O surgimento de juntas é inevitável em certas construções em concreto armado e para garantir que a estrutura trabalhe de forma monolítica, deve-se proporcionar uma adequada transferência de esforços entre os elementos, para isso, faz-se necessário dispor de uma emenda adequada entre os elementos. Emendas com barras retas ocupam muito espaço devido ao comprimento de traspasse necessário, dessa forma, em situações em que há uma limitação de espaço para a emenda, uma armação que constitui uma boa solução é a emenda por meio de laço, que, apesar de ter poucos estudos relacionados, vem sendo bastante difundida na construção civil. O objetivo desse trabalho é estudar o comportamento de emendas em laço em juntas de estruturas de concreto armado submetidas à tração. Para isso, realizam-se simulações numéricas no software DIANA® em modelos numéricos 3D. Inicialmente, fez-se a calibração do modelo numérico com base em ensaios experimentais da literatura, depois foi realizada uma análise paramétrica variando parâmetros geométricos das peças e da armação em laço. Os resultados mostraram que traspasses menores que o diâmetro de dobra dos laços e espaçamentos maiores que 100 mm se mostram insuficientes para a formação de bielas de compressão entre laços. Dessa forma, ao se utilizar emendas em laço em juntas de concreto armado, recomenda-se dispor as barras o mais próximo possível até um espaçamento máximo de 60 mm entre eixos, como também um traspasse mínimo igual ao diâmetro de dobra dos laços. / The appearance of joints is inevitable in certain constructions of reinforced concrete and aiming to guarantee that the structure works monolithically, it is important to provide an appropriate transfer of stresses between elements, for that, it is necessary using a proper overlapping between them. Straight bars overlappings take up too much space due to the required overlapping length, therefore, in limited space situations, a reinforcement that represents a good solution is the loop joint, which has spread a lot in civil construction, although there are very few studies about it. The aim of the present work is to study the loop joint behaviour in reinforced concrete structures under tension. In order to do so, numerical simulations with numerical 3D models are made using the software DIANA®. Initially, it was made the calibration of the numerical model based on experimental tests of the literature, after that, parametric analyses were performed, varying geometric parameters of the elements and of the loop reinforcement. The results showed that overlapping lengths smaller than the loop diameter and distances between loops axes greater than 100 mm are not sufficient for the development of compression struts between loops. Thus, when the loop joint in reinforced concrete structures is used, it is recommended that the bars are placed as near as possible until a distance between the loops axes of 60 mm and a minimum overlapping length equal to the loop diameter of the reinforcement.

La simulation numérique des éoliennes flottantes est essentielle pour le développement des Energies Marines Renouvelables. Les outils de simulation classiquement utilisés supposent un écoulement stationnaire sur les rotors. Ces théories sont généralement assez précises pour calculer les forces aérodynamiques et dimensionner les éoliennes fixes (à terre ou en mer) mais les mouvements de la plateforme d’une éolienne flottante peuvent induire des effets instationnaires conséquents. Ceux-ci peuvent par exemple impacter la force de poussée sur le rotor. Cette thèse de doctorat cherche à comprendre et à quantifier les effets de l’aérodynamique instationnaire sur la tenue à la mer des éoliennes flottantes, dans différentes conditions de fonctionnement. L’étude montre que les forces aérodynamiques instationnaires impactent les mouvements de la plateforme lorsque le rotor est fortement chargé. Les modèles quasi-stationnaires arrivent néanmoins à capturer la dynamique des éoliennes flottantes avec une précision suffisante pour des phases de design amont. Les éoliennes flottantes à axe vertical sont elles aussi étudiées pour des projets offshore puisqu’elles pourraient nécessiter des coûts d’infrastructure réduits. Après avoir étudié l’influence de l’aérodynamique instationnaire sur la tenue à la mer de ces éoliennes, une comparaison est menée entre éoliennes flottantes à axe horizontal et à axe vertical. Cette dernière subit une importante poussée aérodynamique par vents forts, induisant de très grands déplacements et chargements. / Accurate numerical simulation of thesea keeping of Floating Wind turbines (FWTs) is essential for the development of Marine Renewable Energy. State-of-the-art simulation tools assume a steady flow on the rotor. The accuracy of such models has been proven for bottom-fixed turbines, but has not been demonstrated yet for FWTs with substantial platform motions. This PhD thesis focuses on the impact of unsteady aerodynamics on the seakeeping of FWTs. This study is done by comparing quasi-steady to fully unsteady models with a coupled hydro-aerodynamic simulation tool. It shows that unsteady load shave a substantial effect on the platform motion when the rotor is highly loaded. The choice of a numerical model for example induces differences in tower base bending moments. The study also shows that state of the art quasi-steady aerodynamic models can show rather good accuracy when studying the global motion of the FWTs. Vertical Axis Wind Turbines (VAWTs) could lower infrastructure costs and are hence studied today for offshore wind projects. Unsteady aerodynamics for floating VAWT sand its effects on the sea keeping modelling have been studied during the PhD thesis,leading to similar conclusions than for traditional floating Horizontal Axis Wind Turbines (HAWTs). Those turbines have been compared to HAWTs. The study concludes that, without blade pitch control strategy, VAWTs suffer from very high wind thrust at over-rated wind speeds, leading to excessive displacements and loads. More developments are hence needed to improve the performance of such floating systems.

