Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-07T15:58:13Z No. of bitstreams: 1 Arquivototal.pdf: 3094040 bytes, checksum: a87167e5afd20391a015f8b70a02bcd3 (MD5) / Made available in DSpace on 2018-05-07T15:58:13Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 3094040 bytes, checksum: a87167e5afd20391a015f8b70a02bcd3 (MD5) Previous issue date: 2017-08-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / research refers to the study of natural cavities in the geological-geomorphological context in the State of Paraíba. This work addressed nine natural cavities (the most representative) distributed in four municipalities of the state that developed in differentiated lithologies, such as: sandstone, limestone and granite. These cavities are distributed in the respective municipalities: two in the municipality of João Pessoa (Caverna da Onça and Caverna do Marés); two in the municipality of Santa Rita (Caverna do Índio and Gruta do Lobo guará); one of municipality of Alhandra (Gruta do Wilson) and four in the municipality of Araruna More precisely in the Parque Estadual da Pedra da Boca - PEPB (Pedra da Boca, Pedra da Caveira, Pedra da Santa and Furna do Caçador). These nine natural cavities constitute the most representative morphological expressions of the genus existing in the state of Paraíba. The main objective of this research is to study the different types of natural cavities on the Coastal and Eastern Agreste paraibano. The methodology employed in this work was envolved in bibliographical surveys regarding the natural cavities in the regional and local context of the researched areas. Several field researches were carried out with the objective of making an external and internal characterization of the cavities, giving data tabulation and thematic mapping of the interior of the cavities using Survex software. It was verified through the prospecting and mapping that the cavities mentioned in this research are in full transformation stage, caused by the dissolution, mechanical action of the water (piping) and the blocking of blocks in steep slopes. It can be verified for the first time, a study of natural cavity of carbonate lithology in the State of Paraíba, called the Gruta do Wilson. During the research it is noticed that all the cavities have a cultural value for the region where it is inserted, where some of them attract a significant number of tourists with the purpose of practicing leisure and adventure sports. / Esta pesquisa refere-se ao estudo sobre cavidades naturais no âmbito geológico-geomorfológico no Estado da Paraíba. Este trabalho abordou nove cavidades naturais (as mais representativas) distribuídas em quatro municípios do estado que se desenvolveram em litologias diferenciadas, como: arenito, calcário e granito. Essas cavidades estão distribuídas nos respectivos municípios: duas no municipio de João Pessoa (Caverna da Onça e Caverna do Marés); duas no município de Santa Rita (Caverna do Índio, Gruta do Lobo guará); um no municipio de Alhandra (Gruta do Wilson) e quatro no municipio de Araruna, mais precisamente no Parque Estadual da Pedra da Boca - PEPB (Pedra da Boca, Pedra da Caveira, Pedra da Santa e Furna do Caçador). Essas nove cavidades naturais constituem as mais representativas expressões morfológicas do gênero existente no estado da Paraíba. O objetivo principal desta pesquisa é estudar os diversos tipos de cavidades naturais existentes no Litoral e porção oriental do Agreste paraibano. A metodologia empregada nesse trabalho envolveu-se em levantamentos bibliográficos o que diz respeito às cavidades naturais no contexto regional e local das áreas pesquisadas. Foram elaboradas diversas pesquisas de campo com o objetivo de fazer uma caracterização externa e interna das cavidades originando a tabulação de dados e confecção de mapas temáticos do interior das cavidades usando o software Survex. Constatou-se através das prospecções e mapeamentos, que as cavidades citadas nesta pesquisa, estão em pleno estágio de transformação, acarretadas pela dissolução, ação mecânica da água (piping) e pelo caimento de blocos em vertentes íngremes. Pode-se constatar pela primeira vez, um estudo de cavidade natural de litologia carbonática no Estado da Paraíba, denominada de Gruta do Wilson. Durante a pesquisa percebe-se que todas as cavidades possuem um valor cultural para a região onde está inserida, onde algumas delas atraem um numero significativo de turistas com o objetivo de praticar lazer e esportes de aventura. Palavras-chave: Cavidades naturais. Geomorfologia e Ambiente Subterrâneo.

