Дисертації з теми "Lois de conservation hétérogènes"
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Sylla, Abraham. "Hétérogénéité dans les lois de conservation scalaires : approximation et applications." Electronic Thesis or Diss., Tours, 2021. http://www.theses.fr/2021TOUR4011.
This thesis is devoted to the treatment of heterogeneity in scalar conservation laws. We call heterogeneous a conservation which is not invariant by spacetranslation. These equations arise for instance in traffic flow dynamics modeling. The presence of traffic lights or roads that have a variable maximum speed limitare examples of mechanisms which lead to heterogeneous conservation laws. Considering such equations is a way to expand macroscopic traffic flow models. We tacklethree classes of inhomogeneous problems for which we extend the mathematical framework for both the theorical analysis and the numerical approximation.We fully investigate the treatment of heterogeneity when one or several moving interfaces are added in the classic LWR model for traffic flow. Flux constraintsare attached to each interfaces. The resulting class of models can be used to take into account the presence of slow moving vehicles that reduce the road capacityand thus generates a moving bottleneck for the surrounding traffic flow. They can also describe the regulating effect of autonomous vehicles. In this framework,the interfaces and the constraints are linked in a nonlocal way to the traffic density and/or to an orderliness marker describing the state of the drivers. Thedescription of the heterogeneity caused by the variations in the drivers' organization leads to the analysis of a so called second order model. The numericalaspect plays a central role in the analysis of these traffic flow models. We construct robust numerical schemes and establish specific techniques to obtaincompactness of the approximate solutions. Proving convergence of these schemes leads to existence results.Finally, with the space-dependent LWR traffic flow model in mind, we theoretically analyze a class of scalar conservation laws with explicit space dependency.Classical results such as well-posedness or the link to the associated Hamilton-Jacobi equation are obtained under a set of assumptions better fitting themodeling hypothesis. With applications that go beyond traffic modeling in mind, we aim to tackle initial data identification problems
Jimenez, Julien. "Modèles non linéaires de transport dans un milieu poreux hétérogène." Phd thesis, Université de Pau et des Pays de l'Adour, 2007. http://tel.archives-ouvertes.fr/tel-00204610.
En premier lieu nous considérons un problème couplé hyperbolique/hyperbolique. Sous une condition de non dégénérescence du flux, nous avons obtenu un résultat d'existence et d'unicité d'une solution faible entropique d'abord en dimension 1 d'espace puis en dimension quelconque. La preuve de l'unicité est basée sur la méthode de dédoublement des variables due à S.N. Kruzkov puis sur un raisonnement presque partout à l'interface. Dans le cas particulier de la dimension 1 l'existence s'obtient par une régularisation adéquate du coefficient discontinu dans le terme de convection alors que nous utilisons la méthode de viscosité artificielle dans le cas général.
En second lieu nous traitons le cas de termes de convection qui apparaissent dans l'ingénierie pétrolière pour lesquels la condition de non dégénérescence de la non linéarité n'est pas vérifiée. Nous ne pouvons donc pas adapter les méthodes précédemment utilisées. Nous nous sommes donc intéressés à un problème couplé perturbé où sur l'un des deux ouverts un terme de diffusion est ajouté. Sous l'hypothèse que les caractéristiques provenant de la zone hyperbolique sont sortantes à l'interface, l'unicité d'une solution faible entropique est établie. La méthode de viscosité artificielle et la notion de processus entropique nous permettent de prouver le résultat d'existence .
Bernardi, Vincent. "Lois de conservation sur automates cellulaires." Aix-Marseille 1, 2007. http://www.theses.fr/2007AIX11055.
Kahouadji, Nabil. "Lois de conservation et plongements isométriques généralisés." Phd thesis, Université Paris-Diderot - Paris VII, 2009. http://tel.archives-ouvertes.fr/tel-00427033.
