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A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells

Daniel Bouche, Alain Decoster, Laurent Desvillettes, Valeria Ricci (2013)

MathematicS In Action

We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.

A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation

Martin Campos Pinto (2007)

International Journal of Applied Mathematics and Computer Science

This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1+1)-dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport...

A Hermite-type adaptive semi-Lagrangian scheme

Michel Mehrenberger, Eric Violard (2007)

International Journal of Applied Mathematics and Computer Science

We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.

About a Variant of the 1 d Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation"

Claude Bardos (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.

Abstracts of theses in mathematics

(2000)

Commentationes Mathematicae Universitatis Carolinae

Žemlička, Jan: Structure of steady rings. Zemek, Martin: On some aspects of subdifferentiality of functions on Banach spaces. Hlubinka, Daniel: Construction of Markov kernels with application for moment problem solution. Somberg, Petr: Properties of the BGG resolution on the spheres. Krump, Lukáš: Construction of Bernstein-Gelfand-Gelfand for almost hermitian symmetric structures. Kolář, Jan: Simultaneous extension operators. Porosity.

An axisymmetric PIC code based on isogeometric analysis⋆

A. Back, A. Crestetto, A. Ratnani, E. Sonnendrücker (2011)

ESAIM: Proceedings

Isogeometric analysis has been developed recently to use basis functions resulting from the CAO description of the computational domain for the finite element spaces. The goal of this study is to develop an axisymmetric Finite Element PIC code in which specific spline Finite Elements are used to solve the Maxwell equations and the same spline functions serve as shape function for the particles. The computational domain itself is defined using splines...

Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space

Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We study the initial value problem for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We show that the corresponding stationary problem in the whole space ℝn admits a unique stationary solution in a general situation. Moreover, it is proved that when n ≥ 3, a unique solution to the initial value problem exists globally in time and converges to the corresponding stationary solution as time tends to infinity, provided that the amplitude of the stationary solution...

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