AMD-stability and the classification of planetary systems

We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in (Laskar, PRL,2000). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database (exoplanet.eu) for which the orbital elements are sufficiently well known.Comment: 18 pages, 13 figures, A&A in pres

AMD-stability in presence of first order Mean Motion Resonances

The AMD-stability criterion allows to discriminate between a-priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the Angular Momentum Deficit (AMD) in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopeadia.Comment: Accepted by A and A 07/10/1

A theory of supervision with endogenous transaction costs

We propose a theory of supervision with endogenous transaction costs. A principal delegates part of his authority to a supervisor who can acquire soft information about an agent's productivity. If the supervisor were risk-neutral, the principal would simply make the better informed supervisor residual claimant for the hierarchy's profit. Under risk-aversion, the optimal contract trades-off the supervisor's incentives to reveal his information with an insurance motive. This contract can be identified with the one obtained in a simple hard information model of hierarchical collusion with exogenous transaction costs. Now, transaction costs are endogenous and depend on the collusion stake, the accuracy of the supervisory technology and the supervisor's degree of risk-aversion. We then discuss various implications of the model for the design and management of organisations

An experimental study of boundary-layer transition induced vibrations on a hydrofoil

This paper aims at characterizing experimentally laminar to turbulent transition induced vibrations. Here, the transition is known to be triggered by a Laminar Separation Bubble that results from a laminar separation of the boundary-layer flow on a hydrofoil. In this study we consider two NACA66312 (Mod) laminar hydrofoils at low angles of incidence (mostly 2° and 4°) and Reynolds numbers ranging from Re=450 000 to 1 200 000, in order to get transitional regimes. The first hydrofoil, made of steel (E=2.1×1011 Pa), is referred to as the rigid hydrofoil, although it is seen to vibrate under the action of the LSB. To better understand the possible interaction between the flow and the foil vibrations, vibration measurements are repeated using a flexible hydrofoil (E=3×109 Pa) of same geometry (under zero loading) and in close configurations. The experiments are carried out at the French Naval Academy Research Institute (IRENav, France). Wall pressure and flow velocity measurements enable a characterization of the laminar separation bubble and the identification of a vortex shedding at a given frequency. It is hence shown that the boundary-layer transition induces important foil vibrations, whose characteristics in terms of frequency and amplitude depend on the vortex shedding frequency, and can be coupled with natural frequencies of the hydrofoils

A Theory of Supervision with Endogenous Transaction Costs

We propose a theory of supervision with endogenous transaction costs. A principal delegates part of his authority to a supervisor who can acquire soft information about an agent's productivity. If the supervisor were risk-neutral, the principal would simply make the better informed supervisor residual claimant for the hierarchy's profit. Under risk-aversion, the optimal contract trades-off the supervisor's incentives to reveal his information with an insurance motive. This contract can be identified with the one obtained in a simple hard information model of hierarchical collusion with exogenous transaction costs. Now, transaction costs are endogenous and depend on the collusion stake, the accuracy of the supervisory technology and the supervisor's degree of risk-aversion. We then discuss various implications of the model for the design and management of organisations.Supervision, soft information, collusion, endogenous transaction costs

Modeling the wind circulation around mills with a Lagrangian stochastic approach

This work aims at introducing model methodology and numerical studies related to a Lagrangian stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian stochastic downscaling method that we have introduced in [3] and [4] to the atmospheric boundary layer and we introduce here a Lagrangian version of the actuator disc methods to take account of the mills. We present our numerical method and numerical experiments in the case of non rotating and rotating actuator disc models. We also present some features of our numerical method, in particular the computation of the probability distribution of the wind in the wake zone, as a byproduct of the fluid particle model and the associated PDF method