A numerical model was developed to understand the time evolution of a wake structure around a CubeSat moving in a plasma with transonic speed. A cubeSat operates in the F2 layer of ionosphere with an altitude of 300 − 600 Km. The average plasma density varies between 10−6cm−3 − 10−9cm−3 and the temperature of ions and electrons is found between 0.1−0.2 eV. The study of a wake structure can provide insights for its effects on the measurements obtained from space instruments. The CubeSat is modeled to have a metal surface, which is a realistic assumption, with a negative electric potential. To solve the equations of plasma, the numerical difference equations were obtained by discretizing the fluid equations of the plasma along with nonlinear Poisson’s equation. The electrons were assumed to follow the Boltzmann’s relation and the dynamics of ions was followed using the fluid equations. The initial and boundary conditions for the evolution of the structure are discussed. The computation was compared to the analytical solution for a 1D problem before being applied to the 2D model. There was a good agreement between the numerical and analytical solution. In the 2D simulation, we observe the formation of plasma wake structure around the CubeSat. The plasma wake structure consists of rarefaction region where ion density and ion velocity decreases compared to the initial density and velocity.

The study considered development of a finite-element numerical simulation model for the analysis of fluid flow and conjugate heat transfer in a zero boil-off (ZBO) cryogenic storage system. A spherical tank was considered for the investigation. The tank wall is made of aluminum and a multi-layered blanket of cryogenic insulation (MLI) has been attached on the top of the aluminum. The tank is connected to a cryocooler to dissipate the heat leak through the insulation and tank wall into the fluid within the tank. The cryocooler has not been modeled; only the flow in and out of the tank to the cryocooler system has been included. The primary emphasis of this research has been the fluid circulation within the tank for different fluid distribution scenario and for different level of gravity to simulate all the potential earth and space based applications. The steady-state velocity, temperature, and pressure distributions were calculated for different inlet positions, inlet velocities, and for different gravity values. The simulations were carried out for constant heat flux and constant wall temperature cases. It was observed that a good flow circulation could be obtained when the cold entering fluid was made to flow in radial direction and the inlet opening was placed close to the tank wall. The transient and steady state heat transfer for laminar flow inside a circular microtube within a rectangular substrate during start up of power has also been investigated. Silicon, Silicon Carbide and Stainless Steel were the substrates used and Water and FC-72 were the coolants employed. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. Within the solid wafer, the heat conduction was solved. The Reynolds number, Prandtl number, thermal conductivity ratio, and diameter ranges were: 1000--1900, 6.78--12.68, 27--2658, and 300 µ m--1000 µ m respectively. It was found that a higher aspect ratio or larger diameter tube and higher thermal conductivity ratio combination of substrate and coolant requires lesser amount of time to attain steady state. It was seen that enlarging the tube from 300 µ m to 1000 µ m results in lowering of the fluid mean temperature at the exit. Nusselt number decreased with time and finally reached the steady state condition. It was also found that a higher Prandtl number fluid attains higher maximum substrate temperature and Nusselt number. A correlation for peripheral average Nusselt number was developed by curve-fitting the computed results with an average error of 6.5%. This correlation will be very useful for the design of circular microtube heat exchangers.

