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Li, Li. "The asymptotic behavior for the Vlasov-Poisson-Boltzmann system & heliostat with spinning-elevation tracking mode /". access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082419f.pdf.
Pełny tekst źródła"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [84]-87)
SALANON, BRUNO. "Stabilite des solutions des equations de transport application a la resolution numerique du systeme de vlasov-poisson". Nice, 1997. http://www.theses.fr/1997NICE5085.
Pełny tekst źródłaZhelezov, Gleb, i Gleb Zhelezov. "Coalescing Particle Systems and Applications to Nonlinear Fokker-Planck Equations". Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624562.
Pełny tekst źródłaVecil, Francesco. "A contribution to the simulation of Vlasov-based models". Doctoral thesis, Universitat Autònoma de Barcelona, 2007. http://hdl.handle.net/10803/3100.
Pełny tekst źródłaLa BTE ha de ser acoplada con una ecuación o sistema de ecuaciones para calcular el campo de fuerza: para estructuras simples se usa la ecuación de Poisson; para plasmas, donde los efectos magnéticos no se pueden despreciar debido a las altas velocidades de las partículas, se usa la fuerza de Lorentz, por lo cual se han de resolver las ecuaciones de Maxwell; en nanoestructuras, por ejemplo transistores con dimensiones confinadas, la ecuación de Poisson necesita ser acoplada con la ecuación de Schrödinger para la descripción de las dimensiones cuánticas y para la descomposición en sub-bandas, o niveles de energía.
Las colisiones son el scattering que las cargas padecen debido a las interacciones con otras cargas o con el retículo cristalino fijo, representado en forma de fonones. En la tesis se emplean diversos operadores de scattering: los más simples son operadores lineales de relajación; se estudia un modelo para la simulación de semiconductores donde se tienen en cuenta colisiones con fonones acústicos, en aproximación elástica, y fonones ópticos.
Tras la introducción, en el primer capítulo se desarrollan los métodos numéricos más importantes: primero un método de interpolación no oscilante (PWENO), necesario para evitar las oscilaciones producidas por la reconstrucción por polinomios de Lagrange, que incrementa la variación total cuando aparecen choques: las oscilaciones en el espacio de fases son características del problema, pero si el método añade oscilaciones espúreas (es decir, debidas al método en sí), entonces el resultado numérico no tiene sentido, o simplemente explota. El segundo método numérico fundamental es la técnica de splitting: cuando se resuelve un problema complicado, si se puede dividir en sub-problemas y resolverlos por separado, entonces se puede reconstruir una aproximación para el problema completo; esta técnica se usa para el time splitting (separación de la parte de transporte y de colisión) y el splitting dimensional (dividir el espacio de fases en posición y velocidad). La tercera herramienta fundamental es un sólver para advección lineal: se usan dos métodos, uno basado en trazar hacia atrás las características a nivel puntual y otro basado en reconstruir valores integrales en segmentos en lugar de puntos; el primero controla mejor las oscilaciones, el segundo fuerza la conservación de masa.
En el capítulo 2 estos métodos se aplican a algunos tests conocidos para averiguar su solidez.
En el capítulo 3 estos métodos se aplican a la simulación de un diodo, y los resultados se comparan con resultados anteriores obtenidos por esquemas Runge-Kutta basados en diferencias finitas para aproximar las derivadas parciales.
El capítulo 4 está dedicado a la construcción y simulación de modelos intermedios entre una ecuación cinética, con operador de colisión de tipo relajación, y su aproximación más grosera, ésta última siendo la ecuación del calor. Para obtener modelos intermedios, se busca un cierre de las ecuaciones de los momentos de orden cero y uno. Se proponen esquemas "asymptotic-preserving" para la ecuación cinética, que evitan la stiffness de la parte de advección a través de una descomposición de la función de distribución en su media más fluctuaciones. En cuanto a las clausuras de las ecuaciones de los momentos, se proponen esquemas de relajación para aislar las no-linealidades. Estos métodos son aplicados a un test conocido, el Su-Olson test.
El último capítulo está dedicado a la simulación de un MOSFET (Metal Oxide Semiconductor Field Effect Transistor) 2D de dimensión nanométrica en el que los electrones se comportan como partículas en una dimensión y como ondas en las dimensiones confinadas. La descomposición en sub-bandas se realiza a través de una ecuación de Schrödinger 1D en estado estacionario. Las dimensiones, así como las sub-bandas, están acopladas por la ecuación de Poisson en la expresión de la densidad, y por el operador de colisión. Se propone un sólver microscópico para estados transitorios, basado en técnicas de splitting para las BTEs (una para cada nivel de energía), métodos de características para el transporte y una iteración de tipo Newton para resolver el problema acoplado Schrödinger-Poisson para el cálculo del campo de fuerza.
