first one is the method of transposition of Lions-Magenes, detailed in Chapter 3 of the thesis, and the second method consists in regularizing the Dirac mass, presented in chapter 4. Each one of the two methods offers a new point of view. In particular, the functional spaces where the existence of a solution is obtained are different. For both methods, however, a singular optimality system is established for the low-regret pointwise control.A final chapter is devoted to the numerical schemes associated to the low-regret pointwise optimal control, where we obtain error estimates using finite elements method (FEM).

A dinêmica caótica, em arranjos de bilhares eletrônicos bidimensionais e tridimensionais , em heteroestruturas semicondutoras de AlxGa1-xAs/GaAs foi estudada tanto de forma experimental como através de simulações numéricas. Como primeira parte, a dinâmica eletrônica caótica em super-redes de antipontos bidimensionais foi tratada sob a influência de campo magnético uniforme aplicado de forma pararela ao plano do gás de elétrons. Nestas circunstâncias, a anisotropia do contorno de Fermi do gás bidimensional de elétrons produzida pelo campo magnético pararelo, distorce fortemente a forma das trajetórias eletrônicas induzindo mudanças drásticas nas oscilações de comensurabilidade da magnetoresistência na região de campo fraco, em temperaturas criogênicas. Como segunda parte, arranjos de bilhares eletrônicos tridimensionais foram realizadas, pela primeira vez, através da gravação de super-redes retangulares de buracos mecânicos cilíndricos em poços quânticos parabólicos, os quais contêm o gás tridimensional de elétrons de alta mobilidade. Medidas de resistividade nestes sistemas revelam a presença de picos anomalos na região de campo fraco, em forma similar às medições em sistemas de antipontos bidimensionais. Foi calculada a dinâmica eletrônica do bilhar tridimensional analisando -se a evolução das trajetórias no espaço de fases através das seções espaciais de Poincaré. Calculou-se também a magnetoresistência pxx do gás tridimensional através da teoria de resposta linear, encontrando-se que a presença de ressonância não lineares é refletida nos picos anômalos observados. A realização destes sistemas permitiu o estudo de fenômenos físicos novos como as oscilações de comensurabilidade em sistemas tridimensionais e os efeitos de tamanho galvano-magnéticos devido às ressonâncias geométricas. / The chaotic electron dynamics in two-dimensional and three-dimensional arrays of elec­ tron billiards in ALx Ga1-xAs/GaAs semiconductor heterostructures has been studied in experimental way and also through numerical simulations. As a first part, the chaotic electron dynamics in two-dimensional antidot super-lattices has been studied under the influence of a uniform magnetic field applied in parallel configuration related to the plane of the electron gas. In this case, the Fermi contour anisotropy of the two-dimensional elec­ tron gas induced by the parallel field highly distorts the shape of the electron trajectories inducing pronounced changes in the commensurability peaks of the low field magnetoresis­ tance, in cryogenic temperatures. In the second part, arrays of three dimensional electron billiards were obtained, by first time, through the patterning of rectangular super-lattices of cylindrical voids in ALx Ga1-xAs/GaAs parabolic quantum wells containing a high mo­ bility three-dimensional electron gas. Resistivity measurements in these systems reveal anomalous peaks in the low magnetic field region in similar way as measurements in two-dimensional antidots systems. The electron dynamics of the three-dimensional bil­ liard was calculated, analyzing the evolution of trajectories in phase space by means of Poincaré space of sections. The magnetoresistance xx of the three-dimensional electron gas was calculated through linear responde theory, being found that nonlinear resonances are reflected in the observed anomalous peaks. The accomplishment os these systems allowed the study of new physical phenomena such as the commensurability oscillations in three-dimensional systems and size-effects due to geometrical resonances.

