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Documents  82C40 | enregistrements trouvés : 6

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The momentum transport in a fusion device such as a tokamak has been in a scope of the interest during last decade. Indeed, it is tightly related to the plasma rotation and therefore its stabilization, which in its turn is essential for the confinement improvement. The intrinsic rotation, i.e. the part of the rotation occurring without any external torque is one of the possible sources of plasma stabilization.
The modern gyrokinetic theory [3] is an ubiquitous theoretical framework for lowfrequency fusion plasma description. In this work we are using the field theory formulation of the modern gyrokinetics [1]. The main attention is focussed on derivation of the momentum conservation law via the Noether method, which allows to connect symmetries of the system with conserved quantities by means of the infinitesimal space-time translations and rotations.
Such an approach allows to consistently keep the gyrokinetic dynamical reduction effects into account and therefore leads towards a complete momentum transport equation.
Elucidating the role of the gyrokinetic polarization is one of the main results of this work. We show that the terms resulting from each step of the dynamical reduction (guiding-center and gyrocenter) should be consistently taken into account in order to establish physical meaning of the transported quantity. The present work [2] generalizes previous result obtained in [4] by taking into the account purely geometrical contributions into the radial polarization.
The momentum transport in a fusion device such as a tokamak has been in a scope of the interest during last decade. Indeed, it is tightly related to the plasma rotation and therefore its stabilization, which in its turn is essential for the confinement improvement. The intrinsic rotation, i.e. the part of the rotation occurring without any external torque is one of the possible sources of plasma stabilization.
The modern gyrokinetic theory [3] ...

82D10 ; 82C40 ; 35L65 ; 35Q83 ; 70S10

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I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ’Hypocoercivity’ are used. I will discuss the connections to hypocoercivity theory and possible advantages and disadvantages of approaches via Harris’s theorem.
I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ...

35Q20 ; 35B40 ; 60J75 ; 82C40

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We analyse the classical Chapman-Enskog expansion for the Boltzmann equation. We show that this expansion should be considered as an intermediate step in constructing the asymptotics of solutions to the Boltzmann equation for small Knudsen numbers. It is explained that the way of transformation of the expansion is quite clear for the linearized case. Difficulties of the nonlinear problem are also briefly discussed.

82C40 ; 76P05

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We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we provide a first analysis of the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density with a moving point charge.

82D10 ; 82C40 ; 35Q35 ; 35Q83 ; 35Q31

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Multi angle  $L^2$ Hypocoercivity
Dolbeault, Jean (Auteur de la Conférence) | CIRM (Editeur )

The purpose of the $L^2$ hypocoercivity method is to obtain rates for solutions of linear kinetic equations without regularizing effects, in asymptotic regimes. Initially intended for systems with confinement in position space and simple local equilibria, the method has been extended to various local equilibria in velocities and non-compact situations in positions. It is also flexible enough to include non-local transport terms associated with Poisson coupling. The lecture will be devoted to a review of some recent results.
The purpose of the $L^2$ hypocoercivity method is to obtain rates for solutions of linear kinetic equations without regularizing effects, in asymptotic regimes. Initially intended for systems with confinement in position space and simple local equilibria, the method has been extended to various local equilibria in velocities and non-compact situations in positions. It is also flexible enough to include non-local transport terms associated with ...

82C40

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We review some results on the joint mean-field and semiclassical limit of the fermionic N-body Schrödinger dynamics leading to the Vlasov equation, which is a model in kinetic theory for charged or gravitating particles. The results we present include the case of singular interactions and provide explicit estimates on the convergence rate, using the Hartree-Fock theory for interacting fermions as a bridge between many-body and Vlasov dynamics.

35Q83 ; 81V19 ; 82C40

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