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Artykuły w czasopismach na temat "Équations Vlasov-Poisson"
Bernis, Laurent. "Solutions stationnaires des équations de Vlasov-Poisson à symétries cylindriques". Annales de la faculté des sciences de Toulouse Mathématiques 14, nr 1 (2005): 51–70. http://dx.doi.org/10.5802/afst.1087.
Pełny tekst źródłaMiot, Evelyne. "Existence globale et propagation des moments pour une équation de Vlasov-Poisson avec une charge ponctuelle". Séminaire Laurent Schwartz — EDP et applications, 2013, 1–16. http://dx.doi.org/10.5802/slsedp.49.
Pełny tekst źródłaRozprawy doktorskie na temat "Équations Vlasov-Poisson"
Bernis, Laurent. "Etude mathématique d'équations aux dérivées partielles issues de la physique des plasmas (Vlasov-Poisson et Vlasov-Poisson-Boltzmann)". Orléans, 2006. http://www.theses.fr/2006ORLE2040.
Pełny tekst źródłaMadaule, Éric. "Schémas numériques adaptatifs pour les équations de Vlasov-Poisson". Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0112/document.
Pełny tekst źródłaMany numerical experiments are performed on the Vlasov-Poisson problem since it is a well known system from plasma physics and a major issue for future simulation of large scale plasmas. Our goal is to develop adaptive numerical schemes using discontinuous Galerkin discretisation combined with semi-Lagrangian description whose mesh refinement based on multi-wavelets. The discontinuous Galerkin formulation enables high-order accuracy with local data for computation. It has recently been widely studied by Ayuso de Dioset al., Rossmanith et Seal, etc. in an Eularian framework, while Guo, Nair and Qiu or Qiu and Shu or Bokanowski and Simarta performed semi-Lagrangian time resolution. We use multi-wavelets framework for the adaptive part. Those have been heavily studied by Alpert et al. during the nineties and the two thousands. Some works merging multi-scale resolution and discontinuous Galerkin methods have been described by Müller and his colleagues in 2014 for non-linear hyperbolic conservation laws in the finite volume framework. In the framework of relativistic Vlasov equation, Besse, Latu, Ghizzo, Sonnendrücker and Bertrand presented the advantage of using adaptive meshes. While they used wavelet decomposition, which requires large data stencil, multi-wavelet decomposition coupled to discontinuous Galerkin discretisation only requires local stencil. This favours the parallelisation but, at the moment, semi-Lagrangian remains an obstacle to highly efficient distributed memory parallelisation. Although most of our work is done in a 1d × 1v phase space, we were able to obtain a few results in a 2d × 2v phase space
Madaule, Éric. "Schémas numériques adaptatifs pour les équations de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2016. http://www.theses.fr/2016LORR0112.
Pełny tekst źródłaMany numerical experiments are performed on the Vlasov-Poisson problem since it is a well known system from plasma physics and a major issue for future simulation of large scale plasmas. Our goal is to develop adaptive numerical schemes using discontinuous Galerkin discretisation combined with semi-Lagrangian description whose mesh refinement based on multi-wavelets. The discontinuous Galerkin formulation enables high-order accuracy with local data for computation. It has recently been widely studied by Ayuso de Dioset al., Rossmanith et Seal, etc. in an Eularian framework, while Guo, Nair and Qiu or Qiu and Shu or Bokanowski and Simarta performed semi-Lagrangian time resolution. We use multi-wavelets framework for the adaptive part. Those have been heavily studied by Alpert et al. during the nineties and the two thousands. Some works merging multi-scale resolution and discontinuous Galerkin methods have been described by Müller and his colleagues in 2014 for non-linear hyperbolic conservation laws in the finite volume framework. In the framework of relativistic Vlasov equation, Besse, Latu, Ghizzo, Sonnendrücker and Bertrand presented the advantage of using adaptive meshes. While they used wavelet decomposition, which requires large data stencil, multi-wavelet decomposition coupled to discontinuous Galerkin discretisation only requires local stencil. This favours the parallelisation but, at the moment, semi-Lagrangian remains an obstacle to highly efficient distributed memory parallelisation. Although most of our work is done in a 1d × 1v phase space, we were able to obtain a few results in a 2d × 2v phase space
Devaux, Stéphane. "Etude cinétique de l’interaction plasma-paroi en présence d’un champ magnétique". Thesis, Nancy 1, 2007. http://www.theses.fr/2007NAN10087.