Au cours de leur durée de vie, les bâtiments importants sont susceptibles d’être soumis à des charges accidentelles, telles que des explosions ou des impacts. Evaluer leur stabilité vis-à-vis de charges traditionnelles statiques et sismiques ne suffit pas. Leurs performances structurelles liées à des scénarios d’effondrement progressif doivent également être examinées.L’étude de l’effondrement progressif est un problème dynamique. Malheureusement, les expériences sur le comportement des structures de génie civil dans des conditions dynamiques sont rares car difficiles à réaliser. Dans cette étude, des sous-assemblages poteaux-poutres en béton armé ont été testés sous chargement dynamique. Le chargement a consisté à placer une masse importante jouant le rôle de « charge morte » sur la colonne centrale d’un sous-assemblage simulant la liaison de 3 poteaux avec 2 poutres. Une pièce fusible jouant le rôle de support sous la colonne centrale est brutalement déverrouillée pour simuler la perte de portance soudaine de cette colonne. Le comportement dynamique et les dommages locaux causés à la structure ont été mesurés et étudiés. Le bâti de chargement et les dispositifs de support ont été conçus spécialement pour cet essai. La charge morte supérieure peut être modifiée et appliquées à différents spécimens. Les supports des colonnes latérales ont une rigidité horizontale contrôlée et sont conçus pour limiter la rotation de ces mêmes colonnes. Ainsi, les conditions aux limites des essais réalisés sont supposées être représentatives de situations réalistes. Au cours des essais, un laser a été installé sous la colonne centrale pour mesurer la vitesse de chute. Une caméra numérique rapide a été utilisée pour visualiser l'ensemble du processus de ruine du sous-assemblage. Les images obtenues de la caméra ont été traitées par une technique de DIC (Digital Image Correlation) afin d’obtenir le champs de déplacement et les déformations correspondantes. Grâce à ces mesures dynamiques, des données importantes ont été produites et enregistrées, notamment la période de vibration, la fréquence, la vitesse et le déplacement des différents échantillons testés. Sur la base de ces données expérimentales, l’effet de la section et de la portée des poutres sur la réponse dynamique et sur le mode d’endommagement des sous-assemblages a été discuté. Cette étude montre que les résultats expérimentaux obtenus, en termes de mécanismes structurels, de schéma de fissuration, de mode d'endommagement, peuvent être utilisés pour analyser le comportement de sous-assemblages de structures réelles.De plus, une modélisation numérique des essais a été réalisée pour simuler le processus de ruine de la structure. Une technique appelée «connecteur» a été proposée dans le modèle aux éléments finis du sous-assemblage poteaux-poutres. Cette technique consiste à ajouter une série de ressorts pour étudier le rôle de l’interaction entre les armatures en acier et le béton. Un modèle d'endommagement anisotrope, appelé modèle DFH-KST, a été utilisé pour caractériser l'évolution de la fissuration et l’endommagement du béton.La polyvalence de la méthodologie adoptée permet d’évaluer l’influence du comportement non-linéaire du matériau et celle de la géométrie de la structure testée. Les études numériques de calibration et de validation montrent que le modèle proposé peut reproduire le comportement et la résistance de la structure avec succès. / Important buildings may be subjected to accidental loads, such as explosions or impacts, during their service life. It is, therefore, necessary not only to evaluate their safety under traditional loads and seismic action. The structural performances related to progressive collapse scenarios need to be investigated.The study of progressive collapse involves a dynamic problem, but unfortunately dynamic experiments on the behavior of the civil engineering structures under dynamic conditions are rare. In this research, beam-column sub-assemblage specimens were tested under dynamic load. The loading program consists in placing a large mass, as a dead load, on the top of the middle column of a beam-column sub-assemblage. The support under the middle column is suddenly removed for simulating the sudden loss of a column and the damage that will result in the structure. The loading system and supporting devices were designed specially for this test. The upper dead load can be changed by increasing or decreasing the applied masse to different specimens. The supports for the side column have a controlled rigidity in the horizontal direction and are designed to restrain rotation of the side-column. Thus, the boundary conditions are supposed to be similar to real situations. During the test, a laser was installed under the middle pillar to collect the falling velocity and a high-speed camera was used to visualize the whole process of the component failure process. The images obtained from the camera were processed by Digital Image Correlation (DIC) technology to get the corresponding displacements and strain fields. By these means, all the information of the structure under dynamic loading was captured and recorded, such as the period of vibration, frequency, velocity and displacement. Based on these experimental data, the effect of section and span of the specimen on dynamic response and damage mode was discussed. Time history of resistance force curves was produced. Compared with previous published quasi-static experiments in terms of structural mechanisms, crack patterns, damage mode, it shows the experimental results from beam-column assemblage with the designed support device can be used to analyze the behavior of the local structure in the entire frame.In addition, numerical simulations were developed for simulating the failing process of the structure. A technique named “connector” was proposed into beam-column finite element model by adding a series of springs to investigate the interaction between steel rebars and concrete. A concrete damage model, named DFH-KST model, was used to characterize the development of concrete crack and damage. The versatility of the adopted methodology allows assessing the influence of the material nonlinear behavior and the geometry of the tested structure. Calibration and validation studies show that the proposed model can successfully represent the resistance of structure and behavior. Furthermore, the transverse component effect on the resistance to progressive collapse was discussed.

