1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary...

Les traitements de surface mécaniques sont appliqués dans la plupart des secteurs industriels comme procédé de finition afin de renforcer les propriétés des composants métalliques. Le grenaillage de précontrainte est probablement l’un des plus répandu. Ce procédé introduit des contraintes résiduelles de compression en générant un gradient de déformation plastique dans la profondeur de la pièce traitée. L’objectif de ce travail est de comprendre et prédire l’effet de la géométrie des composants sur la redistribution des contraintes résiduelles post-grenaillage. En effet, même lorsqu’elle est maîtrisée, l’opération de grenaillage peut générer un champ de contraintes résiduelles complexe qui dépend fortement de la géométrie de la pièce. Par suite, parmi les paramètres influents sur le comportement en fatigue des composants grenaillés, le paramètre géométrique peut donc avoir un rôle majeur. Puisque les approches conventionnelles de modélisation ne sont pas transposables aux géométries non planes, et ne sont pas conformes aux contraintes industrielles en termes de temps de calcul, une méthodologie basée sur la Méthode de Reconstruction des Eigenstrains est proposée. L’approche développée est construite à partir de relations analytiques pour des massifs plans traités de façon homogène. La principale contribution est la comparaison entre modélisation et expérimentation. Les données expérimentales sont obtenues à partir d’analyses de la microstructure et par diffraction des rayons X réalisées sur des échantillons d’un superalliage base nickel, pour plusieurs géométries complexes élémentaires (plaques minces, formes convexes et concaves). Par ailleurs cette étude vise à prendre en compte l’effet des contraintes résiduelles équilibrées sur la durée de vie en fatigue. A partir du critère de fatigue multiaxial de Crossland, la méthodologie complète est appliquée à des démonstrateurs industriels à géométrie complexe. / Most manufacturing industries perform mechanical surface treatments at the end of the manufacturing chain to reinforce relevant working parts. Shot peening is probably the most common of those processes. This treatment induces compressive residual stresses by generating in-depth plastic strains. The objective of this work is to understand and predict the effect of the geometry on the redistribution of residual stresses into shot peened mechanical parts. Indeed, even when properly controlled, shot peening treatment may induce a complex residual stress field depending on the geometry of the treated part. Hence, among the variables which affect the fatigue behaviour of shot peened components, the geometry could play a major role. Because the traditional approaches for the modelling of residual stresses are not convenient for complex non-flat geometries and not consistent with industrial constraints in terms of computing time, a methodology based on the Eigenstrains Reconstruction Method is proposed. The developed approach is built with analytical relationships for massive and plane geometries homogeneously treated. The main contribution lies in the capacity to provide a comparison between modelling and experiment. Experimental data are obtained by microstructural observation and by X-ray diffraction analyses, which are carried out on Ni-based superalloy samples with elementary complex geometries (thin sheets, convex and concave shapes). In addition, this study aims to take into account the effect of the rebalanced residual stresses for fatigue life prediction. Thus, using a Crossland criterion for high cycle fatigue regime, the complete methodology is applied on industrial demonstrator samples with complex geometry.

