Cette thèse présente deux sujets de recherche indépendants concernant l'application de méthodes stochastiques à des problèmes issus de la dynamique moléculaire. Dans la première partie, nous présentons des travaux liés à l'interprétation probabiliste de l'équation de Poisson-Boltzmann qui intervient dans la description du potentiel électrostatique d'un système moléculaire. Après avoir introduit l'équation de Poisson-Boltzmann et les principaux outils mathématiques utilisés, nous nous intéressons à l'équation linéaire parabolique de Poisson-Boltzmann. Avant d’énoncer le résultat principal de la thèse, nous étendons des résultats d'existence et unicité des équations différentielles stochastiques rétrogrades. Nous donnons ensuite une interprétation probabiliste de l'équation non-linéaire de Poisson-Boltzmann sous la forme de la solution d'une équation différentielle stochastique rétrograde. Enfin, dans une seconde partie prospective, nous commençons l'étude d'une méthode proposée par Paul Malliavin de détection des variables lentes et rapides d'une dynamique moléculaire. / This thesis presents two independent research topics. Both are related to the application of stochastic problems to molecular dynamics. In the first part, we present a work related to the probabilistic interpretation of the Poisson-Boltzmann equation. This equation describes the electrostatic potential of a molecular system. After an introduction to the Poisson-Boltzmann equation, we focus on the parabolic and linear equation. After extending an existence and uniqueness result for backward stochastic differential equations, we establish a probabilistic interpretation of the nonlinear Poisson-Boltzmann equation with backward stochastic differential equations. Finally, in a more prospective second part, we initiate a study of a slow and fast variables detection method due to Paul Malliavin.

Le travail présenté ici s'insère dans le cadre des études amont financées par le CNES et SNECMA qui visent à mieux appréhender, et simuler les écoulements cavitants dans les inducteurs à l'amont des turbopompes spatiales. Compte tenu de la complexité des mécanismes mis en jeu dans ce type de géométrie, il a été décidé de réaliser une étude dans une géométrie académique de type marche descendante cavitante comportant les différents mécanismes physiques inhérents aux écoulements de backflow (écoulements instationnaires décollés) présents dans les inducteurs. Cette géométrie simplifiée a permis la mise en place d'une instrumentation de pointe telle que la densitométrie par absorption de rayons X résolue en temps ou encore la PIV-LIF 2D, 3C haute cadence pour la mesure du champ de vitesse liquide. Ces techniques étant couplées à la mesure du champ de pression pariétale, il a donc été possible d'estimer les interactions mutuelles entre la turbulence et la cavitation dans ce type d'écoulement.Les mesures couplées aux champ de pression ont également permis d'utiliser des techniques de traitement POD-LSE pour estimer des termes de corrélations densité-vitesse nécessaires à la validation des modèles de type transport de taux de vide. De manière générale, la cavitation engendre des modifications notables d'origine dilatatoire sur l'agitation turbulente et modifie la dynamique tourbillonnaire. Ces résultats permettent de tirer des conclusions sur les stratégies de modélisation. En effet en régime cavitant l'augmentation de l'énergie cinétique turbulente étant décorrélée du cisaillement moyen, les modèles basés sur une viscosité turbulente semblent inadaptés . D'autre part à fort taux de vide les résultats semblent être en contradiction totale avec les modèles barotropes. / The present study is inserted in the framework of previous research which aim to get a better understanding of turbulent and cavitating phenomena which occur in the spatial turbopump. Actually, the specific topology of the detached flow which takes place upstream the inducer is today miss-predicted by the standard numerical models.Taking into account the huge complexity of such a flow it has been decided to experimentally investigate the backward-facing step flow which is recognized as a benchmark for numerical simulations and cover a large area of similitude with the backflow upstream the inducers.For this purpose, the mean and turbulent quantities of the liquid phase in the presence of the vapor phase as well as spatio-temporal correlations have been investigated using stereoscopic time resolved PIV, the void ratio has been determined using X-Ray attenuation techniques and measurements have been made for different cavitation levels. The main originality of the present work is based on instantaneous measurements of the wall pressure signals correlated with high speed visualizations, PIV and X-Ray measurements. Specific signal processing as Proper Orthogonal Decomposition and Linear Stochastic Estimation has been performed in order to estimate the velocity-density correlations useful to evaluate the void ratio transport. In this experimental work the physical mechanisms of the vapour phase effects on the large vortex structures, shear layer instability, reattachment wall and reverse flow have been investigated to determine what physical assumptions can be applied in the usual cavitation and turbulence models.It has been found for the cavitating cases that the growth of turbulent kinetic energy is not correlated to mean and turbulent shear stresses. This experimental observation is in contradiction with the Boussinesq hypothesis used for the linear eddy viscosity models.Moreover concerning the phase-change modelization for high void fraction, the barotropic models seem to disagree with our experiments.