A identificação e caracterização geométrica e físico-química de espaços vazios na estrutura tridimensional de proteínas é capaz de agregar informações importantes para guiar o desenho racional de drogas e a caracterização funcional de sítios de ligação e sítios catalíticos. Dessa forma, algumas ferramentas computacionais foram desenvolvidas nas últimas duas décadas, visando efetuar essas caracterizações. Contudo, as ferramentas existentes lidam com uma série de limitações, dais quais merecem destaque a falta de precisão, falta de capacidade de integração em protocolos de larga escala, falta de capacidade de customização e a falta de uma caracterização eletrostática . Tendo em mente estas limitações, desenvolvemos uma nova ferramenta, denominada KV-Finder, com o objetivo de estender as funcionalidades dos programas existentes, fornecendo assim uma caracterização sistemática mais eficiente e mais informativa dos espaços vazios da estrutura tridimensional de proteínas. Através de uma modelagem matricial baseada em um direcionamento realizado pelo usuário, nossa ferramenta identifica e caracteriza espaços vazios em topologias proteicas. O utilitário é capaz de quantificar o volume, a forma, a extensão de sua superfície, os resíduos proteicos que interagem com os espaços vazios e um mapa de cargas parciais da superfície encontrada. Nossa rotina foi integrada com ferramentas gráficas de modelagem molecular, fornecendo uma interação fácil e eficiente com o usuário. A validação de nosso algoritmo foi realizada em um conjunto de proteínas cujos diversos tipos de espaços vazios englobam os mais variados sítios de ligação e sítios catalíticos. O cálculo do volume de cavidades enzimáticas foi efetuado em larga escala, acompanhando a evolução do tamanho de bolsões na superfamília ALDH. Com relação aos outros softwares existentes, nossa ferramenta apresenta uma série de vantagens das quais merecem destaque menor tempo de execução, maior precisão, maior acessibilidade e facilidade de integração com outros programas, além das características únicas de permitir que a busca ocorra em regiões específicas dentro da proteína e de realizar um mapeamento parcial de cargas da superfície encontrada. / The identification and characterization of geometrical and physical-chemical properties in protein vacant spaces aggregates important information for steering rational drug designing and functional characterization of binding and catalytic sites. Therefore, several softwares have been develop during the past two decades in order to perform such characterization. Nevertheless, the existing tools still present a series of limitations such as lack of precision, lack of integrability in large scale protocols, lack of customization capacity and the lack of a proper electrostatic depiction. We developed a new software, dubbed KV-Finder, in order to complement and extend the functionality of existing softwares, providing a systematic and more descriptive portrayal of protein vacant spaces. By employing a user-driven matrix modeling, our tool identifies and characterizes empty spaces in all sorts of protein topologies. The software quantifies the volume, the area and the shape of the surface, the residues that interact with the vacant spaces and a partial charge map of the computed surface. Our routine was integrated with a graphical molecular modeling software, providing the user with a simple and easy-to-use interface. KV-Finder has been validated with a distinct set of proteins and binding sites. The volume computation was carried in large scale, accompanying the evolution of the pocket volume in the ALDH superfamily. Compared with existing software, KV-Finder presents greater precision, greater accessibility and ease of integration in large scale protocols and visualization softwares. Also, the software possesses unique and innovative features such as the ability to segment and subsegment the empty spaces, a electrostatic depiction and a ligand interaction highlight feature.