Direct numerical simulations (DNS) of an initially quiescent coupled air-water interface driven by an air flow with free stream speed of 5 m/s have been conducted. The DNS solves a scalar advection-diffusion equation for dissolved gas (or scalar) concentration in order to determine the impact of the water-side turbulence on scalar (mass) transfer from the air side to the water side and subsequent vertical transport in the water column. Two simulations are compared: one with a freely deforming interface and a second one with a flat interface. In the first simulation, the deforming interface evolves in the form of gravity-capillary waves generating aqueous Langmuir turbulence characterized by small-scale (centimeter-scale) Langmuir cells (LCs). The second simulation is characterized by pure shear-driven turbulence in the absence of LCs as the interface is intentionally held flat. It is concluded that the Langmuir turbulence serves to enhance vertical transport of the scalar in the water side and in the process increases scalar transfer efficiency relative to the shear-dominated turbulence in the flat interface case. Furthermore, transition to Langmuir turbulence was observed to be accompanied by a spike in scalar flux via molecular diffusion across the interface characterized by an order of magnitude increase. Such episodic flux increases, if linked to gusts and overall unsteadiness in the wind field, are expected to be an important contributor in determining the long-term average of the air-sea gas fluxes. The effectiveness of popular transfer velocity models, namely the small eddy model and the surface divergence model, in predicting this spike is evaluated via the DNS. In addition to LCs, DNS reveals that the water side turbulence is characterized by smaller, shear-driven turbulent eddies at the surface embedded within the LCs. LES with momentum equation augmented with the well-known Craik-Leibovich (C-L) vortex force is used to understand the roles of the wave and shear-driven LCs (i.e. the Langmuir turbulence) and the smaller shear-driven eddies (i.e. the shear turbulence) in determining molecular diffusive scalar flux from the air side to the water side and vertical scalar transport beneath. The C-L force consists of the cross product between the Stokes drift velocity (induced by the interfacial waves) and the flow vorticity. It is observed that Stokes drift shear intensifies the smaller eddies (with respect to purely wind-driven flow, i.e. without wave effects) leading to enhanced diffusive scalar flux at the air-water interface. LC leads to increased vertical scalar transport at depths below the interface and thus greater scalar transfer efficiency.

In a shallow shelf region, turbulent motion can have a major effect on coastal processes including ecosystem functioning, surface gas exchange and sediment resuspension. Many factors contribute to such turbulence; wind and wave forcing, buoyancy induced by surface heat fluxes and tidal forcing all play a key role in generating vertical mixing in this shallow region. Alongside these independent sources of turbulence, combinations thereof can lead to full-depth turbulent structures acting secondary to the mean flow and leading to enhanced vertical mixing throughout the entire water column. Field and laboratory experiments can often prove to be costly and time consuming, and reproducing or maintaining the complex flow dynamics of real world ocean flows is a constant challenge to these methods of research. As such, those interested in developing realistic and useful models of the marine environment to further understand its behavior often rely on 3-dimensional mathematical modeling and simulation. In this dissertation, simulations will be presented of turbulent flow and associated vertical mixing in a domain representative of the shallow coastal ocean, sufficiently far off shore that the land-ocean boundary does not significantly affect the flow behavior. This will be done using a large-eddy simulation (LES) method; solving the governing Navier-Stokes equations over a finite grid designed to capture the large, energy containing turbulent scales, and modeling the smaller, sub-grid scales. The simulations to be presented feature combinations of coastal forcing mechanisms which are either presently unexplored or the analysis of which has been hindered by the complexity of field measurements and the challenge of isolating independent causes of turbulent motion. This will include surface heat fluxes, tidal forcing and Langmuir (or wave) forcing, acting both in isolation and in conjunction with each other, in order to bridge existing gaps in knowledge and provide a more complete understanding of the generation of full-depth turbulent structures in this shallow coastal water column.