En simulation dynamique des réservoirs, un des artéfacts les plus gênants pour la prédiction de production est l’effet de l’orientation du maillage. Bien que celui-ci soit « normal » pour tout schéma numérique, il se trouve amplifié par l’instabilité du modèle physique, ce qui a lieu lorsque le contraste de mobilités entre l’eau (fluide poussant, utilisé dans les procédés de récupération secondaires) et l’huile (fluide poussé, contenant les hydrocarbures) dépasse un certain seuil critique. On parle alors d’écoulements à rapport de mobilités défavorable. Connu depuis longtemps, ce problème a fait l'objet de nombreux travaux dans les années 1980 ayant abouti au schéma dit à neuf points. Actuellement implanté dans PumaFlow, logiciel développé et commercialisé par IFPEN, ce schéma fonctionne relativement bien en maillages carrés et dépend d’un paramètre scalaire dont le réglage varie selon les auteurs sur la base de considérations heuristiques. Dans cette thèse, nous proposons une nouvelle démarche méthodologique afin non seulement d’ajuster ce paramètre libre de manière optimale mais aussi de généraliser le schéma aux maillages rectangulaires. La stratégie que nous préconisons repose sur une analyse d’erreur du problème, à partir de laquelle il est possible de définir une notion d’erreur angulaire et de garantir que le comportement du schéma obtenu soit le « moins anisotrope » possible via une minimisation de son écart par rapport à un comportement idéal. Cette procédure de minimisation est ensuite appliquée à deux autres familles de schémas numériques~ : (1) un schéma multidimensionnel proposé par Kozdon, dans lequel le paramètre libre est une fonction~ ; (2) un autre schéma à neuf points faisant intervenir deux paramètres scalaires. C’est ce dernier qui réduit le mieux l’effet de l’orientation lorsque le rapport des pas de maillage s’éloigne de 1. Enfin, une extension de la méthode à des modèles physiques plus complets est envisagée. / In dynamic reservoir simulation, one of the most troublesome artifacts for the prediction of production is the grid orientation effect. Although this normally arises from any numerical scheme, it happens to be amplified by the instability of the physical model, which occurs when the mobility contrast between the water (pushing fluid, used in the processes of secondary recovery) and the oil (pushed fluid, containing the hydrocarbons) exceeds a some critical threshold. We then speak of flows with adverse mobility ratio. This GOE issue has received a lot of attention from the engineers. Numerous works dating back to the 1980s have resulted in the so-called nine-point scheme. Currently implemented in the IFPEN software PumaFlow, this scheme performs relatively well in square meshes and depends on a scalar parameter whose value varies from one author to another, on the grounds of heuristic considerations. In this thesis, we propose a new methodological approach in order not only to optimally adjust this free parameter, but also to extend the scheme to rectangular meshes. The strategy that we advocate is based on an error analysis of the problem, from which it is possible to define a notion of angular error and to guarantee that the behavior of the obtained scheme is the "least anisotropic" possible through a minimization of its deviation from some ideal behavior. This minimization procedure is then applied to two other families of numerical schemes: (1) a multidimensional scheme proposed by Kozdon, in which the free parameter is a function; (2) another nine-point scheme involving two scalar parameters. The latter provides the best results regarding GOE reduction when the ratio of the mesh steps is far away from 1. Finally, an extension of the method to more sophisticated physical models is envisaged.

In the last few decades, combinatorial families exhibiting noncrossing or cluster phenomena have proven useful in understanding and connecting mathematical objects arising in seemingly unrelated branches of mathematics and theoretical physics. These phenomena can be modeled in the context of Coxeter groups and play an important role in algebraic combinatorics. In finite type, such families are enumerated by generalized Catalan numbers. In this thesis, we consider the extension of this theory to parabolic quotients of Coxeter groups. We outline the history, present the basic definitions and constructions, and provide a number of conjectures and research challenges arising in this context. We then solve these questions in linear type A and exhibit surprising connections of this theory to certain Hopf algebras and to the theory of diagonal harmonics. We end this thesis by proposing related directions for future research.:Chapter 0. Prologue Noncrossing partitions Triangulations Stack-sortable permutations Dyck paths Chapter 1. Preliminaries 1.1. Posets