This thesis is dedicated to the development, application and test of numerical methods for the numerical simulation of problems arising from physics and electronic engineering. The main tool which is used all along the work is the Vlasov (transport) equation in the form of the Boltzmann Transport Equation (BTE) for the description of the transport and collisions of charged particles in plasmas and electronic devices: charge carriers are driven by a force field and scattered by other carriers or phonons (pseudo-particles giving an effective representation of the oscillating field produced by the vibrating ions).
The BTE must be coupled to an equation or a system of equations for the computation of the force field: for simple structures the Poisson equation is used; for plasmas, where the magnetic phenomena cannot be neglected due to the high velocities of the particles, the Lorentz force is used, so the Maxwell equations have to be solved; for nanostructures, e.g. transistors with confined dimensions, the Poisson equation needs coupling with Schrödinger equation for the description of the quantum dimensions and the decomposition into subbands, or energy levels.
Collisions mean the scattering the carriers suffer due to the interactions with other carriers or the fixed lattice, in form of phonons. All along the thesis several scattering operator are used: the simplest ones are linear relaxation-time operators; a model for the simulation of a semiconductor is studied in which collisions are taken into account with acoustic phonons, in the elastic approximation, and optical phonons.
After the introduction, in the first chapter the most important numerical methods are developed: first of all a pointwise non-oscillatory interpolation method (PWENO) needed to avoid the simple Lagrange polynomial reconstruction, which increases the total variation when shocks appear: oscillations are part of the physics of the problem, but if the method adds spurious, non-physical oscillations, then the numerical result is meaningless, or it simply blows up. The second fundamental numerical method is the splitting technique: when solving a complicated problem, if we are able to subdivide it into sub-problem and solve them for separate, then we can reconstruct an approximation for the complete problem; this technique is used for both time splitting (separate transport from collisions) and dimensional splitting (split the phase space into either dimensions). The third fundamental instrument is the solver for linear advections: two methods are used, one based on pointwise following backwards the characteristics and another one based on reconstructing integral values along segments instead of point values; the first one controls better oscillations, the second one forces mass conservation.
These methods are applied in chapter 2 to some well-known benchmark tests to control their robustness.
In chapter 3 these methods are applied to the simulation of a diode, and the results compared to previous results obtained by Runge-Kutta schemes based on finite differences schemes for the approximation of the partial derivatives.
Chapter 4 is dedicated to the construction and simulation of intermediate models between a kinetic equation, with relaxation-time collision operator, and its coarsest approximation, this one being the heat equations. In order to obtain intermediate models, the moment equations are closed at zeroth and first order. Asymptotic-preserving schemes are proposed for the kinetic equation, which avoid the stiffness of the advection part by decomposing the distribution function into its average plus fluctuations. As for the moment closures, relaxation schemes are proposed in order to confine the non-linearities in the right hand side. These methods are then applied to a known benchmark, the Su-Olson test.
The last chapter is dedicated to the simulation of a nanoscaled 2D MOSFET (Metal Oxide Field Effect Transistor) in which electrons behave as particles in one dimension and as waves in the confined dimensions. The subband decomposition is realized through a stationary-state 1D Schrödinger equation. The dimensions as well as the subbands are coupled by the Poisson equation in the expression of the density and by the collision operator. A transient-state microscopic solver is proposed, based on splitting techniques for the BTE's (one for each energy level), characteristics methods for the transport and a Newton iteration for the solution of the coupled Schrödinger-Poisson system for computing the force field.
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
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.
Zhang, Mei. "Some problems on conservation laws and Vlasov-Poisson-Boltzmann equation /". access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749465f.pdf.
Pełny tekst źródła"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [90]-94)
Bourne, Emily. "Non-uniform numerical schemes for the modelling of turbulence in the 5D GYSELA code". Electronic Thesis or Diss., Aix-Marseille, 2022. http://www.theses.fr/2022AIXM0412.
Pełny tekst źródłaThis thesis lies within the context of fusion plasma simulations and it has a double objective: (i) develop new scalable numerical methods, adapted to the semi-lagrangian scheme used in the 5D gyrokinetic GYSELA code, capable of solving the problem of large fluctuations and temperature variations at the edge of the plasma, and (ii) take into account more realistic magnetic configurations than the concentric circles currently simulated by the code. I present a new approach for quadrature using splines, which limits the condition number for the procurement of such quadrature coefficients. I present a local spline method where derivatives are transported between patches, and show its stability for semi-lagrangian advection. The semi-lagrangian method based on non-uniform splines on a Vlasov-Poisson 1D-1V model is used for studies of the plasma sheath. The existing VOICE code (which is a mini version of GYSELA), designed to study such problems, has been modified and optimised on a GPU to operate on a non-uniform mesh. Co-variant and contra-variant transformation matrices of a new realistic magnetic configuration were derived and implemented in the code to allow the 5D Vlasov equations to take into account new geometry. The inclusion of this new magnetic configuration has been successfully numerically validated on the linear benchmarks used for GAM studies. In parallel, a test platform for the 2D Poisson solver was developed in order to numerically compare this spline finite elements solver to two other multi-grid solvers: (i) a solver using finite volumes on a uniform cartesian mesh with embedded boundaries, and (ii) a solver using finite differences on a logical mesh
Badsi, Mehdi. "Etude mathématiques et simulations numériques de modèles de gaines bi-cinétiques". Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066178.