Made available in DSpace on 2014-10-09T12:54:11Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:08:59Z (GMT). No. of bitstreams: 1 12698.pdf: 772894 bytes, checksum: be69d4e1e623ce5d0dc821671a2724dc (MD5) / Dissertacao (Mestrado Profissionalizante em Lasers em Odontologia) / IPEN/D-MPLO / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP; Faculdade de Odontologia, Universidade de Sao Paulo , Sao Paulo

Orientador: Jose Antonio Roversi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-09T01:48:12Z (GMT). No. of bitstreams: 1 Yabu-uti_BrunoFerreiradeCamargo_M.pdf: 1406553 bytes, checksum: 938ab0006a4b98ac2e95d69ce2f1f39f (MD5) Previous issue date: 2007 / Resumo: Nessa dissertação de mestrado estudamos a dinâmica do emaranhamento entre dois átomos remotos localizados em cavidades distintas. O foco principal é a produção de estados maximamente emaranhados entre átomos de dois níveis em cavidades distintas e, em particular, acopladas. Inicialmente apresentamos os principais conceitos da Teoria de Informação Quântica, aspectos qualitativos e quantitativos do emaranhamento quântico, em seguida partimos para o sistema físico proposto: átomos em cavidades. Apresentamos o modelo de Jaynes-Cummings (MJC) e uma breve análise do emaranhamento que surge da interação átomo-campo descrita por esse modelo. No sistema de duas cavidades desacopladas apresentamos como gerar emaranhamento entre átomos remotos de forma condicional. É apresentado então o sistema formado por duas cavidades acopladas interagindo com átomos de dois níveis idênticos, fato que corresponde a constantes de acoplamento átomo-campo iguais (g1= g2). A interação àtomo-campo ainda é descrita pelo MJC já o sistema das cavidades acopladas pode ser modelado conforme a proposta de Zoubi et. al [1](para cavidades separadas por um meio físico a uma curta distância) ou pela proposta de Pellizzari [2](para cavidades conectadas por uma fibra ótica). Para escolhas adequadas dos parâmetros relevantes em cada caso, a dinâmica dos dois sistemas é equivalente a interação dos áomos com um campo mono-modo. Em conseqüência da aparente simplicidade, investigamos a dinâmica do emaranhamento entre átomos distantes, incluindo a geração de estados maximamente emaranhados (essencial para o processamento de informação quântica, comunicação quântica [3] e computação quântica distribuída [4, 5] ) de forma determinística e sem a necessidade de uma interação indireta entre os modos das cavidades para gerar um estado inicial emaranhado compartilhado / Abstract: In this work, we study the dynamics of the entanglement between two remote atoms in distinct cavities. The main focus is the production of maximal entangled states between identical atoms of two levels in distinct cavities and, in particular, coupled cavities. Initially we present the main concepts of the Theory of Quantum Information, qualitative and quantitative aspects of the quantum entanglement, after that we consider the physical system: atoms in cavities. We present the Jaynes-Cummings model (JCM) and make one brief analysis of the entan-glement that appears due to such atom-field interaction. In the system of two uncoupled cavities we present how to generate entanglement between remote atoms in conditional form. We introduce the system formed by two coupled cavities interacting with identical atoms, fact that corresponds to identical coupling constant (g1= g2). The atom-field interaction is still described by the JCM and the system of coupled cavities can be modeled by the Zoubi et. al.¿s proposal [1] (for separate cavities for an environment for a short distance) or for the Pellizzari¿s proposal [2] (for cavities connected by a optical fiber). For appropriate choices of parameters in each case, the dynamics of the two systems is equivalent to the interaction of atoms with a mono-mode field. Due to the apparent simplicity, we investigate the dynamics of the entanglement between distant atoms, including the generation of maximal entangled states (essential for the processing of quantum information, quantum communication [3] and distributed quantum computation [4,5] ) in determinist form and without necessity of an indirect interaction between the modes of the cavities to generate a shared entangled initial state / Mestrado / Física / Mestre em Física