Submitted by Lucienne Costa (lucienneferreira@ufcg.edu.br) on 2017-12-12T20:48:31Z No. of bitstreams: 1 JAIR STEFANINI PEREIRA DE ATAÍDE – TESE (PPGEP) 2014.pdf: 4947088 bytes, checksum: 8019d110744376ffaadc9a31152768ad (MD5) / Made available in DSpace on 2017-12-12T20:48:31Z (GMT). No. of bitstreams: 1 JAIR STEFANINI PEREIRA DE ATAÍDE – TESE (PPGEP) 2014.pdf: 4947088 bytes, checksum: 8019d110744376ffaadc9a31152768ad (MD5) Previous issue date: 2014-10-24 / O aumento na demanda por produtos alimentícios por parte da população requer uma indústria alimentícia moderna e de qualidade, na qual se faz necessário avaliar e ter conhecimento profundo, dentre outras coisas, das propriedades termofísicas dos alimentos, principalmente daqueles submetidos a uma tecnologia de conservação pelo uso do calor. Neste estudo, o fenômeno da difusão transiente de calor foi estudado em gêneros alimentícios pastosos contidos em recipientes com forma geométrica arbitrária. Dessa forma, tem-se o intuito de disponibilizar as análises das implicações da consideração de uma difusividade térmica constante (ou dependente da temperatura média) no estudo de transferência de calor durante a pasteurização de produtos cuja forma possa ser obtida pela revolução de áreas planas. Em adição, propôs que a difusividade térmica seja uma função da temperatura local no interior do produto, possibilitando uma maior precisão na descrição da transferência de calor. Para isso, foi discretizada e resolvida numericamente a equação de difusão escrita em coordenadas generalizadas, através do método dos volumes finitos, com uma formulação totalmente implícita, para condições de contorno de primeiro tipo. O código computacional foi desenvolvido em FORTRAN, usando o estúdio CVF 6.6.0, na plataforma Windows XP. As ferramentas numéricas foram validadas através de dados obtidos na literatura para o cilindro infinito. Para comprovação da eficiência do método de pasteurização realizou-se análises físico-químicas e microbiológicas antes e após o tratamento térmico. A análise e comparação dos resultados mostraram que ocorre uma redução dos micro-organismos totais, sem proporcionar tanta alteração nutricional, particularmente no valor proteico das polpas, proporcionando segurança alimentar com um menor gasto energético. Bem como, uma vez conhecida a expressão da difusividade térmica em função da temperatura local, é possível definir o tempo necessário para que o alimento acondicionado em um recipiente com uma geometria qualquer e simetria de revolução, entre em equilíbrio térmico com uma temperatura previamente definida, através de simulações. Dessa forma, torna-se desnecessário a realização de experimentos a cada vez que um novo recipiente for utilizado para acondicionar o produto. / The increase in demand for food products by the population requires a modern and quality food industry, where it is necessary to evaluate and have deep knowledge, among other things, the thermophysical properties of foods, especially those subjected to a conservation technology by use of heat. In this study, the phenomenon of transient heat diffusion was studied in pasty foodstuffs in containers of arbitrary geometric shape. Thus, it has been the aim of the analysis of the implications of an account (or dependent on the average temperature) to study the transfer of heat during pasteurisation of products whose shape can be obtained by the flat areas provide thermal diffusivity constant revolution. In addition, proposed that the thermal diffusivity is a function of the local temperature inside the product, providing greater precision in the description of the heat transfer. For it was discretized and numerically solved the diffusion equation written in generalized coordinates by the finite volume method with a fully implicit formulation for boundary conditions of the first kind. The computer code was developed in FORTRAN, using the CVF Studio 6.6.0 on Windows XP platform. The numerical tools were validated using data from the literature for the infinite cylinder. To prove the efficiency of the pasteurization method was carried out physicochemical and microbiological before and after heat treatment analysis. The analysis and comparison of the results showed that a reduction in total micro-organisms occurs, without providing much nutritional changes, particularly in the pulp protein value of providing food security to a lower energy expenditure. And, once known the thermal diffusivity of the expression depending on the local temperature, it is possible to set the time required for the food packed in a container with any geometry and symmetry of revolution, comes into thermal equilibrium with a previously set temperature, through simulations. Thus, it becomes unnecessary to perform experiments each time a new container is used for packaging the product.