No description available.

Made available in DSpace on 2016-12-06T17:07:19Z (GMT). No. of bitstreams: 1 Vanessa Herber.pdf: 2070207 bytes, checksum: 249e6056643655f931fa3aebf9693642 (MD5) Previous issue date: 2009-04-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The backward walking (BW) has been used in protocols for rehabilitation and training in individuals with stroke, however little is known about their characteristics in terms of kinematic variables and motor pattern. The literature describes that for the execution of BW it is necessary to combine hip extension with knee flexion, components that are compromised in this population. The aim of this study is to compare the spatial, temporal and angular variables between the BW and forward walking (FW) and between the lower limbs [affected (AF) and non affected (NA)] in the BW in individuals with hemiparesis following stroke. Participated in the study 10 adults (56.4±8.4 years) with chronic hemiparesis (30.6±25.1 months after the stroke onset), with lower limb motor score of 25±4.4 in the Fugl-Meyer Scale, and gait speed of 0,92±0.3 m/s. Reflexive markers were placed in the acromion, greater trochanter, lateral condyle of the knee and lateral malleolus, on both sides of lower limb. The subjects were instructed to walk at comfortable speed and five trials on each side of the sagital plane (right and left) were captured with a digital camcorder with a frequency of 30 Hz, in both tasks, FW and BW. The Kinematics variables analyzed were the stride length, duration and speed and stance phase duration, and angular variables of knee and kip. For statistical analyses the ANOVA 2X2 (2 directions BW and FW and 2 legs AF and NF lower limbs) was used. In addition, it was used contrasts with T Student test and Bonferroni correction. The angular variables were submitted to the ANCOVA, and the speed was the co-variable. The individuals with hemiparesis have shown a decreased stride length and speed (p=0,001 e p=0,001) and increased duration and percentage of support in the stride (p=0,001) in BW compared to FW. The NA lower limb remained longer in stance in both conditions (BW and FW). Both lower limbs have presented a decrease in maximum knee flexion (p=0,001 e p=0,005) and maximum hip extension (p=0,001 e p=0,001) in BW. In general, the differences in the hip kinematics between the FW and BW remained when the speed was used as a co-variable. Regarding the comparison between the lower limbs during the BW, the NA lower limb has shown increased angular values (p values between p=0,006 e p=0,009) except for the maximum knee extension, where the AF lower limb showed increased extension values, probably because of a hyperextension which is typical in this population. Qualitative analyses of the coordination has shown a different behavior between legs, with a preference to simultaneous movements between hip and knee in 8 of the 10 participants, and anterior inclination of the trunk during swing in the BW. The BW could be and appropriate way of treatment that could be added to conventional gait rehabilitation programs in individuals with hemiparesis. We suggest further investigation on the effects of a BW training on the intra joint coordination between hip and knee. / O andar para trás (AT) tem sido utilizado corno forma de treinamento locomotor em indivíduos com hemiparesia pós acidente vascular encefálico (AVE). No entanto pouco se sabe sobre as características cinemáticas do AT nesta população. A literatura descreve que na execução do AT é necessária a extensão do quadril combinada com a flexão do joelho, componentes que estão comprometidos nesta população. O objetivo deste estudo é comparar em indivíduos com hemiparesia as variáveis espaço-temporais e angulares entre o andar para frente (AF) e o AT e entre membros inferiores (MMII) no AT. Participaram do estudo 10 indivíduos (56.4±8.4 anos) com hemiparesia crônica (30.6±25,1 meses pós AVE). Os participantes apresentaram comprometimento motor de 25±4.4 pontos no Fugl-Meyer-MI velocidade de marcha de 0.92±0.3 m/s. Marcadores foram colocados no acrômio, trocânter maior do fêmur; côndilo lateral do joelho e maléolo lateral em ambos os lados. Os participantes foram filmados caminhando em uma velocidade confortável em cinco tentativas no plano sagital direito e cinco no esquerdo, nas tarefas do AF e AT. com uma câmera filmadora digital com freqüência de 60 Hz. As variáveis cinemáticas analisadas foram comprimento, duração e velocidade da passada e duração do apoio, além das variáveis angulares do joelho e quadril. Os dados foram submetidos a ANOVA 2X2 [2 direções e 2 lados - MI não afetado (naf) e MI afetado (af)] e posterior contrastes com teste t de Student com correção de Bonferroni. As variáveis angulares foram