Une caractéristique remarquable de la convection de Rayleigh-Bénard qui concerne une couche de fluide horizontale chauffée par le bas et refroidie par le haut, est l’établissement spontané de l’ordre spatial et la formation d’une circulation cohérente à grande échelle. Comment les différents facteurs, tels que la géométrie du domaine et les conditions limites, influencent l’écoulement à grande échelle, restent une question ouverte. Malgré sa simplicité apparente, la convection de Rayleigh-Bénard présente une dynamique à grande échelle incroyablement riche et complexe, tels que des modes de torsion et du battement, la rotation du plan et des cessations de la circulation, qui coexistent souvent et se concourent. Une approche couramment utilisée dans l’étude des cessations, consiste à contraindre la circulation à grande échelle à un plan en limitant le domaine fluide à une cellule carrée (2D) ou à une cellule rectangulaire mince (quasi-2D). Cependant, il n’est pas tout à fait clair si les retournements 2-D et (quasi-)2-D correspondent au même phénomène. Le présent document est consacré à l’étude des modes d’écoulement à grande échelle dans la convection turbulente de Rayleigh-Bénard et de l’influence exercée par différents facteurs sur les structures d’écoulement et sur leur évolution temporelle. La caractérisation proposée combine une analyse statistique avec une approche physique s’appuyant sur le moment angulaire ainsi que sur les énergies cinétiques et potentielles pour mettre en évidence les mécanismes physiques sous-jacents. Nous essayons ensuite de relier ces mécanismes à chacun des modes d’écoulement distinctifs observés et à leur évolution. / One outstanding feature of the Rayleigh-Bénard problem which concerns a horizontal fluid layer heated from below and cooled from above, is the spontaneous establishment of spatial ordering and the formation of a coherent large-scale circulation. How different factors, such as the domain geometry and boundary conditions, influence the sizes and shapes of the large-scale flow remains an open question. Despite its apparent simplicity, Rayleigh-Bénard convection exhibits some incredibly rich and complex large-scale dynamics such as torsional modes, rotation, sloshing, and cessations, which often coexist and compete to each other. One approach, commonly used in the study of cessations is to constrain the large scale circulation to a plane by restricting the fluid domain to a (2-D) square cell or to a slim rectangular cell of small aspect ratio in the transversal direction. However, it is not entirely clear whether the 2-D and (quasi-)2-D reversals correspond to the same phenomenon. The present document is dedicated to the study of the large-scale flow patterns in turbulent Rayleigh-Bénard convection, and of the influence exerted by different factors on the flow structures and on their temporal evolution. The proposed characterization combines a statistical analysis with a physical approach relying on the angular momentum as well as the kinetic and potential energies to highlight the underlying physical mechanisms. We subsequently attempt to tie these mechanisms together to each of the distinctive flow patterns observed and to their evolution.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Tree cavities are an important natural resource found in many habitats, providing breeding sites and shelter for arthropods, birds and mammals. However, nest boxes have been more frequently used in Brazil as a tool aiming the conservation of endangered psittacids. In view of this fact, the general objective of the present dissertation was to verify how the use of the artificial tree cavities by vertebrates and invertebrates occurs. In this study we tested the following hypotheses: 1) due to a possible lack of natural cavities at the forest edge, there will be a greater use of the artificial cavities at the edge than inside; 2) there will be an increased use of the artificial cavities by the exotic species at the edge than inside; 3) because there are natural predators, native species should prefer little depth nests and nests with small openings; 4) due to the edge effect, there will be a decline in the availability of natural cavities of the interior in the edge direction and 5) in transects with lower availability of natural cavities, there will be a greater use of the nest boxes. To carry out this work, we selected a subtropical Atlantic forest fragment, with an area of 80 ha, located in Santa Maria, Rio Grande do Sul, Brazil. Ten transects were established (five in edge and five inside the fragment), in which 120 artificial nests were hung (60 nests on the edge and 60 inside). The nests were installed in August 2013 and monitored every six days, between September and December 2013 and between September and December 2014. In order to allow the use of the nests by various groups of animals, these nests were made with medium and large-sizes (20 x 30 cm base and 30 cm high x 45 cm), with little or great depth (opening at the top or in the middle of the nest) and small openings (5 cm diameter), medium (10 cm) and large (15 cm). Inside the fragment, there were 29 uses and in the edge 31 uses. Hymenoptera was the most frequent group, corresponding to 61.40% of the occupations (35 of the 60 occupied boxes). Araneomorphae was the second most frequent group with 13 occupied nests; nine nests were occupied by birds (generating 17 chicks, 16 of Pyrrhura frontalis and a chick of Dendrocolaptes platyrostris). Mammals were the least frequent group