Equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model

This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson model to the astrophysical systems like globular clusters or galaxies. In a second part we will recall some recent numerical results which may give us some some quantitative hints about the equilibrium state associated to those systems.Comment: 8 pages, no figures, accepted in Communications in Nonlinear Science and Numerical Simulatio

The Jungle Universe

In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaitre universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaitre cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserve the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.Comment: 26 pages, 4 figure

Les comptes individuels de formation : fondements et enseignements

International audienceIndividual Learning Accounts (ILAs) represent a new tenet of the European's Lifelong Learning Strategy. They pretend to be an innovatory response to the problem of adult participation in training, solving the dilemma between efficiency and equity. The underlying rationale of ILAs relies on the Social Active Welfare State and the principle of "empowerment". Three ILAs are examined, in the United States, the United Kingdom and the Netherlands. Despite that ILAs share these theoretical and political basements, their concrete patterns and their goals (explicit or implicit) appear quite different. The analysis of their implementation and their (partially) assessed outcomes, can be useful to understand more recent device such as the French "Droit Individuel à la Formation".Dans le champ de la formation continue, les "comptes individuels de formation " sont introduits et visent, du moins selon leurs promoteurs, à mieux concilier efficacité et équité en promouvant la responsabilité individuelle. La logique sous-jacente à ces "comptes " renvoie de façon plus large à la problématique de l'Etat social actif et à l'objectif central " d'empowerment " des individus. Trois expériences de comptes individuels de formation sont étudiées, aux Etats-Unis, au Royaume-Uni et aux Pays Bas. Les enseignements tirés de leur mise en œuvre sont utiles à mieux comprendre la genèse et les enjeux d'un dispositif similaire récent : le Droit Individuel à la Formation en France

Promoting Life Long Learning through Individual Accounts: from Asset-Based to Capability-Based Policies

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2012.21 - ISSN : 1955-611X - Version révisée : février 2013The promotion of Life Long Learning (LLL) has become a high priority in the economic and social agenda of OECD countries. It is considered as one of the corner stones of the "active welfare state". Several countries have introduced (or at least experimented) Individual Learning Accounts as a way to promote LLL. ILAs designate all the schemes that provide the individual with funds he/she can use to take-up further training on his/her own initiative. Our aim here is to analyze the theoretical and political underpinnings of ILAs policies and to make a link between those underpinnings and both the design, the implementation and the potential outcomes of existing schemes. In section 1 we introduce the distinction between two political paradigms which may provide underpinnings for ILAs : the asset-based view versus capability-based view. In section 2 we analyze some experiences of ILAs in the light of this distinction, focusing mainly on three countries : The United-Kingdom, the United-States and France.La formation tout au long de la vie (FTLV) est devenue une priorité importante des politiques sociales dans les pays de l'OCDE. Elle est considérée comme un des piliers de " l'Etat Social Actif ". Plusieurs pays ont introduit (ou au moins expérimenté) des Comptes Individuels de Formation pour promouvoir la FTLV. Par Compte Individuel de Formation nous désignons ici l'ensemble des dispositifs qui attribuent aux individus une dotation financière qu'ils peuvent mobiliser pour entreprendre une formation à leur initiative. Notre objectif est ici d'analyser les fondements théoriques et politiques des Comptes Individuels de Formation, et de faire le lien entre ces fondements et la conception, la mise en oeuvre et les effets potentiels des dispositifs existants. Dans une première partie, nous introduisons la distinction entre deux paradigmes politiques : l'approche par les " capitaux " (" assets ") d'une part, l'approche par les " capabilités " (" capabilities ") d'autre part. A la lumière de cette distinction, nous analysons dans la deuxième partie des expériences de Comptes Individuels de Formation en nous focalisant principalement sur trois pays : le Royaume-Uni, les Etats-Unis et la France

The Geometry of Isochrone Orbits: from Archimedes' parabolae to Kepler's third law

In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and Harmonic potentials are called \it{isochrone}. In this paper, we solve the following general problem: are there any other isochrone potentials, and if so, what kind of orbits do they contain? To answer these questions, we adopt a geometrical point of view initiated by Michel H\'enon in 1959, in order to explore and classify exhaustively the set of isochrone potentials and isochrone orbits. In particular, we provide a geometric generalization of Kepler's third law, and give a similar law for the apsidal angle, for any isochrone orbit. We also relate the set of isochrone orbits to the set of parabolae in the plane under linear transformations, and use this to derive an analytical parameterization of any isochrone orbit. Along the way we compare our results to known ones, pinpoint some interesting details of this mathematical physics problem, and argue that our geometrical methods can be exported to more generic orbits in potential theory.Comment: 54 pages, 18 figure

Gravity, dimension, equilibrium, and thermodynamics

International audienceIt is actually possible to interpret gravitation as a property of space in a purely classical way. We note that an extended self-gravitating system equilibrium depends directly on the number of dimensions of the space in which it evolves. Given these precisions, we review the principal thermodynamical knowledge in the context of classical gravity with arbitrary dimension of space. Stability analyses for bounded 3D systems, namely the Antonov instability paradigm, are then associated to some amazing properties of globular clusters and galaxies