em seguida submetidas a ANCOVA utilizando-se a velocidade do andar como co-variável. Os indivíduos com hemiparesia apresentam redução do comprimento e velocidade da passada e aumento da duração e do percentual de apoio da passada (p=0,001 para todos) no AT comparativamente ao AF. O MInaf permaneceu mais tempo apoiado tanto no AT quanto no AF. Ambos os MMII apresentaram valores de máxima flexão de joelho (p=0,001 e p=0,005) e máxima extensão de quadril significativamente menor (p=0,001 para ambos) no AT. Em geral, as diferenças na cinemática do quadril entre AF e AT permanecem quando a velocidade é utilizada como co-variável. Com relação à comparação entre os MMII no AT, observou-se que o MInaf apresentou maiores valores angulares (valor de p entre p=0,006 e p=0,009), exceto para máxima extensão do joelho. onde o MIaf apresentou valores maiores dc extensão, isso devido a hiperextensão característica nesta população. A análise qualitativa da coordenação evidenciou um comportamento diferente entre MMII com uma preferência para movimentos simultâneos entre o quadril e joelho para 8/10 participantes assim como uma inclinação anterior do tronco durante o balanço no AT. O AT pode ser utilizado como recurso terapêutico apropriada para somar aos programas convencionais de reabilitação da marcha em indivíduos com hemiparesia. Sugere-se investigar o efeito do treinamento do AT sobre coordenação inter-articular entre quadril e joelho.

Le travail présenté dans ce mémoire de thèse porte sur la modélisation discrète de l’évolution régressive du front d’un conduit d’érosion qui peut se produire dans les barrages ou digues en remblai. Des outils numériques ont été développés en se basant sur le couplage entre la méthode des éléments discrets (DEM) et la méthode de Boltzmann sur réseau (LBM) pour la description, respectivement, des phases solide et fluide. L’implémentation de la méthode DEM suit une approche standard de type dynamique moléculaire (DM) et les interactions intergranulaires sont modélisées par des contacts unilatéraux visco-élastiques frottants ou bilatéraux (ponts solides) viscoélastiques, afin de permettre la modélisation d’un sol légèrement cohésif. La méthode LBM est implémentée ici avec des temps de relaxation multiples (MRT) et une condition de rebondissement interpolée pour les frontières solides en mouvement, afin d’améliorer la stabilité numérique des calculs. Le schéma du couplage entre les deux méthodes, ainsi que les critères pour le choix des paramètres numériques des deux méthodes. Pour étudier le phénomène visé, un échantillon représentatif de sol granulaire situé au front d’un conduit d’érosion est d’abord assemblé par une procédure de préparation “à sec”, puis testé dans des conditions saturées sous un chargement hydraulique monotone croissant. L’érosion régressive se produit par amas de grains au niveau du front d’érosion ayant subi au préalable une dégradation due à de nombreuses ruptures de ponts solides en traction. L’autre phénomène important observé est la présence d’arcs associés a` des chaines de forces en compression qui parviennent à maintenir parfois totalement, parfois partiellement l’intégrité du matériau non érodé. / The work reported in this thesis consists in a discrete modelling of the backward front propagation of an erosion pipe, as can take place in embankment dams or dikes. Some numerical tools have been developed to this end, based on the coupling between the Discrete Element Method (DEM) and the Lattice Boltzmann Method (LBM) for the representation of the solid and uid phases, respectively. The implementation of DEM follows a standard molecular dynamics approach and the interaction among grains are regulated by unilteral frictional visco-elastic and breakable visco-elastic bonds, in order to take into account a slightly cohesive soil behaviour. The LBM was implemented according to the Multiple Relaxation Time (MRT) scheme along with an interpolated non-slip conditions for moving boundaries, in order to improve the numerical stability of the calculations. The coupling scheme is described along with the criteria for the numerical parameters of the two methods. A representative specimen of a granular soil located at the front of an erosion pipe is first assembled by a \dry" preparation precedure and then tested under fully-saturated conditions and increasing hydraulic load over time. Backward erosion is takes place in the form of clusters of grain being eroded at the erosion front after a degradation of the material due to the breakage of tensile bonds. The other interesting feature that was observed is the creation of arches of compressive force chains. These arches enabled the specimen to maintain a stable or metastable configuration under the increasing hydraulic load.