and lattices 1.1.1. A notion of order 1.1.2. Diagrams and labelings 1.1.3. Duality and multichains 1.1.4. Zeta polynomial and Möbius function 1.1.5. Lattices 1.1.6. Distributivity 1.1.7. Semidistributivity 1.1.8. Trimness 1.1.9. Congruence-uniformity 1.1.10. The core label order 1.2. Coxeter groups 1.2.1. Coxeter systems 1.2.2. The geometric representation 1.2.3. Ordering a Coxeter group 1.2.4. Orienting a Coxeter group Chapter 2. Cataland 2.1. Catalan numbers 2.2. Aligned elements 2.2.1. Cambrian lattices 2.3. Noncrossing partitions 2.4. Clusters 2.5. Nonnesting partitions 2.5.1. v-Tamari lattices 2.6. Chapoton Triangles Chapter 3. Parabolic Cataland: Origins 3.1. Parabolic quotients of Coxeter groups 3.2. Parabolic aligned elements 3.3. Parabolic noncrossing partitions 3.4. Parabolic clusters 3.5. Parabolic nonnesting partitions 3.6. Parabolic Chapoton triangles Chapter 4. Parabolic Cataland: Linear type A 4.1. Definitions 4.1.1. Parabolic quotients of the symmetric group 4.1.2. The longest α-permutation 4.1.3. The root poset of S_α and α-Dyck paths 4.1.4. c-clusters for S_α 4.1.5. c-aligned elements for S_α 4.1.6. c-noncrossing partitions for S_α 4.1.7. α-trees 4.2. Bijections 4.2.1. Noncrossing α-partitions and (α, 231)-avoiding permutations 4.2.2. Noncrossing α-partitions and α-Dyck paths 4.2.3. α-trees and (α, 231)-avoiding permutations 4.2.4. α-trees and noncrossing α-partitions 4.2.5. α-trees and α-Dyck paths 4.3. Posets 4.3.1. The weak order on S_α(231) 4.3.2. The rotation order on Dyck(α) 4.3.3. The core label order of Tam(α) 4.4. Chapoton triangles 4.5. Applications 4.5.1. A Hopf algebra on pipe dreams 4.5.2. A zeta map from diagonal harmonics Chapter 5. Epilogue 5.1. Arbitrary type A 5.2. Linear type B 5.3. (α, m)-Tamari lattices 5.4. Parabolic multiclusters Chapter A. Data A.1. Parabolic Catalan numbers in rank 3 A.2. Parabolic Catalan numbers in rank 4 A.3. Answers to Research Challenge 3.3.4 in rank 4 / Kombinatorische Familien, die nichtkreuzende oder Cluster-Phänomene aufweisen, haben sich in den letzten Jahrzehnten als wichtiges Werkzeug für das Verständnis und die Verbindung mathematischer Objekte aus scheinbar unverbundenen Teilgebieten der Mathematik und der theoretischen Physik erwiesen. Diese Phänomene können im Zusammenhang mit Coxeter-Gruppen modelliert werden, und spielen eine wichtige Rolle in der algebraischen Kombinatorik. Im endlichen Fall werden derartige kombinatorische Familien von verallgemeinerten Catalanzahlen abgezählt. In dieser Schrift betrachten wir eine Erweiterung dieser Theorie auf parabolische Quotienten von Coxeter-Gruppen. Wir stellen die historische Entwicklung und die grundlegenden Definitionen und Konstruktionen dar und präsentieren eine Reihe von Vermutungen und Forschungsfragen, die in diesem Zusammenhang entstehen. Anschließend lösen wir diese Fragen im sogenannten 'linearen Typ A' und decken überraschende Zusammenhänge dieser Theorie zu bestimmten Hopf-Algebren und zur Theorie der diagonal-harmonischen Polynome auf. Am Ende dieser Schrift schlagen wir weiterführende Forschungsrichtungen vor.:Chapter 0. Prologue Noncrossing partitions Triangulations Stack-sortable permutations Dyck paths Chapter 1. Preliminaries 1.1. Posets and lattices 1.1.1. A notion of order 1.1.2. Diagrams and labelings 1.1.3. Duality and multichains 1.1.4. Zeta polynomial and Möbius function 1.1.5. Lattices 1.1.6. Distributivity 1.1.7. Semidistributivity 1.1.8. Trimness 1.1.9. Congruence-uniformity 1.1.10. The core label order 1.2. Coxeter groups 1.2.1. Coxeter systems 1.2.2. The geometric representation 1.2.3. Ordering a Coxeter group 1.2.4. Orienting a Coxeter group Chapter 2. Cataland 2.1. Catalan numbers 2.2. Aligned elements 2.2.1. Cambrian lattices 2.3. Noncrossing partitions 2.4. Clusters 2.5. Nonnesting partitions 2.5.1. v-Tamari lattices 2.6. Chapoton Triangles Chapter 3. Parabolic Cataland: Origins 3.1. Parabolic quotients of Coxeter groups 3.2. Parabolic aligned elements 3.3. Parabolic noncrossing partitions 3.4. Parabolic clusters 3.5. Parabolic nonnesting partitions 3.6. Parabolic Chapoton triangles Chapter 4. Parabolic Cataland: Linear type A 4.1. Definitions 4.1.1. Parabolic quotients of the symmetric group 4.1.2. The longest α-permutation 4.1.3. The root poset of S_α and α-Dyck paths 4.1.4. c-clusters for S_α 4.1.5. c-aligned elements for S_α 4.1.6. c-noncrossing partitions for S_α 4.1.7. α-trees 4.2. Bijections 4.2.1. Noncrossing α-partitions and (α, 231)-avoiding permutations 4.2.2. Noncrossing α-partitions and α-Dyck paths 4.2.3. α-trees and (α, 231)-avoiding permutations 4.2.4. α-trees and noncrossing α-partitions 4.2.5. α-trees and α-Dyck paths 4.3. Posets 4.3.1. The weak order on S_α(231) 4.3.2. The rotation order on Dyck(α) 4.3.3. The core label order of Tam(α) 4.4. Chapoton triangles 4.5. Applications 4.5.1. A Hopf algebra on pipe dreams 4.5.2. A zeta map from diagonal harmonics Chapter 5. Epilogue 5.1. Arbitrary type A 5.2. Linear type B 5.3. (α, m)-Tamari lattices 5.4. Parabolic multiclusters Chapter A. Data A.1. Parabolic Catalan numbers in rank 3 A.2. Parabolic Catalan numbers in rank 4 A.3. Answers to Research Challenge 3.3.4 in rank 4