Pełny tekst źródłaThis thesis focuses on the construction and the numerical simulation theoretical models of plasmas in interaction with an absorbing wall. These models are based on two species Vlasov-Poisson or Vlasov-Ampère systems in the presence of boundary conditions. The expected stationary solutions must verify the balance of the flux of charges in the orthogonal direction to the wall. This feature is called the ambipolarity.Through the study of a non linear Poisson equation, we prove the well-posedness of 1d-1v stationary Vlasov-Poisson system, for which we determine incoming particles distributions and a wall potential that induces the ambipolarity as well as a non negative charge density hold. We also give a quantitative estimates of the thickness of the boundary layer that develops at the wall. These results are illustrated numerically. We prove the linear stability of the electronic stationary solution for a non-stationary Vlasov-Ampère system. Finally, we study a 1d-3v stationary Vlasov-Poisson system in the presence of a constant and parallel to the wall magnetic field . We determine incoming particles distributions and a wall potential so that the ambipolarity holds. We study a non linear Poisson equation through a non linear functional energy that admits minimizers. We established some bounds on the numerical parameters inside which, our model is relevant and we propose an interpretation of the results
Ben-Aïm, Laurence. "Applications des methodes particulaires en mecanique des fluides et en physique des plasmas". Paris 6, 1988. http://www.theses.fr/1988PA066060.
Pełny tekst źródłaPham, Thi Trang Nhung. "Méthodes numériques pour l'équation de Vlasov réduite". Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAD051/document.
Pełny tekst źródłaMany numerical methods have been developed in order to selve the Vlasov equation, because computing precise simulations in a reasonable time is a real challenge. This equation describes the time evolution of the distribution function of charged particles (electrons/ions), which depends on 3 variables in space, 3 in velocity and time. The main idea of this thesis is to rewrite the Vlasov equation in the form of a hyperbolic system using a semi-discretization of the velocity. This semi-discretization is achieved using the finite element method. The resulting model is called the reduced Vlasov equation. We propose different numerical methods to salve this new model efficiently: finite volume methods, semi-Lagrangian methods and discontinuous Galerkin methods
Manfredi, Giovanni. "Sur les modèles de Vlasov, Schrödinger et Wigner en physique des plasmas : redimensionnement et expansion dans le vide". Orléans, 1994. http://www.theses.fr/1994ORLE2027.
Pełny tekst źródłaCHANE-YOOK, Martine. "Etude d'une equation cinetique liee a l'effet Compton - Modelisation et simulation 3D de la charge d'un satellite en environnement plasmique". Phd thesis, Université de Provence - Aix-Marseille I, 2004. http://tel.archives-ouvertes.fr/tel-00008427.
Pełny tekst źródłaLutz, Mathieu. "Etude mathématique et numérique d'un modèle gyrocinétique incluant des effets électromagnétiques pour la simulation d'un plasma de Tokamak". Thesis, Strasbourg, 2013. http://www.theses.fr/2013STRAD036/document.
Pełny tekst źródłaThis thesis is devoted to the study of charged particle beams under the action of strong magnetic fields. In addition to the external magnetic field, each particle is submitted to an electromagnetic field created by the particles themselves. In kinetic models, the particles are represented by a distribution function f(x,v,t) solution of the Vlasov equation. To determine the electromagnetic field, this equation is coupled with the Maxwell equations or with the Poisson equation. The strong magnetic field assumption is translated by a scaling wich introduces a singular perturbation parameter 1/ε
Campos, Serrano Juan. "Modèles attractifs en astrophysique et biologie : points critiques et comportement en temps grand des solutions". Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00861568.
Pełny tekst źródłaLind, Crystal. "The gravitational Vlasov-Poisson system on the unit 2-sphere with initial data along a great circle". Thesis, 2014. http://hdl.handle.net/1828/5613.
Pełny tekst źródłaGraduate
Shen, Shengyi. "Vlasov's Equation on a Great Circle and the Landau Damping Phenomenon". Thesis, 2014. http://hdl.handle.net/1828/5768.
Pełny tekst źródłaGraduate
0405
shengyis@uvic.ca
Hagstrom, George Isaac. "Infinite-dimensional Hamiltonian systems with continuous spectra : perturbation theory, normal forms, and Landau damping". Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-08-3753.
Pełny tekst źródłatext