Le tube à onde progressive (TOP) est un dispositif où un faisceau d’électrons se déplaçant sur l’axe d’une hélice interagit avec les ondes électromagnétiques propagées par cette hélice. Il est le siège de nombreuses instabilités : des oscillations (génération d’ondes hyperfréquences parasites), mais aussi des instabilités du faisceau qui ont pour conséquence une dissipation parasite due à l'interception du faisceau par l'hélice. L’objectif de cette thèse est de développer une formulation hamiltonienne au problème permettant des modèles approchés plus compacts, plus précis et plus complets. Après l'avoir exposée, nous présentons un schéma numérique contenant notre modèle discret pour la simulation du TOP. Ce modèle discret a été mis au point pour tenir compte des conditions d'adaptation et de changements de géométrie. Le couplage avec les électrons met en jeu des champs de base simples, et le modèle tient compte de la charge d'espace. Différentes méthodes d'intégration numérique sont développées, dont nous comparons l'efficacité. Nous comparons ce modèle discret avec divers modèles d'amplification des ondes à froid, dont le modèle actuellement utilisé chez Thales pour la conception des tubes ({texttt{MVTRAD}}). Nous montrons aussi que les modèles d'amplification des ondes à froid à deux ou trois dimensions comme {texttt{MVTRAD}} ou {texttt{BWIS}} (prenant en compte les ondes inverses) ne respectent pas nécessairement l'équation de Maxwell-Faraday, contrairement au nôtre. Enfin, nous comparons notre modèle discret de circuit et le modèle d'amplification des ondes à froid dans le cas d'un faisceau linéaire. / A traveling-wave tube (TWT) is a device where an electron beam traveling along the axis of a helix interacts with the electromagnetic waves propagated by this helix. It is sensitive to many instabilities : oscillators (generating noise microwave), but also beam instabilities that generate a noise dissipation due to the interception of the beam by the helix. The aim of this thesis is to find a Hamiltonian formulation of the problem to allow more compact, more accurate and more complete approximate models. Having found one, we start to develop a numerical scheme containing our discrete model for the simulation of TOP. This discrete model has been developed to take into account the tapering sections, geometry changes and adaptations. The coupling with electrons involves simple functions of space, and the model takes space charge into account. Different methods of numerical integration are developed, of which we compare the efficiency. We compared the discrete model with various cold waves amplification models, especially with the model currently used at Thales for the design of their tubes ({texttt{MVTRAD}}). Moreover, we showed that two- or three-dimensional cold wave amplification models like {texttt{MVTRAD}} or {texttt{BWIS}} (which takes into account the backward waves) fail to respect the Maxwell-Faraday equation, contrary to ours. Finally we made a comparison between our circuit discrete model and the amplification model of cold waves in the case of a linear beam.

