Relative periodic orbits in point vortex systems

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.Comment: 27 pages, 17 figure

CII in the Interstellar Medium: Excitation by H2 Revisited

C$^+$ is a critical constituent of many regions of the interstellar medium, as it can be a major reservoir of carbon and, under a wide range of conditions, the dominant gas coolant. Emission from its 158$\mu$m fine structure line is used to trace the structure of photon dominated regions in the Milky Way and is often employed as a measure of the star formation rate in external galaxies. Under most conditions, the emission from the single [CII] line is proportional to the collisional excitation rate coefficient. We here used improved calculations of the deexcitation rate of [CII] by collisions with H$_2$ to calculate more accurate expressions for interstellar C$^+$ fine structure emission, its critical density, and its cooling rate. The collision rates in the new quantum calculation are $\sim$ 25% larger than those previously available, and narrow the difference between rates for excitation by atomic and molecular hydrogen. This results in [CII] excitation being quasi-independent of the molecular fraction and thus dependent only on the total hydrogen particle density. A convenient expression for the cooling rate at temperatures between 20 K and 400 K, assuming an LTE H$_2$ ortho to para ration is $\Lambda ({\rm LTE~OPR}) = \left(11.5 + 4.0\,e^{-100\,\mathrm K/T^{\rm kin}}\right)\;e^{-91.25\,\mathrm K/T^{\rm kin}}\,n ({\rm C}^{+})\,n({\rm H}_2)\times 10^{-24}\;{\rm ergs}~{\rm cm}^{-3}~{\rm s}^{-1}$. The present work should allow more accurate and convenient analysis of the [\CII] line emission and its cooling

Mapping the Decoupling : Transfer Efficiency of the Single Farm Payment Scheme

This paper focuses on the question of the transfer efficiency of the SFP scheme and represents graphically the results of an analytical framework with the seminal Surplus Transformation Curve initiated by Josling (1974) and developed by Gardner (1983). The special feature of the SFP scheme resides in the paradox that exists between the tradability of the entitlements and the activation constraint that creates a particular link to the land. The main result is that redistributive effects between landowners and farmers depend on the total number of entitlements, so they have to be considered as a lever to increase the transfer efficiency of the scheme.Single Farm Payment, transfer efficiency, surplus transformation curve, Agricultural and Food Policy, Agricultural Finance,

Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method

The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. (2004). The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox (2005) to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver