Finite Larmor radius approximation for the Fokker-Planck-Landau equation

The subject matter of this paper concerns the derivation of the finite Larmor radius approximation, when collisions are taken into account. Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyroaverage of the Fokker-Planck-Landau operator, which plays a major role in plasma physics. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, kinetic energy and dissipates the entropy.Comment: 62 page

Finite Larmor radius approximation for collisional magnetic confinement. Part I: The linear Boltzmann equation

International audienceThe subject matter of this paper concerns the derivation of the finite Lar-mor radius approximation, when collisions are taken into account. Several studies are performed, corresponding to different collision kernels : the relaxation and the Fokker-Planck operators. Gyroaveraging the relaxation operator leads to a position-velocity integral operator, whereas gyroaveraging the linear Fokker-Planck operator leads to diffusion in velocity but also with respect to the perpendicular position coordinates

Approximation de rayon de Larmor fini pour les plasmas magnétisés collisionnels. Finite Larmor radius approximation for collisional magnetized plasmas

International audienceIn this Note, we present the derivation of the finite Larmor radius approximation, when collisions are taken into account. We concentrate on the Boltzmann relaxation operator whose study reduces to the gyroaverage computation of velocity convolutions, which are detailed here. We emphasize that the resulting gyroaverage collision kernel is not local in space anymore and that the standard physical properties (i.e., mass balance, entropy inequality) hold true only globally in space and velocity. This work is a first step in this direction and it will allow us to handle more realistic collisional mechanisms, like the Fokker-Planck or Fokker-Planck-Landau kernels (Bostan and Caldini-Queiros (submitted for publication))Cette note présente la dérivation de l'approximation de rayon de Larmor fini, en prenant en compte les collisions. On se concentre sur le noyau linéaire de Boltzmann, de relaxation. Le principal sujet en est la recherche d'une expression explicite pour la gyromoyenne de cet opérateur,ce qui revient à analyser la gyromoyenne d'une convolution en vitesse. On note que l'opérateur moyenné qui en résulte n'est plus local en espace et que les propriétés physiques standards ( i.e. conservation de la masse et inégalité d'entropie) sont vérifiées seulement globalement en espace et vitesse. C'est un premier travail qui nous permettra d'aborder d'autres modèles plus réalistes pour la physique des plasmas, comme les noyaux de Fokker-Planck ou Fokker-Planck-Landau

Generic uniqueness for the Plateau problem

Given a complete Riemannian manifold $\mathcal{M}\subset\mathbb{R}^d$ which is a Lipschitz neighbourhood retract of dimension $m+n$, of class $C^{h,\beta}$ and an oriented, closed submanifold $\Gamma \subset \mathcal M$ of dimension $m-1$, which is a boundary in integral homology, we construct a complete metric space $\mathcal{B}$ of $C^{h,\alpha}$-perturbations of $\Gamma$ inside $\mathcal{M}$, with $\alpha<\beta$, enjoying the following property. For the typical element $b\in\mathcal B$, in the sense of Baire categories, there exists a unique $m$-dimensional integral current in $\mathcal{M}$ which solves the corresponding Plateau problem and it has multiplicity one.Comment: Minor change

Cum in Africam venissem hoc Manilio consule (Cic., Rep. 6.9)

In this passage of Cicero’s Republic, instead of Sigonius’ reading M’. Manilio consuli, widely accepted by modern editors, we should read hoc Manilio consule

Os bastiões da nacionalidade: nação e nacionalismo nas obras de Elysio de Carvalho

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Filosofia e Ciências Humanas, Programa de Pós-Graduação em História, Florianópolis, 2010O objetivo deste estudo é investigar a nação e o nacionalismo nas obras de Elysio de Carvalho entre 1921 e 1925. Elysio de Carvalho (1880-1925) foi um escritor alagoano que participou ativamente do campo intelectual na Primeira República. Através da sua idéia de nação, do seu nacionalismo desabrido e da utilização da história para dar suporte às suas interpretações sobre a realidade brasileira, podemos observar correntes estéticas e movimentos artísticos, políticos e de intelectuais que estavam em movimento e participaram do debate sobre a questão nacional na Primeira República

Perseo coniunx di Andromeda negli Aratea di Cicerone? (Per un restauro testuale al v. 21)

At lines 20 f., the repetition of Perseus’ name raises a problem; the comparison with Aratus’ text revealsthat Perseus of line 21 possibly took the place of a Latin word translating γαμβρός: probably coniunx

L’oscurità dell’Ariete da Arato ad Avieno

On the astronomical value and ancient reception of Aratus 255 ff., whose remarks on the feeble light of Aries are not exact