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2016-10-05T11:43:24Z No. of bitstreams: 1 TeseTSS.pdf: 1911413 bytes, checksum: cd75532daece2c08f25c9489203e56ca (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-10-05T17:59:07Z (GMT) No. of bitstreams: 1 TeseTSS.pdf: 1911413 bytes, checksum: cd75532daece2c08f25c9489203e56ca (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-10-05T17:59:18Z (GMT) No. of bitstreams: 1 TeseTSS.pdf: 1911413 bytes, checksum: cd75532daece2c08f25c9489203e56ca (MD5) / Made available in DSpace on 2016-10-05T18:15:58Z (GMT). No. of bitstreams: 1 TeseTSS.pdf: 1911413 bytes, checksum: cd75532daece2c08f25c9489203e56ca (MD5) Previous issue date: 2015-07-23 / Fundação Araucária de Apoio ao Desenvolvimento Científico e Tecnológico do Paraná (FAADCT/PR) / The manner Teaching Activities (TAs) of different types of Geometry may be presented as a unity between teaching and learning, or rather, as Teaching Guiding Activity (TGA) in the initial formation of teachers, is discussed. It has thus been presumed that the logical and historical perspective may become a didactic factor in teachers´ initial formation when TAs are developed as from the subject-group-class-narrative dynamics. Current qualitative research was developed based on the following questions: Did teaching activities developed in the disciplines ‘Geometry’ and ‘Euclidian Geometry and Topic for Non-Euclidian Geometries’ generate aims and motives to teach and learn to teach Geometries? Did the activities experienced by the subject-group-class dynamics and posting of narratives become a TGA? Which are the productions of meanings, aims and motives explicit in the narratives prepared by undergraduates of the Math course during their experience in TAs of Geometries within the logical and historical perspective as from the subject-group-class dynamics? Data were retrieved from questionnaires, TAs, field diaries and narratives posted on the Internet. The empirical material was analyzed by four descriptive and analytic categories emerging from three-fold data, namely, From the isolated to the collective; The New; From Learning to Learning to Teach; Contradictions. Results show that Geometry TAs within the logical-historical perspective as from the subject-group-class-narrative dynamics trigger information related to the appropriation of theoretical knowledge, teaching of theoretical knowledge, organization of teaching, pedagogical activities and research in most people involved in the teaching-learning process. / Objetivamos com essa pesquisa, analisar, se as Atividades de Ensino (AE) de Geometrias na perspectiva lógico-histórica podem se configurar como unidade entre o ensino e a aprendizagem, ou seja, como Atividade Orientadora de Ensino (AOE) na formação inicial de professores. Dessa forma, tivemos como pressuposto que a perspectiva lógico-histórica pode se tornar didática para a formação inicial de professores, quando as AE forem desenvolvidas, a partir da dinâmica indivíduo-grupo-classe-narrativas. A pesquisa, de cunho qualitativo, foi conduzida pelas seguintes questões: As atividades de ensino desenvolvidas nas disciplinas de “Geometria” e de “Geometria Euclidiana e Tópicos de Geometrias não euclidianas” foram geradoras de objetivos e motivos para se ensinar e aprender a ensinar geometrias? Essas atividades vivenciadas pela dinâmica indivíduo-grupo-classe e postagem das narrativas se tornaram uma AOE? Quais são as produções de sentidos, de significados, os objetivos e motivos que são explicitados nas narrativas elaboradas por licenciandos do curso de matemática, enquanto vivenciaram AE de geometrias na perspectiva lógico-histórica, a partir da dinâmica relacional indivíduo-grupo-classe? Para a construção dos dados utilizamos os seguintes instrumentos: questionário, AE, diário de campo e as narrativas postadas em ambiente virtual. A análise do material empírico foi feita a partir de quatro categorias descritivas e analíticas que emergiram da triangulação dos dados, são elas: Do isolado ao coletivo; O Novo; Do aprender ao aprender a ensinar; Contradições. Os resultados permitem inferir que as AE de Geometrias na perspectiva lógica-histórica, a partir da dinâmica indivíduo-grupo-classe-narrativas desencadearam (re)significações relacionadas à apropriação do conhecimento teórico, ao ensino do conhecimento teórico, à organização do ensino, às ações pedagógicas e pesquisa, na maioria dos sujeitos envolvidos no processo de ensino e aprendizagem.