Andouze-Bernard, Séverine. "Lois de conservation scalaires a coefficients discontinus." Antilles-Guyane, 1999. http://www.theses.fr/1999AGUY0048.
Dutercq, Sébastien. "Métastabilité dans les systèmes avec lois de conservation." Thesis, Orléans, 2015. http://www.theses.fr/2015ORLE2016/document.
This thesis contains an abstract with mathematical formulae. You can consult it via the complete text of the document in the back page
Sévennec, Bruno. "Géométrie des systèmes hyperboliques de lois de conservation." Lyon 1, 1992. http://www.theses.fr/1992LYO10097.
Sahel, Amina. "Etude d'une classe de systèmes de lois de conservation." Aix-Marseille 1, 1997. http://www.theses.fr/1997AIX11004.
MEHDI, MOHAMAD. "Existence de lois de conservation et de systemes bihamiltoniens." Toulouse 3, 1991. http://www.theses.fr/1991TOU30049.
Delle, Monache Maria Laura. "Lois de conservation pour la modélisation du trafic routier." Thesis, Nice, 2014. http://www.theses.fr/2014NICE4056/document.
In this thesis we consider two coupled PDE-ODE models. One to model moving bottlenecks and theother one to describe traffic flow at junctions. First, we consider a strongly coupled PDE-ODE systemthat describes the influence of a slow and large vehicle on road traffic. The model consists of a scalarconservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle isgiven by an ODE depending on the downstream traffic density. The moving constraint is expressed byan inequality on the flux, which models the bottleneck created in the road by the presence of the slowerDépôt de thèse – Donnéescomplémentairesvehicle. We prove the existence of solutions to the Cauchy problem for initial data of bounded variation.Moreover, two numerical schemes are proposed. The first one is a finite volume algorithm that uses alocally nonuniform moving mesh. The second one uses a reconstruction technique to display thebehavior of the vehicle. Next, we consider the Lighthill-Whitham-Richards traffic flow model on ajunction composed by one mainline, an onramp and an offramp, which are connected by a node. Theonramp dynamics is modeled using an ordinary differential equation describing the evolution of thequeue length. The definition of the solution of the Riemann problem at the junction is based on anoptimization problem and the use of a right of way parameter. The numerical approximation is carriedout using a Godunov scheme, modified to take into account the effects of the onramp buffer. Aftersuitable modification, the model is used to solve an optimal control problem on roundabouts. Two costfunctionals are numerically optimized with respect to the right of way parameter
Brénier, Yann. "Quelques schémas numériques pour l'approximation des lois de conservation." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37603440f.
Dotti, Sylvain. "Approximation numérique de lois de conservation hyperboliques stochastiques scalaires." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0568/document.
In this thesis, we study a scalar hyperbolic conservation law of order one, with stochastic source term and non-linear flux. The source term can be seen as the superposition of an infinity of Gaussian noises depending on the conserved quantity. We give a definition of solution of this stochastic partial differential equation (SPDE) with an intermediate point of view between that of the analyst (non regularsolution in space, introduction of an additional kinetic variable) and that of the probabilist (right continuous with left limits in time stochastic process solution). Uniqueness of the solution is proved thanks to a doubling of variables à la Kruzkov. We study the stability of the conservation law, in order to give a general theorem where the conditions of existence of a solution and conditions of convergence of a sequence of approximate solutions towards the solution of the conservation law are given. This study is done thanks to probabilistic tools : representation of martingales in the form of stochastic integrals, existence of a probability space on which the convergence of probability measures is equivalent to the almost sure convergence of random variables.To finish the study, we prove the existence of a solution thanks to the properties of the approximation of the SPDE given by an explicit in time Finite Volumes numerical scheme, then the convergence of this approximation towards the solution of the SPDE. The tools used are those of the numerical analysis, especially those of the Finite Volume Method, and those of the stochastic calculs (probabilistic tools)
Dalibard, Anne-Laure. "Homogénéisation de lois de conservation scalaires et d'équations de transport." Phd thesis, Université Paris Dauphine - Paris IX, 2007. http://tel.archives-ouvertes.fr/tel-00182850.
Dalibard, Roux Anne-Laure. "Homogénéisation de lois de conservation scalaires et d'équations de transport." Paris 9, 2007. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2007PA090055.
In this thesis, we study the asymptotic behavior of solutions of a class of partial differential equations with strongly oscillating coefficients. First, we focus on a family of nonlinear evolution equations, namely parabolic scalar conservation laws. These equations are encountered in various problems of fluid mechanics and nonlinear electromagnetism. The flux is assumed to be periodic with respect to the space variable, and the period of the oscillations goes to zero. The asymptotic profiles in the microscopic and macroscopic variables are first identified. Then, we prove a result of strong convergence; in particular, when the initial data does not match the microscopic outline dictated by the equation, it is shown that there is an initial layer in time during which the solution adapts itself to this profile. The other equation studied in this thesis is a linear transport equation, modeling the evolution of the density of charged particles in a highly oscillating random electric potential. It is proved that the density has fast oscillations in time and space, as a response to the excitation by the electric potential. We also derive explicit formulas for the homogenized transport operator when the space dimension is equal to one
CHAI, PENG. "Singularites faibles de solutions de systemes de lois de conservation." Paris 11, 1991. http://www.theses.fr/1991PA112305.
Dymski, Nikodem. "Lois de conservation pour la modélisation de dynamiques de groupe." Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4073.
This thesis is devoted to macroscopic traffic flow modelling, which describes traffic flow by variables averaged over multiple vehicles. It mainly focuses on a situation in which the maximum flow of cars is limited at a fixed point along the road. Thanks to such considerations, we can model traffic flow through toll gates or construction sites. From a mathematical point of view we consider systems of hyperbolic conservation laws with constraint condition. Research is based on three macroscopic models, namely Lighthill-Witham-Richards model (LWR), Aw-Rascle-Zhang model (ARZ) and phase transition model (PT). The aim of thesis is to establish the existence and properties of a weak solutions. The thesis consists of 6 chapters and 2 appendices. In the first chapter, we introduce basic ideas of traffic modelling. The second chapter is devoted to a detailed discussion of basic macroscopic traffic flow models. In the third chapter, we describe the LWR model with a local point constraint on the flow. The fourth chapter is devoted to ARZ model with local point constraint on the flow. We prove there the existence of the weak solutions, corresponding to a non-conservative Riemann solver, in the class of functions with bounded variation. The goal is obtained by showing the convergence of a sequence of approximate solutions constructed via the Wave Front Tracking method. In the fifth chapter, we describe two PT models with the local point constraint on the flow. Then we examine their consistency, L1loc-continuity and invariant domains. The remainder of the chapter is devoted to the existence result of a weak solution in the class of function with bounded variation for one of these models with a metastable phase. The goal is obtained by showing the convergence of a sequence of approximate solutions constructed via Wave Front Tracking method. The sixth chapter is devoted to two macroscopic models on road networks. The first is the LWR model with moving constraint on the flow and the second is the PT model introduced in the second chapter
Mimault, Matthias. "Lois de conservation pour la modélisation des mouvements de foule." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4102/document.