with only three used boxes (two nests occupied by Didelphis albiventris and one by Guerlinguetus sp.). It was also observed a greater availability of natural cavities inside (50) than at the edge (14), which was considered significant through the statistical test of Mann-Whitney, since the p value was 0.047. Generally the native species sought more cavities with small and little depth openings, while the exotic species (A. mellifera) proved generalist. It was verified, therefore, that it was more difficult for birds and mammals to accept artificial cavities in a short time while the exotic species has demonstrated a rapid acceptance of these structures. / Cavidades arbóreas constituem um importante recurso natural presente em diversos hábitats, fornecendo sítios de reprodução e abrigo para artrópodes, aves e mamíferos. Entretanto, cavidades artificiais têm sido mais frequentemente utilizadas, no Brasil, como uma ferramenta que visa a conservação de psitacídeos ameaçados de extinção. Tendo em vista este fato, a presente dissertação teve como objetivo geral verificar como ocorre a utilização de ninhos artificiais por vertebrados e invertebrados. Neste trabalho foram testadas as seguintes hipóteses: 1) devido a uma possível carência de cavidades arbóreas na borda, haverá maior utilização de ninhos artificiais na borda do que no interior; 2) haverá maior utilização de cavidades artificias por abelha-doméstica na borda do que no interior; 3) por possuírem predadores naturais, as espécies nativas devem preferir ninhos grandes e ninhos com aberturas pequenas; 4) devido ao efeito de borda, haverá uma menor disponibilidade de cavidades arbóreas no interior do que na borda e 5) nas transecções com menor disponibilidade de cavidades arbóreas, haverá maior utilização de caixas-ninho. Para a realização deste trabalho foi selecionado um fragmento de Mata Atlântica subtropical, com área de 80 ha, localizado no município de Santa Maria, Rio Grande do Sul, Brasil. Foram delimitadas 10 transecções (cinco na borda e cinco no interior do fragmento) onde foram instalados 120 ninhos artificiais (60 ninhos na borda e 60 no interior). Os ninhos foram instalados no mês de agosto de 2013 e monitorados a cada seis dias, entre setembro e dezembro de 2013 e entre setembro e dezembro de 2014. A fim de permitir a utilização dos ninhos por diversos grupos de animais, estes foram confeccionados com tamanhos médio e grande (20 cm de base x 30 de altura e 30 cm x 45 cm), com pouca ou grande profundidade (abertura no alto ou no meio do ninho) e aberturas pequenas (5 cm de diâmetro), médias (10 cm) e grandes (15 cm). No interior do fragmento, ocorreram 29 utilizações e na borda 31 utilizações. Hymenoptera foi o grupo mais frequente, correspondendo a 61,40% das ocupações (35 das 60 caixas ocupadas). Araneomorphae foi o segundo grupo mais frequente com 13 ninhos ocupados; nove ninhos foram ocupados por aves (gerando 17 filhotes, 16 de Pyrrhura frontalis e um filhote de Dendrocolaptes platyrostris). Os mamíferos foram o grupo menos frequente com apenas três caixas utilizadas (dois ninhos ocupados por Didelphis albiventris e um Guerlinguetus sp.). Foi constatada ainda uma maior disponibilidade de cavidades naturais no interior (50) do que na borda (14), o que através do teste estatístico de Mann-Whitney foi significativo (p = 0,04). De modo geral as espécies nativas procuraram mais cavidades com aberturas pequenas e pouco profundas, enquanto a espécie exótica (A. mellifera) mostrou-se generalista. Portanto a conservação de áreas florestadas é de extrema importância para manutenção de sítios reprodutivos, como as cavidades arbóreas, utilizados por diversas espécies da fauna silvestre.

Many methods of analyzing both the physical and chemical behavior of proteins require information about its structure and stability. Also various other parameters such as energy function, solvation, hydrophobic/hydrophilic effects, surface area and volumes too play an important part in such analysis. The contribution of cavities to these parameters are very important. Existing methods to compute and measure cavities are limited by the inherent inaccuracies in the method of acquisition of data through x-ray crystallography and uncertainities in computation of radii of atoms. We present a topological framework that enables robust computation and visualization of these structures. Given a fixed set of atoms, voids and pockets are represented as subsets of the weighted Delaunay triangulation of atom centers. A novel notion of (ε,π)-stable voids helps identify voids that are stable even after perturbing the atom radii by a small value. An efficient method is described to compute these stable voids for a given input pair of values (ε,π ). We also provide an implementation to visualize, explore (ε.π)-stable voids and also calculate various properties such as volumes, surface areas of the proteins and also of the cavities.