Made available in DSpace on 2015-03-13T17:08:40Z (GMT). No. of bitstreams: 1 VeronicaDA.pdf: 5709097 bytes, checksum: 4074580aee5ec2b7d354ddab1d446e43 (MD5) Previous issue date: 2006-05-19 / This work presents geophysical and geological results obtained in a dunefield located in the east coast of Rio Grande do Norte State, with the aim to recognize the aeolian body depositional geometries to a future geologic modeling of the aeolian petroliferous reservoirs. The research, which was done in blowouts region situated at Nisia Floresta Municipally, included the characterization of external geometries with GPS and internal geometry analysis by GPR. Data was integrated in GoCAD software, where it was possible the three-dimensional characterization and interpretation of the studied deposits. The interpretation of GPR profiling allowed identifying: First-order bounding surfaces that separated the aeolian deposits of the Barreiras Formation rocks; Second-order bounding surfaces, which limit dune generations and Third-order bounding surfaces, a reactivation surface. This classification was based and adapted by the Brookfield (1977) and Kocurek (1996) propose. Four radarfacies was recognized: Radarfacies 1, progradational reflectors correlated to foresets of the dunes, Radarfacies 2, plain parallels reflectors related to sand sheets, Radarfacies 3, plain parallels reflectors associated to reworking of the blowout dune crest and Radarfacies 4, mounded reflectors associated to vegetated mound of sand or objects buried in subsurface. The GPR and GPS methods was also employed to the monitoring of dunefields susceptible to human activities in Buzios Beach, where the constructions along the blowout region and the tourism are changing the natural evolution of the deposits. This fact possibly to cause negative impacts to the coastal zone. Data obtained in Dunas Park, a unit environmental conservation, was compared with information of the Buzios Beach. There is a major tendency of erosion in Buzios, specifically in blowout corridor and blowout dune / Este trabalho apresenta os resultados geol?gicos e geof?sicos obtidos em um campo de dunas situados no litoral oriental do Rio Grande do Norte e teve como objetivo definir as geometrias deposicionais dos corpos e?licos para posterior aplica??o na modelagem geol?gica de campos produtores de ?leo e g?s de origem e?lica. A pesquisa foi realizada em uma regi?o de blowouts, situada no munic?pio de N?sia Floresta - RN, onde foi poss?vel definir a superf?cie externa com o uso do GPS geod?sico e a estrutura??o interna utilizando o GPR (Ground Penetrating Radar). Estes dados foram integrados no software de modelagem geol?gica Gocad, permitindo a visualiza??o tridimensional e interpreta??o dos dep?sitos estudados. O levantamento de perfis geof?sicos permitiu a investiga??o da geometria interna dos dep?sitos, nos quais foi poss?vel reconhecer superf?cies limitantes de 1? ordem (superf?cie deposicional que separa os dep?sitos e?licos de rochas da Forma??o Barreiras), 2? ordem (superf?cie que separa diferentes pulsos de sedimenta??o e?lica) e 3? ordem (superf?cies de reativa??o). A classifica??o destas superf?cies acima descritas foi baseada e modificada das propostas de Brookfield (1977) e Kocurek (1996). Foram ainda definidas quatro radarf?cies, com base na forma e termina??o dos refletores: Radarf?cies 1, representada por refletores progradantes, os quais se relacionam aos foresets das acumula??es e?licas; Radarf?cies 2, que ? constitu?da por refletores suscept?veis ? a??o antr?pica na praia de B?zios, onde constru??es ao longo da regi?o de blowouts e a pr?tica intensiva de turismo est?o modificando o desenvolvimento natural destas acumula??es e?licas, podendo gerar impactos ambientais negativos para a zona costeira. Dados obtidos numa ?rea situada no Parque das Dunas (unidade de conserva??o ambiental) foram utilizados para compara??o com as informa??es adquiridas em B?zios. H? uma tend?ncia maior de eros?o na ?rea de B?zios, notadamente no corredor do blowout e na duna de blowout

The main goal of this thesis is a contribution to the classification of all incidence geometries<p>of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively.<p>Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1<p>(doubly transitive on every residue of rank one). In fact our definition of RWPRI requires<p>the geometry to be firm (each residue of rank one has at least two elements) and RC<p>(residually connected).<p><p>The main goal is achieved in this thesis.<p>It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages.<p><p>Quite surprisingly, our proof in the direction of the main goal uses essentially the classification<p>of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn).<p><p>Our proof requires to work with all ordered pairs of subgroups up to conjugacy.<p><p>The restrictions such as RWPRI and (2T)1 allow for a complete analysis.<p><p>The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive<p>graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of<p>the numerous connections they have with other fields of mathematics. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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The binding of different proteins involved in processes such as transcription, replication and chromatin compaction to regions of the genome is regulated by the structure of DNA. Thus, DNA structure acts as the crucial link modulating evolutionary selection of the DNA sequence based on its own function, and the function of the proteins it encodes. The aim of this work is to examine the role of intrinsic, sequence-dependent structural variations vis-a -vis the protein-induced variations, in allowing DNA to assume geometries necessary for binding by proteins. For this purpose, we carried out analyses of datasets of X-ray crystal structures of free and protein-bound DNA, and molecular dynamics simulation studies of few free DNA structures and a protein-DNA complex. Each of the projects described below will appear as a separate chapter in the thesis. Analysis of X-ray crystal structure datasets Dataset of high-resolution X-ray crystal structures of free and protein-bound DNA This project was initiated with the aim of investigating the variation in A-and B-forms of DNA and the role they play in the binding of proteins. However, a survey of the existing literature indicated that the terms ‘A-DNA’ and ‘B-DNA’ were being used rather loosely and several different parameters at the local structural level were being used by various investigators to characterise these structures. Hence a systematic study was taken up to analyse all high-resolution free DNA structures comprising of sufficient number of contiguous Watson-Crick basepairs, irrespective of how they were classified by the existing databases. We also carried out a study of double-helical, Watson-Crick basepaired, free RNA structures for comparison. The structures in the RNA dataset were observed to rigidly assume the A-form and hence the average values of different parameters for that dataset were used to characterise the A-form. The analysis of free DNA and RNA structures was accompanied by an analysis of protein-bound DNA crystal structures. DNA structures bound to the helix-turn-helix motif in proteins were also analysed separately. The analysis of free DNA and RNA structures allowed us to pinpoint the parameters suitable for discriminating A-and B-forms of DNA at the local structural level. The results illustrated that the free DNA molecule, even in the crystalline state, samples a large amount of conformational space, encompassing both the A-and the B-forms. Most protein-bound DNA structures, including those with large, smooth curvature, were observed to assume the B-form. The A-form was observed to be limited to a small number of dinucleotide steps in DNA structures bound to the proteins belonging to a few specific families. Thus our study highlighted the structural versatility of B-form DNA, which allowed it to take up a range of global geometries to accommodate most DNA-binding protein motifs. Dataset of X-ray crystal structures of the nucleosome The study of high-resolution structures of free and protein-bound DNA was followed by an analysis of a dataset of X-ray crystal structures of the nucleosome, which is the fundamental repeating unit of the eukaryotic chromosome, and has been shown to play an important role in transcription regulation. Our results indicated that there is an ensemble of dinucleotide and trinucleotide level parameters that can give rise to similar global nucleosome structures. We therefore raise doubts about the use of the best resolved nucleosome structure as the template to calculate the energy required by putative nucleosome-forming sequences for adopting the nucleosome structure. Based on our results, we have proposed that the local and global level structural variability of DNA may act as a significant factor influencing the formation of nucleosomes in the vicinity of high-plasticity genes, and in determining the probability of binding by regulatory proteins. Molecular dynamics simulation studies of free and protein-bound DNA structures The analysis of crystal structure databases was complemented by molecular dynamics (MD) studies to investigate the dynamic evolution of the DNA structure in its free and protein-bound states. The following three simulation studies were carried out: Study to examine the biological relevance of the presence of 5-methyl group in thymine nucleotides An investigation of the biological relevance of the 5-methyl group in thymine nucleotides was carried out. For this purpose, comparison of molecular dynamics studies on structures with sequences d(CGCAAAUUUGCG)2and d(CGCAAATTTGCG)2was carried out. Our results showed that the presence of the thymine 5-methyl group was necessary for the A-tract to assume characteristic properties such as a narrow minor groove. It was also shown to modulate local level structural parameters and consequently, the curvature of the longer DNA fragment in which the A-tract was embedded. The analysis also provided possible explanation for the experimentally observed interaction of A-tracts with drugs and DNase-I in the presence and the absence of the thymine 5-methyl group. This project was the first of a series of MD studies, and hence several protocols were tested before finalising the correct protocol. Simulations were carried out using the Berendsen temperature equilibration scheme as well as the Langevin temperature equilibration scheme on both the structures. The Langevin temperature equilibration scheme was found to be unsuitable for nucleic acid simulations, as it caused long-term and possibly permanent