In this thesis, we consider nonclassical problems brought out by the macroscopic modeling of pedestrian flow. The first model consists of a conservation law with a discontinuous flux, the second is a mixed hyperbolic-elliptic system of conservation laws and the last one is a nonlocal equation. In the first chapter, we use the Hughes model in one space-dimension to represent the evacuation of a corridor with two exits. The model couples a conservation law with discontinuous flux to an eikonal equation. We implement the wave front tracking scheme, treating explicitly the solution nonclassical behavior at the turning point, to provide a reference solution, which is used to numerically test the convergence of classical finite volume schemes. In the second chapter, we model the crossing of two groups of pedestrians walking in opposite directions with a system of conservation laws whose flux depends on the two densities. This system loses its hyperbolicity for certain density values. We assist to the rising of persistent but bounded oscillations, that lead us to the recast of the problem in the framework of measure-valued solutions. Finally we study a nonlocal model of pedestrian flow in two space-dimensions. The model consists of a conservation law whose flux depends on a convolution of the density. With this model, we solve an optimization problem for a room evacuation with a descent method, evaluating the impact of the explicit computation of the cost function gradient with the adjoint state method rather than approximating it with finite differences
Milisic, Vuk. "Approximation cinétique discrète de problèmes de lois de conservation avec bord." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2001. http://tel.archives-ouvertes.fr/tel-00005164.
Pham, Van thang. "Contributions à la commande prédictive des systèmes de lois de conservation." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00770985.
Pham, Van Thang. "Contributions à la commande prédictive des systèmes de lois de conservation." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENT051/document.
The predictive control or Receding Horizon Optimal Control (RHOC) is becoming increasingly popular in many practical applications due to its significant advantages such as the stabilization and constraints handling. It has been well studied for finite dimensional systems even in the nonlinear case. However, its extension to infinite dimensional systems has not received much attention from researchers. This thesis proposes contributions on the application of this approach to systems of conservation laws. We present a complete proof of stability of RHOC for some classes of infinite dimensional systems. This result is then used for 2x2 hyperbolic systems with boundary control, and applied to an irrigation canal. We also propose the extension of this strategy to networks of cascaded 2x2 hyperbolic systems with an application to a set of connected irrigation canals. Furthermore, we study the benefits of RHOC in the context of nonlinear and semi-linear systems in particular with respect to the problem of shocks. All theoretical analyzes are validated by simulation in order to illustrate the effectiveness of the proposed approach
Vasseur, Alexis. "Contributions a l'approche cinetique des systemes de lois de conservation hyperboliques." Paris 6, 1999. http://www.theses.fr/1999PA066513.
Vasseur, Alexis. "Contributions à l'approche cinétique des systèmes de lois de conservation hyperboliques." Paris 6, 1999. http://www.theses.fr/1999PA06A002.
Gowda, Veerapa. "Eléments finis discontinus pour les lois de conservation scalaires non linéaires." Paris 9, 1988. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1988PA090038.
Corrias, Lucilla. "Convexité en analyse numérique des lois de conservation hyperboliques non-linéaires." Paris 6, 1995. http://www.theses.fr/1995PA066295.
Bonnefille, Max. "Propagation des oscillations dans les systèmes hyperboliques de lois de conservation." Saint-Etienne, 1987. http://www.theses.fr/1987STET4008.
Milišić, Vuk. "Approximation cinétique discrète de problèmes de lois de conservation avec bord." Bordeaux 1, 2001. http://www.theses.fr/2001BOR12449.
Bonnefille, Max. "Propagation des oscillations dans les systèmes hyperboliques de lois de conservation." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37603153z.
G, D. Gowda Veerappa. "Eléments finis discontinus pour les lois de conservation scalaires non linéaires." Grenoble 2 : ANRT, 1988. http://catalogue.bnf.fr/ark:/12148/cb376139165.
LaalaiI, Iyadh. "Effets d'échelle dans les matériaux quasi-fragiles à microstructure aléatoire : approches locale et non locale." Marne-la-vallée, ENPC, 1993. http://www.theses.fr/1993ENPC9308.
Lafitte-Godillon, Pauline. "Stabilité des profils de chocs dans les systèmes de lois de conservation." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2001. http://tel.archives-ouvertes.fr/tel-00396376.
Rouvre, Emilie. "Solutions fortes entropiques pour des lois de conservation hyperboliques-paraboliques fortement dégénérées." Pau, 2001. http://www.theses.fr/2001PAUU3010.