We studied the effect of a first order irreversible chemical reaction on mass transfer for two-phase flow systems in which the continuous phase is a fluid and the dispersed phase consists in catalystspherical particles. The reactive solute is transported by the fluid flow and penetrates through the particle surface by diffusion. The chemical reaction takes place within the bulk of the particle. Wehandle the problem by coupling mass balance equations for internal-external transfer with two boundary conditions: continuity of concentration and mass flux at the particle surface. We start with the case of a single isolated sphere. We propose a model to predict mass transfer coefficient (`reactive' Sherwood number) accounting for the external convection-diffusion along with internal diffusion-reaction. We validate the model through comparison with fully resolved Direct Numerical Simulations (DNS) performed by means of a boundary-fitted mesh method. For the simulation of multi-particle systems, we implemented a Sharp Interface Method to handle strong concentration gradients. We validate the implementation of the method thoroughly thanks to comparison with existing analytical solutions in case of diffusion, diffusion-reaction and by comparison with previously established correlations for convection-diffusion mass transfer. In case of convectiondiffusion- reaction, we validate the method and we evaluate its accuracy through comparisons with single particle simulations based on the boundary-fitted method. Later, we study the problem of three aligned-interacting spheres with internal chemical reaction. We propose a `reactive' Sherwood number model based on a known non-reactive prediction of mass transfer for each sphere. We validate the model by comparison with direct numerical simulations for a wide range of dimensionless parameters. Then, we study the configuration of a fixed bed of catalyst particles. We model the cup-mixing concentration profile, accounting for chemical reaction within the bed, and the mean surface and volume concentration profiles of the particles. We introduce a model for `reactive' Sherwood number that accounts for the solid volume fraction, in addition to the aforementioned effects. We compare the model to numerical simulations to evaluate its limitations

[pt] O impactador inercial em cascata é um instrumento no qual uma amostra de ar e poluentes (aerossóis) é obrigada a percorrer um trecho contendo obstáculos, chamados placas de impactação. Os obstáculos forçam o jato a mudar de direção, mas como as partículas têm maior inércia do que o fluido, não acompanham as linhas de corrente do escoamento e acabam por depositar-se sobre estes obstáculos. Diferenças na geometria envolvendo diminuição de área de passagem de escoamento e conseqüente aumento de velocidades, fazem com que, a cada estágio, partículas de diâmetros menores sejam coletadas. O desafio é projetar um instrumento que maximize a eficiência de coleta, diminuindo as perdas por deposição indesejável de partículas nas paredes, recirculações e outros efeitos. Nesta Dissertação de Mestrado foi realizado o projeto de um impactador de três estágios coletando, respectivamente, partículas com diâmetro aerodinâmico de 10, 2,5 e 1 (mi)m, operando com vazão de 30 lpm (litros por minuto) e pressão atmosférica. Na análise de desempenho do instrumento, foram realizadas simulações numéricas com o objetivo de analisar características do escoamento e da trajetória de partículas e levantar as curvas de eficiência de coleta. Foram realizados, também, testes experimentais reproduzindo condições de uso com o intuito de levantar as curvas de eficiência reais. Os resultados numéricos e experimentais foram comparados e apresentam-se ao final, conclusões sobre o desempenho do instrumento e recomendações para trabalhos futuros. / [en] Impactors are simple devices in which a sample flows of air and pollutants flow around an obstacle, called impaction plate. Particles with sufficient inertia will slip across the flow streamlines and impact on the obstacle. Particles with less inertia will follow the airflow away from the impaction surface. Inertial cascade impactors have more than one impaction area. Each one has an impaction plate and a nozzle plate. From one stage to the other, the nozzle diameters become smaller and, consequently, the velocities are higher. This allows for the collection of smaller particles. The challenge is to design an instrument with the higher collection efficiency as possible, reducing wall losses, recirculation regions and other effects. In this study a 3-stages inertial cascade impactor was designed and tested. The cut-point aerodynamic diameters for each stage were 10, 2.5 and 1 (mi)m, respectively, when operating with a flow rate of 30 l/min at atmospheric pressure. To evaluate the instrument, some numerical simulations were performed. They provided results for the flow field, particle trajectories and the collection efficiency curves. Experimental tests were also done to allow for the determination of the real efficiency curves. The numerical and experimental data were compared. Finally, the conclusions of the work and recommendations for future studies are presented.