Pełny tekst źródłaIn fusion devices, the region of plasma directly in contact with a material surface (limiter, divertor) can erode the surface and release impurities, which mirgrate toward the bulk plasma and deteriorate its confinement. In this thesis, we studied the plasma-wall interaction using a Vlasov-Poisson model. This kinetic model allowed us to investigate the three different regions (Debye sheath, magnetic and collisional presheaths) that compose the transition between a low-pressure plasma and a wall when a tilted magnetic field is present. Particular attention was devoted to the physical properties of ions entering the Debye sheath and the role of ion-neutral collisions on the Bohm criterion. Moreover, we showed that, in the presence of a tilted magnetic field, the ion distribution function is significantly distorted from its Maxwellian shape in the bulk plasma, thus requiring a fully kinetic study. Using the computed ion distributions on the wall, we estimated the wall sputtering rate in terms of the magnetic field strength and angle of incidence. We showed in particular that, for grazing incidence, the sputtering rate is reduced because of two effects: first, the ion flux is spread over a larger area and, second, the grazing magnetic field limits the kinetic energy of ion population. As plasmas are generally composed of more than one species, we extended our model to simulate an argon-helium plasma. Our study focussed on the Bohm criterion at the Debye sheath entrance and its modifications brought by the introduction of a second ion species
Saidi, Karima. "Stabilisation d’une classe d’EDP non linéaire. Application à l’équation de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0225.
Pełny tekst źródłaThe work presented in this thesis concerns the stabilization of a class of nonlinear partialdifferential equations. It is a discretized model of the Vlasov-Poisson equation describing the spatial and temporal evolution, in a plasma, of a distribution function of charged particles. In a first step, we addressed the stabilization of the dynamical systems in fixed time (i.e. stabilization in finite time with a uniformly bounded). Criteria relaxing existing results in the literature have been established. Indeed, we have shown that, for a dynamical system, the combination of slow stability (in the polynomial sense) and fast stability (in the finite time sense) leads to a stability in fixed time. Various applications on the discretized Vlasov-Poisson system also concern the double integrator system with observer and the bilinear systems in infinite dimension where for each of these systems, the stabilizing feedback and/or observers in fixed time are constructed and numerically tested. In a second step, we are interested in the small time stabilization of time varying dynamical systems. In fact, the notion of small time is commonly used in theory of controllability. For stabilization, this small time is located between finite time and the fixed time. We have developed theoretical results based on the energy method guaranteeing the disappearance of the solution in small time. This is obtainedby means of a time excitation of a positive function not integrable in the sense of Lebesgue. Then, we have applied our results on model examples such as the transport equation with boundary control, the wave equation subject to a boundary control of the Wentzell type. Also, for finite and infinite dimensional bilinear systems which are, in addition, typical discretized Vlasov-Poisson models. For each system, we have elaborated its feedback whose construction is based on the integration of temporal and uniform excitations
Cisse, Amadou. "Observation et commande d'une classe d'équations aux dérivées partielles couplées : Application à l'équation de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0234.
Pełny tekst źródłaThis subject of research, addresses the problem of the observation and control of a class of nonlinear Partial Differential Equations (PDEs) in finite and infinite dimension. One of the main motivations concerns the application of these approaches to the Vlasov-Poisson equation (VP) in dimension 1Dx1D. The latter describes the evolution of the distribution function of charged particles in a fusion plasma.Most of the work in the literature on the Vlasov-Poisson equations concerns the analysis and discretisation of these equations, but very few results exist on the control and even fewer on the observation. It deals on the one hand with the observer synthesis, the stabilization by state feedback of the control and the observer-based stabilization under LMI conditions of the discretized system obtained by the discontinuous Galerkin method. And on the other hand by the design of state observer in infinite dimension by the technique of backstepping
Le, Bourdiec Solène. "Méthodes déterministes de résolution des équations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen". Phd thesis, Ecole Centrale Paris, 2007. http://tel.archives-ouvertes.fr/tel-00146258.
Pełny tekst źródłaLe travail de cette thèse a consisté à concevoir un schéma numérique original pour la résolution du système d'équations modélisant ces interactions : les équations de Vlasov-Maxwell relativistes. Notre choix s'est orienté vers des méthodes d'intégration directe. Nous proposons trois nouvelles méthodes spectrales pour discrétiser en impulsion les équations : une méthode de Galerkin et deux méthodes de type collocation. Ces approches sont basées sur des fonctions de Hermite qui ont la particularité de dépendre d'un facteur d'échelle permettant d'obtenir une bonne résolution en vitesse.
Nous présentons dans ce manuscript les calculs conduisant à la discrétisation et à la résolution du problème de Vlasov-Poisson monodimensionnel ainsi que les résultats numériques obtenus. Puis nous étudions les extensions possibles des méthodes au problème complet relativiste. Afin de réduire les temps de calcul, une parallélisation et une optimisation des algorithmes ont été mises en \oe uvre. Enfin, les calculs de validation du code 1Dx-3Dv, à partir d'instabilités de types Weibel et whistlers, à une ou deux espèces d'électrons, sont détaillés.
Giorgi, Pierre-Antoine. "Analyse mathématique de modèles cinétiques en physique des plasmas". Electronic Thesis or Diss., Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0609.
Pełny tekst źródłaThis thesis deals with the study of some kinetic models encountered in plasma physics.The first model considered is a 1D Vlasov-Poisson system representing the dynamics of two species of particles (ions and electrons) in a bounded set, x ∈ (0,1), with direct reflection boundary conditions. In the linear case, generalized characteristics are defined, ensuring the time s=0 to be reached after a finite number of bounces, the problematic case being when the electric field points outward of the boundary. Then, for initial conditions even in the velocity variable, a global continuous solution is built by means of generalized characteristics and a fixed point argument. Local uniqueness of a continuous solution is shown, in a frame where two successive bounces at the same boundary cannot occur. The second model was obtained as the limit of a Vlasov-Poisson system in the finite Larmor radius regime.For solutions satisfying a decay assumption, a Wasserstein stability estimate is proven, and a new proof of the existence of such solutions is given. The advection field is then Lipschitz continuous. Finally, numerical simulations are performed to investigate the kinetic response of electrons to an external drive. A beating between two waves, one at the external frequency, the other at the Landau frequency, is revealed
Herda, Maxime. "Analyse asymptotique et numérique de quelques modèles pour le transport de particules chargées". Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1165/document.
Pełny tekst źródłaThis thesis is devoted to the mathematical study of some models of partial differential equations from plasma physics. We are mainly interested in the theoretical study of various asymptotic regimes of Vlasov-Poisson-Fokker-Planck systems. First, in the presence of an external magnetic field, we focus on the approximation of massless electrons providing reduced models when the ratio me{mi between the mass me of an electron and the mass mi of an ion tends to 0 in the equations. Depending on the scaling, it is shown that, at the limit, solutions satisfy hydrodynamic models of convection-diffusion type or are given by Maxwell-Boltzmann-Gibbs densities depending on the intensity of collisions. Using hypocoercive and hypoelliptic properties of the equations, we are able to obtain convergence rates as a function of the mass ratio. In a second step, by similar methods, we show exponential convergence of solutions of the Vlasov-Poisson-Fokker-Planck system without magnetic field towards the steady state, with explicit rates depending on the parameters of the model. Finally, we design a new type of finite volume scheme for a class of nonlinear convection-diffusion equations ensuring the satisfying long-time behavior of discrete solutions. These properties are verified numerically on several models including the Fokker-Planck equation with magnetic field
Filbet, Francis. "Contribution à l'analyse et la simulation numérique de l'équation de Vlasov". Nancy 1, 2001. http://docnum.univ-lorraine.fr/public/SCD_T_2001_0068_FILBET.pdf.
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