Poëtte, Gaël. "Propagation d'incertitudes pour les systèmes de lois de conservation, méthodes spectrales stochastiques." Paris 6, 2009. http://www.theses.fr/2009PA066801.
In this thesis, we are interested in the quantification of uncertainty with stochastic spectral methods applied to systems of conservation laws. These are nonlinear and develop discontinuities: these difficulties can foster a loss of the hyperbolicity of the truncated system resulting from the application of sG-gPC (Galerkin projection). We introduce a well suited formalisme based on both kinetic theory and moment theory so as to ensure, by construction, the hyperbolicity of the resulting truncated system. The idea is to close the truncated thanks to a nonlinear Galerkin projection via introduction of a system entropy - strictly convex function. In the case this entropy is the mathematical entropy of the non truncated system, hyperbolicity is ensured. We establish several properties of the truncated system obtained with the new method for an arbitrary conservation law. We apply the new method to Burgers equation and Euler. In the vicinity of discontinuities, the new method bounds the oscillations due to Gibbs phenomenon without the use of an adaptive procedure. The method reveals to be more precise than classical intrusive method on several test problems. In a last chapter, we present two prospective tracks: we suggest an uncertainty quantification method coupling truncated system and non truncated system. We finally emphasize the potential of modelization of the intrusive approach so as to take into account tridimensional perturbations of a monodimensional mean flow
Benyounes, Michèle. "Action des symétries généralisées sur les lois de conservation des systèmes lagrangiens." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376028947.
Hubert, Florence. "Dynamique lente-rapide pour des perturbations de systèmes de lois de conservation." Lyon, École normale supérieure (sciences), 1995. http://www.theses.fr/1995ENSL0005.
Mai, Duc Thanh. "Sur les solutions entropiques non classiques de certains systèmes de lois de conservation." Palaiseau, Ecole polytechnique, 2003. http://www.theses.fr/2003EPXX0019.
Jacquet, Denis. "Modélisation Macroscopique du Trafic et Contrôle des Lois de Conservation Non Linéaires Associées." Phd thesis, Grenoble INPG, 2006. http://tel.archives-ouvertes.fr/tel-00150434.
Chiarello, Felisia Angela. "Lois de conservation avec flux non-local pour la modélisation du trafic routier." Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4076.
In this thesis, we provide mathematical traffic flow models with non-local fluxes and adapted numerical schemes to compute approximate solutions to such kind of equations. More precisely, we consider flux functions depending on an integral evaluation of the conserved variables through a convolution product. First of all, we prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. This model is intended to describe the reaction of drivers that adapt their velocity with respect to what happens in front of them. Here, the support of the convolution kernel is proportional to the look-ahead distance of drivers. We approximate the problem by a Lax- Friedrichs scheme and we provide some estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained through the doubling of variable technique. We study also the limit model as the kernel support tends to infinity. After that, we prove the stability of entropy weak solutions of a class of scalar conservation laws with non-local flux under higher regularity assumptions. We obtain an estimate of the dependence of the solution with respect to the kernel function, the speed and the initial datum. We also prove the existence for small times of weak solutions for non-local systems in one space dimension, given by a non-local multi-class model intended to describe the behaviour of different groups drivers or vehicles. We approximate the problem by a Godunov-type numerical scheme and we provide uniform L∞ and BV estimates for the sequence of approximate solutions, locally in time. We present some numerical simulations illustrating the behavior of different classes of vehicles and we analyze two cost functionals measuring the dependence of congestion on traffic composition. Furthermore, we propose alternative simple schemes to numerically integrate non-local multi- class systems in one space dimension. We obtain these schemes by splitting the non-local conservation laws into two different equations, namely, the Lagrangian and the remap steps. We provide some estimates recovered by approximating the problem with the Lagrangian- Antidiffusive Remap (L-AR) schemes, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the LAR schemes in comparison with classical first and second order numerical schemes. Moreover, we recover the numerical approximation of the non-local multi-class traffic flow model proposed, presenting the multi-class version of the Finite Volume WENO (FV-WENO) schemes, in order to obtain higher order of accuracy. Simulations using FV-WENO schemes for a multi-class model for autonomous and human-driven traffic flow are presented. Finally, we introduce a traffic model for a class of non-local conservation laws at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes. We use an upwind type numerical scheme to construct a sequence of approximate solutions and we provide uniform L∞ and BV estimates. Using a Lax-Wendroff type argument, we prove the well-posedness of the proposed model. Some numerical simulations are compared with the corresponding (discontinuous) local model
MANCIP, Martial. "Couplage de méthodes numériques pour les lois de conservation. Application au cas de l'injection." Phd thesis, INSA de Toulouse, 2001. http://tel.archives-ouvertes.fr/tel-00001960.