Les arythmies auriculaires constituent une pathologie majeure en cardiologie, et leur étude constitue un vaste sujet de recherche. Pour les étudier, de nombreux modèles mathématiques de la propagation du potentiel d'action dans les oreillettes ont été développés. La plupart de ces modèles génériques permettent de reproduire des séquences d'activations typiques des oreillettes. De tels modèles peuvent avoir un intérêt expérimental, voir clinique, par exemple dans l'aide à la localisation des foyers arythmiques ou encore dans l'analyse des échecs du traitement de ces arythmies. Néanmoins, pour atteindre ce but, il faut être capable de recaler au mieux le modèle, dans ses dimensions géométriques ou fonctionnelles, sur des données individuelles. L'assimilation de données, discipline mathématique dans laquelle nous cherchons à combiner de manière optimale théorie et observations, est alors un bon candidat à la personnalisation des modèles de la propagation du potentiel d'action. Dans cette thèse, nous proposons d'étudier différentes méthodes d'assimilation de données -- séquentielles et variationnelles -- dans le but de combiner les modèles de propagation avec des données électroanatomiques. Plus précisément, nous nous intéressons à deux applications possible de l'assimilation de données que sont l'estimation d'état et l'estimation de paramètres. Dans un premier temps, nous étudions un observateur d'état permettant de corriger la position du front de propagation simulé en se basant sur la position du front observé. Cet observateur est alors utilisé afin de compléter une carte d'activation obtenue lors d'une procédure clinique. Ensuite, ce même observateur est combiné à un filtre de Kalman d'ordre réduit afin d'estimer les paramètres de conductivités du modèle mathématique de propagation du potentiel d'action. Une étude de la stratégie d'estimation liée état-paramètre est ensuite réalisée pour voir comment la méthode se comporte face aux erreurs de modélisation. La méthode est ensuite testée sur un jeu de données acquis cliniquement. Puis, nous regardons du côté des méthodes d'assimilation de données variationnelles qui permettent l'estimation de paramètres spatialement distribués. Plusieurs problèmes de minimisation, permettant d'estimer un paramètre de conductivité distribué dans l'espace, sont alors introduits et analysés. Nous montrons alors que la discrétisation de ces problèmes de minimisation, dans le but d'obtenir des méthodes numériques de résolution, peut s'avérer complexe. Une méthode numérique est ensuite mise en place pour un des problèmes de minimisation étudié, et trois cas tests unidimensionnels sont analysés.Enfin, nous démontrons l'existence d'un minimum pour une des fonctions objectif étudiées en nous basant sur des résultats d'analyse fonctionnelle de la littérature. / Atrial arrhythmias are a major pathology in cardiology, and their study is alarge research topic. To study them, many mathematical models of the actionpotential propagation in atria have been developed. Most of those generic models can be used to reproduce typical activation sequences of the atria. Such models may have an experimental or even clinical interest, for example in helping the location of arrhythmic foci or in the analysis of treatment failures for these arrhythmias. Nevertheless, to achieve this goal, it isnecessary to be able to adjust the model at best, based on experimental orclinical data. Data assimilation, a mathematical discipline in which we seek to optimally combine theory and observations, is then a good candidate for the customization of action potential propagation models.In this thesis, we propose to study different data assimilation methods-- sequential and variational -- in order to adjust action potential propagation model on electroanatomical data. More precisely, we are interested in two possible applications of data assimilation: state estimation and parameter estimation.First, we study a state observer which is able to correct the simulatedpropagation front localization based on the observed front localization. Thisobserver is then used to complete an activation map obtained during a clinical procedure.Then, this observer is combined with a reduced order Kalman filterin order to estimate the conductivity parameters of the action potentialpropagation model. A study of the joint state-parameter estimationstrategy is then realized to see how the method behaves faced with modelingerrors. The method is then tested on a clinically acquired dataset.Then, we look at variational data assimilation methods that allow the estimation of spatially distributed parameters. Several minimization problems, allowing to estimate a conductivity parameter distributed in space, are then introduced and analyzed. We then show that the discretization of these minimization problems, in order to obtain numerical methods of resolution, can be complex. A numerical method is then implemented for one of the studied minimization problems, and three 1D test cases are analyzed.Finally, we demonstrate the existence of a minimum for one of the studiedobjective function based on functional analysis results from theliterature.