Cette thèse s'inscrit dans le cadre d'un projet international (MARS) dont le but est d'améliorer l'efficacité du transport aérien par contrôle d'écoulement. Dans ce contexte, les travaux expérimentaux présentés ici sont focalisés sur l'utilisation d'un actionneur plasma à Décharge à Barrière Diélectrique (DBD) pour contrôler l'écoulement turbulent en aval d'une marche descendante (BFS) à Reh = 30000. Deux types de décharges sont étudiés : une ac-DBD qui produit une force électrohydrodynamqiue et une ns-DBD qui produit une onde de pression. Plusieurs positions de l'actionneur sont étudiés, de façon à optimiser les effets de la décharge sur l'écoulement. A l'aide d'un système PIV stéréoscopique, une étude étendue est destinée à l'évaluation des paramètres électriques du signal. Parmi tous les résultats obtenus, la zone de recirculation est réduite de 20%. De plus, d'autres quantités moyennes telles que les composantes de Reynolds, l'énergie cinétique et l'épaisseur de la couche cisaillée ont été aussi analysées. La dernière partie de la thèse comprend une analyse dynamique des modifications produites par l'actionneur. Pour cela, les structures dominantes sont examinées par leur signature fréquentielle et par une décomposition orthogonal aux valeurs propres (POD). Tous les résultats conduisent à la définition d'un cas d'action optimal pour lequel il est obtenu une réduction maximal de la longueur de rattachement. Le lâcher tourbillonnaire est renforcé par un mécanisme de type "lock-on". / This thesis is part of an international project (MARS) to improve air transport efficiency by active flow control strategy. In this context, the presented experimental works are focused on a surface Dielectric Barrier Discharge (DBD) as a solution to control the turbulent flow separation downstream a backward-facing step (BFS) at Reh = 30000. Two different plasma discharges are investigated: an ac-DBD resulting in a electrohydrodynamic force and a ns- DBD producing a pressure wave. Thanks to the versatility of plasma discharges and in order to optimize its effects on the flow, different locations of the DBD actuator have been investigated. Furthermore, an extended parametric study regarding the input variables of the discharge has been carried out by stereoscopic PIV. Among the obtained results, the mean reattachment length has been reduced up to 20%. In addition, other averaged quantities such as Reynolds stress components, the kinetic energy and the vorticity thickness of the separated shear layer have been analyzed to provide more extended information about the effects of the DBD actuator. The last part includes a dynamical analysis of the modifications produced by an optimal actuation. For that aim, the dominant structures are investigated by their signature in the frequency domain and by proper orthogonal decomposition (POD). All the results lead to the definition of an optimal actuation for which the mean reattachment position is reduced and the vortex shedding street can be reinforced by a lock-on control mechanism.

New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form $\sum_{k=0}^p\varphi_k(A)u_k$ that arise in exponential integrators, where the $\varphi_k$ are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension $n+p$ built by augmenting $A$ with additional rows and columns. Third, a general framework for simultaneously computing a matrix function, $f(A)$, and its Fréchet derivative in the direction $E$, $L_f(A,E)$, is established for a wide range of matrix functions. In particular, we extend the algorithm of Higham and $\mathrm{expm_{new}}$ to two algorithms that intertwine the evaluation of both $e^A$ and $L(A,E)$ at a cost about three times that for computing $e^A$ alone. These two extended algorithms are then adapted to algorithms that simultaneously calculate $e^A$ together with an estimate of its condition number. Finally, we show that $L_f(A,E)$, where $f$ is a real-valued matrix function and $A$ and $E$ are real matrices, can be approximated by $\Im f(A+ihE)/h$ for some suitably small $h$. This approximation generalizes the complex step approximation known in the scalar case, and is proved to be of second order in $h$ for analytic functions $f$ and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating $f$ employs complex arithmetic. The complex step approximation is attractive when specialized methods for evaluating the Fréchet derivative are not available.