complexe - lorsqu'il y a plusieurs modèles physiques à calculer sur des zones difficiles à délimiter, on utilise des méthodes de couplage par recouvrement de domaine.
Nous présentons ici un algorithme, nouveau et performant, calculé grâce à une superposition de deux maillages correspondant à deux schémas différents. On utilise des projections conservatives de la solution d'un maillage vers l'autre.
Cette méthode de décomposition de domaine ne fait
pas intervenir de conditions aux limites artificielles. Elle est basée sur une régularisation de la fonction de Heaviside sur la zone de couplage. Elle est parfaitement conservative et donc bien indiquée pour l'étude des lois de conservation.
L'analyse mathématique est réalisée pour les problèmes hyperboliques, dans le cas scalaire multidimensionnel. Elle est basée sur le convergence des schémas volumes finis. Tout d'abord, on obtient la convergence de la solution mesure grâce aux travaux de Diperna, puis on estime l'erreur de convergence en $h^(^1/_4)$. Une nouvelle estimation de type $H^1$ faible permet d'estimer les erreurs induites par le couplage.
De nombreuses applications numériques en mécanique des fluides avec les tubes à chocs et de détente montrent que la méthode est très stable et conservative. Nous utilisons aussi la méthode sans grille appelée Smooth Particule Hydrodynamics - plus précisément sa nouvelle variante renormalisée - pour calculer la création d'un jet en couplant la méthode volumes finis à la méthode SPH. On montre ainsi la robustesse de l'algorithme de couplage et sa souplesse pour le calcul des écoulement complexes.
Cette étude à fait l'objet d'une collaboration avec l'équipe du Pr. D. Kröner de l'Institut des Mathématiques Appliquées à l'Université de Frieburg (Allemagne).
Peyroutet, Fabrice. "Etude d'une méthode Splitting pour des lois de conservation scalaires avec terme de source." Pau, 1999. http://www.theses.fr/1999PAUU3029.
Mancip, Martial. "Couplage de méthodes numériques pour les lois de conservation : application au calcul de l'injection." Toulouse, INSA, 2001. https://tel.archives-ouvertes.fr/tel-00001960v2.
This thesis deals with numerical methods for solving systems of conservative partial differential equations. When the flow is a complex one, we need many physical models without known boundaries. We can use different numerical schemes for different domains, with some overlap of the domains. We present here a new and efficient algorithm to compute the solution on these overlaps. It needs a conservative projection of the numerical solution from one scheme to the other one. There is no artificial condition on the boundary of the coupling domain. To do so we use a regularization of the Heaviside function on this domain. Thus the whole algorithm is conservative and is adapted for Conservative Laws. The mathematical analysis has been done for scalar hyperbolic equations in any dimension. It is based on the convergence of Finite Volume Methods. We prove the convergence of the measure solution with Diperna's theorem, and then we give an error estimation in order of hơ. We did so by using a new estimation of the type weak H1 to deal with the new coupling error terms. A lot of numerical applications in Fluid Mechanics such as shock tube show that the method is stable and conservative. We use also the meshless method called Smooth Particle Hydrodynamics, in its renormalized form, to compute the birth of a jet by coupling a Finite Volumes with a Particle Method. It shows the stiffness of the algorithm and its efficiency with complex flows. This study was done in collaboration with the team of Pr. D. Kröner from the Institute Applied Mathematics of Frieburg University of Germany
BENMOUSSA, BACHIR. "Analyse numerique de methodes particulaires regularisees de type sph pour les lois de conservation." Toulouse, INSA, 1998. http://www.theses.fr/1998ISAT0003.