disruption of the double-helical structure at the terminal and the neighbouring two positions in the sequence. The Berendsen temperature equilibration scheme was not observed to cause such disruptions. Simulations were also carried out on both structures, with or without initialising the initial ion positions. The position of minimum electrostatic potential, where AMBER8 placed the first counterion, was observed to act as a minimum energy trap from which the counterion could not escape even during the course of several nanoseconds of simulation. Hence, the actual simulations were carried out using the Berendsen temperature equilibration scheme, and after randomisation of initial ion positions. The results of protocol testing have been reported in an appendix. Study of DNA bending and curvature An analysis of DNA bending and curvature was carried out, by MD simulation on structures of three, ∼thirty basepair long sequences, namely, d(G-3(CA4T4G)-C)2, d(G-3(CT4A4G)-C)2and d(T-GACTA5T-GACTA6T-GACTA5T-G). For each molecule, snapshots belonging to a particular global geometry (linear, curved, bent in a particular direction etc.) were grouped together, and the average values of the dinucleotide step parameters for different groups were compared. It was observed that for all the three molecules, the average values for groups corresponding to different global geometries were within 1of each other, indicating that ensemble average values of dinucleotide level parameters are incapable of predicting the global geometry of a DNA molecule. Study of the TraR-Trabox complex The study on DNA bending and curvature was followed by simulations of a protein-DNA complex comprising of the bacterial quorum sensing transcription factor TraR with its promoter region known as Trabox. Simulations of a protein-free wild-type Trabox and a Trabox with two mutations in the spacer region were also carried out. Grouping of DNA snapshots in all the three simulations based on average values of dinucleotide parameters in the spacer region shows how selection of the ‘right’ DNA geometry by proteins works at several levels. The number of snapshots of free mutated Trabox assuming a geometry favourable for protein-binding in terms of average twist alone are less than one-fourth of the corresponding number for free wild-type Trabox. When one applies further selection criteria in terms of other parameters such as roll and slide, the number of mutated Trabox snapshots with a geometry favourable for protein-binding drops to less than 0.5%ofthe total number of MD snapshots. Thus our results highlight how sequence-dependent changes in the structrure of DNA regions, adjacent to those that directly hydrogen-bond to proteins, can also critically influence processes such as transcription. General Conclusion Overall, our results indicate that intrinsic, sequence-dependent structural variations in free B-DNA allow it to sample a large volume of the double-helical conformational space, and assume global geometries that can accomodate most DNA-binding proteins.

Ion traps used in mass spectrometers are of two classes. One class consists of traps having three electrode geometries which have rotational symmetry about central axis. They are called axially symmetric ion traps. Paul trap, Cylindrical Ion Trap(CIT) are examples in this class. Other class of traps contain 2D electric field inside them which has same profile along the central axis due to translational symmetry. Linear Ion Trap(LIT) and Rectilinear Ion Trap(RIT) are examples in this class. In the ideal hyperbolic geometries of Paul trap and LIT, electric field is a perfectly linear function of distance from the center of the trap. But when these ideal geometries are simplified in to simpler geometries of the CIT and the RIT for ease in machining, linearity of field, which is a specialty of Paul trap and LIT is lost. In this thesis, an effort is made to optimize the field within the traps by using split electrodes. The ring electrode of the CIT and both pairs of electrodes in the RIT are divided into more number of parts. Suitable voltages are applied on these parts to improve the linearity of the field. This thesis contains six chapters. Chapter 1 contains a background information about mass spectrometry. Chapter 2 discusses the Boundary Element Method (BEM) used to calculate charge distribution and Nelder-Mead method used for optimization. It also shows the calculation of multipoles. In Chapter 3, two new geometries namely split-electrode RIT and split-electrode CIT are considered with the objective of improving the linearity of electric field inside them. It is shown here that by applying certain external potential on various parts of split electrodes of these geometries, it is possible to improve the linearity of electric field inside them. In Chapter 4, capacitor models of new geometries proposed in chapter 3 are discussed. The use of external capacitors as a replacement to external power supply is also discussed in this chapter. InChapter5, study similar to that ofChapter3is carried out by splitting the geometries in more number of parts. The possibility of improved field profile is investigated by applying full potential to some of these parts and keeping other parts at ground potential. In Chapter 6, concluding remarks are discussed.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.