A5002294097- Magnetic confinement fusion research
- Laser-Plasma Interactions and Diagnostics
- Computational Fluid Dynamics and Aerodynamics
- Gas Dynamics and Kinetic Theory
- Ionosphere and magnetosphere dynamics
- Navier-Stokes equation solutions
- Fluid Dynamics and Turbulent Flows
- Advanced Mathematical Physics Problems
- Fusion materials and technologies
- Laser-induced spectroscopy and plasma
- Particle accelerators and beam dynamics
- Particle Dynamics in Fluid Flows
- Solar and Space Plasma Dynamics
- Laser-Matter Interactions and Applications
- Optical properties and cooling technologies in crystalline materials
- Quantum chaos and dynamical systems
- High-pressure geophysics and materials
- Cosmology and Gravitation Theories
- Fractional Differential Equations Solutions
- Model Reduction and Neural Networks
- Fluid Dynamics Simulations and Interactions
- Advanced Thermodynamics and Statistical Mechanics
- Plasma Diagnostics and Applications
- Atomic and Molecular Physics
- Mathematical Biology Tumor Growth
Observatoire de la Côte d’Azur
2016-2024
Université Côte d'Azur
2016-2023
Lagrange Laboratory
2016-2021
Centre National de la Recherche Scientifique
2009-2020
Université de Lorraine
2004-2016
Institut Jean Lamour
2005-2016
Institut national de recherche en informatique et en automatique
2009-2013
Institut Élie Cartan de Lorraine
2003-2011
Institut Henri Poincaré
2007-2008
Institute of Rural Management Anand
2006
"Generalized Hydrodynamics" (GHD) stands for a model that describes one-dimensional \textit{integrable} systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic type, where the main unknown, statistical distribution function $f(t,z,\theta)$, lives phase space which is constituted by position variable $z$, and "kinetic" $\theta$, actually wave-vector, called "rapidity". Two key features are first non-local coupling...
The validity of quasilinear (QL) theory describing the weak warm beam–plasma instability has been a controversial topic for several decades. This issue is tackled anew, both analytically and by numerical simulations which benefit from power modern computers development in last decade Vlasov codes endowed with accuracy diffusion. Self-consistent within Vlasov-wave description show that QL remains valid strong chaotic diffusion regime. However, there non-QL regime before saturation, confirms...
Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp. 499-505, Podvigina et al., J. Comput. 306, 2016, 320-342). Looking at such with modern tools differential geometry and geodesic on space SDiff volume-preserving transformations (Arnold, Ann. Inst. Fourier, 16, 1966, 319-361), all manners generalisations here derived. The equation formula, relating...
In this paper we present some classes of high-order semi-Lagran- gian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that distribution function $f(t,x,v)$ and electric field $E(t,x)$ converge $L^2$ norm with a rate \[ \mathcal {O}\left (\Delta t^2 +h^{m+1}+ \frac {h^{m+1}}{\Delta t}\right ),\] where $m$ is degree polynomial reconstruction, $\Delta t$ $h$ are respectively time discretization parameters.
This contribution concerns a one-dimensional version of the Vlasov equation dubbed Vlasov$-$Dirac$-$Benney (in short V$-$D$-$B) where self interacting potential is replaced by Dirac mass.Emphasis put on relations between linearized version, full nonlinear problem and equations fluids. In particular connection with so-called Benney leads to new stability results. Eventually V$-$D$-$B appears be at ``cross road' several problems mathematical physics which have as far concerned very similar properties.
A semi-Lagrangian scheme is proposed for solving the periodic one-dimensional Vlasov--Poisson system in phase space on unstructured meshes. The distribution function f(t,x,v) and electric field E(t,x) are shown to converge exact solution values $L^{\infty}$ norm. rate of convergence O(h4/3 ).
Predicting turbulent transport in nearly collisionless fusion plasmas requires one to solve kinetic (or, more precisely, gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although accurate, the calculation is much demanding computer resources than fluid simulations. An alternative approach based on a water-bag representation distribution function that not an approximation but rather special class initial conditions, allowing reduce full Vlasov equation...
In this paper we consider the multi-water-bag model for collisionless kinetic equations.The representation of statistical distribution function particles can be viewed asa special class exact weak solution Vlasov equation, allowing to reduce latter intoa set hydrodynamic equations while keeping its character.After recalling link with formulationof conservation laws, derive different (MWB) models, namely Poisson-MWB,the quasineutral-MWB and electromagnetic-MWB models. These models are very...
Finite-dimensional, inviscid equations of hydrodynamics, obtained through a Fourier-Galerkin projection, thermalize with an energy equipartition. Hence, numerical solutions such equations, which typically must be Galerkin-truncated, show behavior at odds the parent equation. An important consequence this is uncertainty in measurement temporal evolution distance complex singularity from real domain leading to lack firm conjecture on finite-time blow-up problem incompressible,...
Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations Vlasov-Maxwell equation in asymptotic limit infinite speed light. These model low-frequency electromagnetic phenomena plasmas, thus "light waves" somewhat supressed, turn allows discretization dispense with Courant-Friedrichs-Lewy condition on time step. construct scheme based...
This work addresses non‐linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity code is to use a fixed grid Semi‐Lagrangian (SL) scheme and this for entire distribution function. 4D drift‐kinetic version already showns interest such SL method which exhibits good properties energy conservation in regime as well an accurate description fine spatial scales. has been upgrated run 5D toroidal ITG turbulence. Linear...
Maxwell-fluid simulations on a flat-topped moderately overdense plasma slab (typically n0∕nc=1–2) by Berezhiani et al. [Phys. Plasmas 66, 062308 (2005)] {see also the previous work of Tushentsov Rev. Lett. 87, 275002 (2001)]} were seen to lead dynamic penetration an ultrahigh intensity laser pulse into plasma. Two qualitatively different scenarios for presented depending background density. In first one, energy occurs soliton-like structures moving last electron cavitation and is possible...
This paper presents the results obtained with a set of gyrokinetic codes based on semi-Lagrangian scheme. Several physics issues are addressed, namely, comparison between fluid and kinetic descriptions, intermittent behaviour flux driven turbulence role large scale flows in toroidal ITG turbulence. The question initialization full-F simulations is also discussed.
A new model is presented, named collisional-gyro-water-bag (CGWB), which describes the collisional drift waves and ion-temperature-gradient (ITG) instabilities in a plasma column. This based on kinetic gyro-water-bag approach recently developed [P. Morel et al., Phys. Plasmas 14, 112109 (2007)] to investigate modes. In CGWB electron-neutral collisions have been introduced are now taken into account. The has validated by comparing linear analysis with other models previously proposed...
We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for induction equations which appear in ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under CFL condition , obtain error estimates L2 where m is degree local polynomials.