Mdarhri, A. "Propriétés électromagnétiques de matériaux hétérogènes: Approche expérimentale et modélisation." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2007. http://tel.archives-ouvertes.fr/tel-00583599.
Soliva, Roger. "Croissance des failles normales dans les séries stratifiées hétérogènes : rôle de la restriction verticale et de la coalescence sur les lois d'échelles et la distribution spatiale des failles : exemples naturels et approche théorique." Paris 11, 2004. http://www.theses.fr/2004PA112156.
?Our field data analysis from different fault systems in various rheological contexts show that two fundamental processes strongly influence fault growth: (i) fault vertical restriction at stratigraphic barriers and (ii) their linkage. Analysis of vertical and horizontal sections of fault populations in layered rocks shows that vertically restricted faults at plastic barriers have low displacement gradient values on the major parts of their planes. We observe a transition from a linear to a power-law relationship between displacement and along strike trace length. The combination of field data and 3-D post yield fracture mechanics shows that this transition is due to the increase of fault aspect ratio (length/height). The displacement gradient drop occurring during the development of a vertically restricted fault is interpreted as the mechanism that limits their horizontal propagation. In homogeneous media, our analysis reveals the strong dependence of fault linkage in (i) fault displacement and (ii) fault separation. Collection of data from the literature suggests that a simple linkage criterion can be established. 3-D numerical modeling approve the previous results and suggests that fault linkage can be self-similar on a broad range of scale. In layered heterogeneous media, the analysis of vertically restricted normal faults shows that segment linkage is limited at a critical value of fault separation, which is in turn a function of the mechanical thickness. Both the thickness of a mechanical unit and the rheology of the barrier levels seems to be the main controlling factors of the 3-D fault distribution
Xudous, Yorgo. "Structure des lois de conservation dans les chaînes de spins avec interactions à longue portée." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ38212.pdf.
Gorsse, Yannick. "Approximation numérique sur maillage cartésien de lois de conservation : écoulements compressibles et élasticité non linéaire." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00796722.
MOREUX, VINCENT. "Approximation par elements finis de type petrov-galerkin de systemes hyperboliques de lois de conservation." Toulouse 3, 1991. http://www.theses.fr/1991TOU30061.
Laurent-Brouty, Nicolas. "Modélisation du trafic sur des réseaux routiers urbains à l’aide des lois de conservation hyperboliques." Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4056.