This thesis focuses on the problem of determining appropriate skeletal configurations for which a virtual animated character moves to desired positions as smoothly, rapidly, and as accurately as possible. During the last decades, several methods and techniques, sophisticated or heuristic, have been presented to produce smooth and natural solutions to the Inverse Kinematics (IK) problem. However, many of the currently available methods suffer from high computational cost and production of unrealistic poses. In this study, a novel heuristic method, called Forward And Backward Reaching Inverse Kinematics (FABRIK), is proposed, which returnsvisually natural poses in real-time, equally comparable with highly sophisticated approaches. It is capable of supporting constraints for most of the known joint types and it can be extended to solve problems with multiple end effectors, multiple targets and closed loops. FABRIK wascompared against the most popular IK approaches and evaluated in terms of its robustness and performance limitations. This thesis also includes a robust methodology for marker prediction under multiple marker occlusion for extended time periods, in order to drive real-time centre of rotation (CoR) estimations. Inferred information from neighbouring markers has been utilised, assuming that the inter-marker distances remain constant over time. This is the firsttime where the useful information about the missing markers positions which are partially visible to a single camera is deployed. Experiments demonstrate that the proposed methodology can effectively track the occluded markers with high accuracy, even if the occlusion persists for extended periods of time, recovering in real-time good estimates of the true joint positions. In addition, the predicted positions of the joints were further improved by employing FABRIK to relocate their positions and ensure a fixed bone length over time. Our methodology is tested against some of the most popular methods for marker prediction and the results confirm that our approach outperforms these methods in estimating both marker and CoR positions. Finally, an efficient model for real-time hand tracking and reconstruction that requires a minimumnumber of available markers, one on each finger, is presented. The proposed hand modelis highly constrained with joint rotational and orientational constraints, restricting the fingers and palm movements to an appropriate feasible set. FABRIK is then incorporated to estimate the remaining joint positions and to fit them to the hand model. Physiological constraints, such as inertia, abduction, flexion etc, are also incorporated to correct the final hand posture. A mesh deformation algorithm is then applied to visualise the movements of the underlying hand skeleton for comparison with the true hand poses. The mathematical framework used for describing and implementing the techniques discussed within this thesis is Conformal GeometricAlgebra (CGA).

Cette thèse traite les jeux différentiels stochastiques de somme non nulle (JDSNN) dans le cadre de Markovien et de leurs liens avec les équations différentielles stochastiques rétrogrades (EDSR) multidimensionnelles. Nous étudions trois problèmes différents. Tout d'abord, nous considérons un JDSNN où le coefficient de dérive n'est pas borné, mais supposé uniquement à croissance linéaire. Ensuite certains cas particuliers de coefficients de diffusion non bornés sont aussi considérés. Nous montrons que le jeu admet un point d'équilibre de Nash via la preuve de l'existence de la solution de l'EDSR associée et lorsque la condition d'Isaacs généralisée est satisfaite. La nouveauté est que le générateur de l'EDSR, qui est multidimensionnelle, est de croissance linéaire stochastique par rapport au processus de volatilité. Le deuxième problème est aussi relatif au JDSNN mais les payoffs ont des fonctions d'utilité exponentielles. Les EDSRs associées à ce jeu sont de type multidimensionnelles et quadratiques en la volatilité. Nous montrons de nouveau l'existence d’un équilibre de Nash. Le dernier problème que nous traitons, est un jeu bang-bang qui conduit à des hamiltoniens discontinus. Dans ce cas, nous reformulons le théorème de vérification et nous montrons l’existence d’un équilibre de Nash qui est du type bang-bang, i.e., prenant ses valeurs sur le bord du domaine en fonction du signe de la dérivée de la fonction valeur ou du processus de volatilité. L'EDSR dans ce cas est un système multidimensionnel couplé, dont le générateur est discontinu par rapport au processus de volatilité. / This dissertation studies the multiple players nonzero-sum stochastic differential games (NZSDG) in the Markovian framework and their connections with multiple dimensional backward stochastic differential equations (BSDEs). There are three problems that we are focused on. Firstly, we consider a NZSDG where the drift coefficient is not bound but is of linear growth. Some particular cases of unbounded diffusion coefficient of the diffusion process are also considered. The existence of Nash equilibrium point is proved under the generalized Isaacs condition via the existence of the solution of the associated BSDE. The novelty is that the generator of the BSDE is multiple dimensional, continuous and of stochastic linear growth with respect to the volatility process. The second problem is of risk-sensitive type, i.e. the payoffs integrate utility exponential functions, and the drift of the diffusion is unbounded. The associated BSDE is of multi-dimension whose generator is quadratic on the volatility. Once again we show the existence of Nash equilibria via the solution of the BSDE. The last problem that we treat is a bang-bang game which leads to discontinuous Hamiltonians. We reformulate the verification theorem and we show the existence of a Nash point for the game which is of bang-bang type, i.e., it takes its values in the border of the domain according to the sign of the derivatives of the value function. The BSDE in this case is a coupled multi-dimensional system, whose generator is discontinuous on the volatility process.