Le stockage de l’énergie constitue un enjeu majeur pour garantir la sécurité des réseaux électriques et favoriser le développement des énergies renouvelables. Véritable alternative aux stations de transfert d’énergie par pompage (STEP), le stockage d’énergie par air comprimé (CAES pour Compressed Air Energy Storage) fait partie des technologies les plus intéressantes. Dans les systèmes classiques utilisés actuellement, l’énergie de compression est perdue et l'air est préchauffé lors de la détente. Il en résulte une émission de CO2 et un rendement faible de l’ordre de 50%. Le système AA-CAES (Advanced Adiabatic Compressed Air Energy Storage) vise à pallier ces deux inconvénients en stockant la chaleur de compression dans un régénérateur thermique et en la restituant avant la détente dans la turbine. Compte tenu des fortes sollicitations thermiques, mécaniques et cycliques que subit cet ouvrage, la conception d'un revêtement capable d'assurer la stabilité, l'isolation et l'étanchéité constitue un enjeu principal du système. Ce point crucial constitue l'axe principal autour duquel s'articule cette thèse. Une campagne d'essais en laboratoire a été mise en oeuvre pour étudier les comportements thermique, hydraulique et mécanique de tous les matériaux impliqués dans un régénérateur souterrain creusé dans une roche cristalline. Pour l'air humide, dont le comportement thermodynamique est mal connu dans la gamme des fortes températures et des pressions envisagées, un nouveau modèle théorique a été développé. De la même façon, un modèle thermo-hydro-mécanique a été développé pour un milieu poreux déformable saturé traversé par un fluide compressible. L'intégration de ce modèle dans un logiciel de calcul de structures par éléments finis a permis d’examiner plusieurs configurations de revêtement et d'étudier l’effet des mécanismes de couplage sur le champ de température et sur la stabilité mécanique. Afin de valider les développements effectués et les solutions de revêtement proposées, un prototype d’un régénérateur à échelle réduite combinant pression et température a été construit dans le laboratoire LITEN du CEA à Grenoble. Les résultats des expériences et des modélisations effectuées ont mis en évidence l'importance du phénomène de convection dans les briques isolantes du revêtement et la nécessité d'assurer l'étanchéité du système avant l'isolation thermique. / Energy storage is a major challenge to ensure the safety of electrical networks and to promote the development of renewable energies. Veritable alternative to Pumped Storage Hydropower (PSH), the energy storage using compressed air (for CAES Compressed Air Energy Storage) is one of the most interesting technologies. In conventional systems currently in use, the compression energy is lost and the air is preheated during the expansion phase. This results in emission of CO2 and a low efficiency of about 50%. The AA-CAES (Advanced Adiabatic Compressed Air Energy Storage) aims to overcome these two drawbacks by storing the heat of compression in a thermal regenerator and restoring it before expansion in the turbine. Given the high thermal, mechanical and cyclic loading subject to the regenerator, the design of a lining capable of ensuring stability, insulation and sealing is a main issue of the system. This crucial point is the main axis around which this research is articulated. A laboratory testing campaign has been conducted to study the thermal, mechanical and hydraulic behavior of all materials involved in the underground regenerator excavated in a crystalline rock. For the humid air, whose thermodynamic behavior is not well studied within the range of the high foreseen temperatures and pressures, a new theoretical model was developed. In the same way, a thermo-hydro-mechanical model was developed for a deformable porous medium saturated with a compressible fluid. The implementation of this last model into a finite element numerical code was used to examine several lining configurations and to study the effect of coupling mechanisms on the temperature field and the mechanical stability. To validate the developments made and the proposed lining solutions, a prototype of a small scale regenerator combining temperature and pressure was built in the LITEN laboratory of CEA in Grenoble. The results of the conducted experiments and modeling revealed the importance of the convection phenomenon in the insulating bricks of the lining and the need to seal the system before thermal insulation.

No description available.

As part of the Large Hadron Collider high luminosity upgrade it is proposed to include crab cavities and large aperture niobium tin final focussing magnets in the lattice in order to enhance the luminosity. In this thesis the dynamics of a proposed cavity design were considered in terms of their impact upon the dynamic aperture of the machine. Taylor maps for the cavity were created and used to perform this analysis with a full assessment of their validity. A set of symplectic thin cavity models were also developed and cross checked with the Taylor maps. Finally, dynamic aperture studies were performed using these models in order to determine which components of the crab cavity dynamics are important when considering the long term stability of the beam in the LHC upgrade. It is shown that crab cavities exhibit little impact on the LHC beam stability. For the final focussing magnets a preliminary study was conducted into the importance of including their fringe fields in a model of the LHC upgrade. A technical study was carried out into developing a symplectic model which was compatible with the current magnet models use for dynamic aperture studies. A preliminary dynamic aperture study was performed with the inclusion of fringe fields for the final focussing magnets from which the fringe fields are shown to have a negative impact on the long term beam stability.