This thesis is devoted to the modeling of traffic flow using hyperbolic conservation laws, with a specific focus on urban applications. Urban areas are today facing severe episodes of air pollution and increasing congestion due to traffic. The objective is to overcome some of the current limitations of macroscopic traffic flow models in urban situations. We first study the seminal Aw-Rascle-Zhang model with relaxation. We prove well-posedness of the model using wave-front tracking approximations and splitting technique in a Lagrangian setting. Besides, we provide an estimate on the decay of positive waves. We then show that the solutions of the Aw-Rascle-Zhang system with relaxation converge to a weak solution of the LWR model when the relaxation parameter goes to zero. Finally, we propose a discussion on the entropy aspect of this weak solution of the LWR model. We then propose a new macroscopic traffic flow model accounting for the boundedness of traffic acceleration, which is required for physical realism. Our model is built on the coupling between the scalar conservation law accounting for the conservation of vehicles and a number of ordinary differential equations describing the trajectories of accelerating vehicles, which we treat as moving constraints. We detail a wave-front tracking algorithm to construct approximate solutions of the model, with general flux functions and show existence of solutions to the Cauchy problem for a piecewise constant initial datum. Finally, we provide numerical simulations of the model in different urban situations, from a single Riemann problem to sequences of traffic lights, and confront the results to numerical simulations of the LWR model. Finally, we introduce a new macroscopic traffic flow model with buffers on road networks. This model features buffers of finite size, enabling backward propagation of congestion on the network, and time-dependent routing functions at the junctions. The dynamics are first defined on the level of conservation laws, and then transformed in an Hamilton-Jacobi formulation. We prove existence, uniqueness and stability of the solutions with respect to the routing ratios and initial datum using a fixed-point problem in a proper Banach space. Thanks to stability, the model provides a controllable framework, using routing ratios as control parameters. This represents an advance towards solving the Dynamic Traffic Assignment (DTA) problem. In the end we detail how this framework applies to a classical road network with several intersections and finite-length links
Khraief, Nahla. "Commande énergétique pour la marche des robots bipèdes planaires." Versailles-St Quentin en Yvelines, 2004. http://www.theses.fr/2004VERS0012.
Biped robots have been studied over the past decade to find stable and efficient walking gaits. The importance of these walking robots in accessing hazardous areas, prosthetics and many other possible areas has been the driving force behind biped research. Many mechanical models and control systems have been found to drive these bipeds on slopes and level ground. The concept of passive walking was introduced a decade ago and since then it has intrigued researchers to find control systems based on the existence of passive limit cycles on some shallow slopes. This research focuses on the development of passivity-based control of planar biped robots. The results are extended from well known control laws developed by McGeer , which use slope invariance to drive the biped on different slopes. In this work it is concerned with the walking of an underactuated biped robot on the level ground, imitating the passive walking on a given slope. First, we present the modelling of the biped robot (that is a kneeless and a kneed robot with torso). Then, we focus on the study of the almost passive dynamic walking. In particular, we show that the application of a nonlinear feedback control to stabilize a nominal posture leads the biped robot to perform a stable almost-passive dynamic walking when dealing with motions on a downhill a slope. More such control also leads the system trajectories to converge towards stable limit cycles. In this context, we present some results based on both Poincaré map method and trajectory sensitivity analysis to efficiently characterize the stability of the almost-passive limit cycles. However, such limit cycles may not exist for all ground configurations especially when dealing with motions on the level ground. This involves to introduce some complementary control scheme. In this purpose, we present some theoretical and simulation results based on the use of recent control method (referred to as Controlled Limit Cycles), which considers the system energy for both controller design and system stabilization
Echenim, Nki. "Modélisation et contrôle multi-échelles du processus de sélection des follicules ovulatoires." Paris 11, 2006. http://www.theses.fr/2006PA112171.
This work first consists in a multi-scale modelling of ovulatory follicles selection process. We describe the follicles through their granulosa cell population, and represent the evolution of the follicular cell density by conservation laws. We introduce the actions of the control, the FSH hormone, in the velocity and loss terms of the conservation laws. Each term of the model has a physiological meaning. The model's equations are solved with the finite volume method. Various physiological and pathological situations are represented, and we propose functioning hypothesis for the ovulation process and the ovulation rate. Secondly, we analytically study the mathematical model, and seek a solution to the system's equations. We propose a way to build the solution, which allows us to show that the model is well-posed. At last, we work on the control of the system, and study its asymptotic behaviour in response to a constant control. Various physiological and pathological behaviours are once again exhibited. We also study ovulation as a reachability problem, and we solve the system which allows to find the initial conditions that lead a follicle to ovulation
Museux, Alexis. "Propagation d'ondes non-linéaires en présence d'une viscosité évanescente." Nice, 2002. http://www.theses.fr/2002NICE5745.