In Sweden, the residential and industrial energy demand is provided by a significant part of district heating. In a decarbonization plan to reduce the CO2 emissions, the integration of a large-scale solar system in the district heating can be a suitable option. The most used types of collectors are flat plate collectors (FPC), for which efficiency drops at high temperature levels. Parabolic through collectors (PTC) have seen increased interest in later years, due to their higher efficiency at higher temperature levels, which could improve system performance both energetically and economically. A hybrid concept using a combination of FPC and PTC for a solar thermal system has previously been studied for a solar district heating system in Denmark, with the aim to maximize the solar production by operating the solar collectors in the temperature ranges where they excel. The first aim of this thesis was to adapt the hybrid solar system in a district heating system for a Swedish case study and to evaluate if the hybrid optimization studied has similar positive effects in the overall thermal production of the system in Sweden, as it did in Denmark. The second aim of this thesis was to investigate the use of photovoltaic thermal collectors (PVT) instead of FPC for parts of the solar thermal system. With PVT, a single solar collector module allows for simultaneous production of heat and electricity and integration of photovoltaic thermal collectors in the solar assisted district heating could improve the overall performance of the system, both in terms of energy production and economical gain.The study was performed using the simulation tool TRNSYS based on a model developed in a danish case study. It was performed a parametric analysis on the percentage of share of the different types of solar collectors in the total area. The results given from the simulations have been used to carry out an economic evaluation based on the levelized cost of substituted energy, the annual operation and maintenance costs, and the marginal operational cost difference between a conventional district heating system supplied by a boiler only and a solar assisted district heating system. Based on the results found, it has been proved that a greater proportion of parabolic trough collectors in the solar field contribute to a greater production of thermal energy but also to higher expenses in the economy of the project. The best configuration which balanced these two factors was composed by 70 % of flat plate collectors and 30 % of parabolic trough collectors, based on the total area. The integration of photovoltaic thermal has been demonstrated to be not cost-effective for the studied location compared to the optimized ratio of FPC to PTC, mainly due to the high and uncertain price of the new technology. The use of photovoltaic thermal system is not yet widely developed in projects and there are only a few existing projects in operation today. In the future, the development of photovoltaic thermal in solar assisted district heating projects might have a higher realizable economic potential due to the industry learning curve, but more studies will need to be performed on this.

Master´s thesis describes the structural design of the load bearing steel structure of exhibition hall located in Brněnské Výstaviště. The structure is designed according to the normative requirements of ČSN EN for ultimate and serviceability limit state. It´s structure formed by the parabolic main frames at a distance of 6 m apart, which are placed in a rectangular plan of 36 x 36 m. As the main material of load bearing elements was used a steel S355. The hall is designed for exhibitions and social occasions. The work contains a statical calculation, which assessed individual cross sections and joins.

This master thesis is dealing with a system for receiving meteorological images from satellites placed on lower orbit. Furthermore it gives basic information about satellites NOAA, METOP and FY. It also includes derivations of equations, that define minimal requirements for receiving antenna and LNA. From reached parametres, energetic balance for connection of the satellite and Earth is calculated. The main part of the master thesis is designing of low-noise amplifier for L band. LNA is implemented on the substrate FR4 and Arlon DiClad 870, circuit is designed with elements of parametres, which are spread out or concentrated. The last part of the thesis describes design of antenna for reception of meteorological images.