Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D Navier-Stokes equation. At high Reynolds number and without global rotation, such solutions are usually unstable to three-dimensional perturbations. By contrast, for strong enough global rotation, we prove rigorously that the 2D (and possibly turbulent) solutions are stable to vertically dependent perturbations: the flow becomes 2D in the long-time limit. These results shed some light on several fundamental questions of rotating turbulence: for arbitrary Reynolds number and small enough Rossby number, the system is attracted towards purely 2D flow solutions, which display no energy dissipation anomaly and no cyclone-anticyclone asymmetry. Finally, these results challenge the applicability of wave turbulence theory to describe stationary rotating turbulence in bounded domains.Comment: To be published in Journal of Fluid Mechanic

A comparative analysis of the demand for higher education: results from a meta-analysis of elasticities

Studies of the demand for higher education have produced numerous estimates of the tuition and income elasticities. Because of widespread variation in the models estimated, this paper performs a meta-analysis of the literature to uncover the extent to which study characteristics influence elasticities. In addition to being more inelastic in the short-run, the results reveal that demand is least responsive to tuition and income in the United States. Also, the measure of quantity and price, coupled with the method of estimation, have important effects on the tuition elasticity. Nonetheless, there are many study characteristics that have little impact on elasticity estimates.

Improved angular momentum evolution model for solar-like stars II. Exploring the mass dependence

We developed angular momentum evolution models for 0.5 and 0.8 $M_{\odot}$ stars. The parametric models include a new wind braking law based on recent numerical simulations of magnetised stellar winds, specific dynamo and mass-loss rate prescriptions, as well as core/envelope decoupling. We compare model predictions to the distributions of rotational periods measured for low mass stars belonging to star forming regions and young open clusters. Furthermore, we explore the mass dependence of model parameters by comparing these new models to the solar-mass models we developed earlier. Rotational evolution models are computed for slow, median, and fast rotators at each stellar mass. The models reproduce reasonably well the rotational behaviour of low-mass stars between 1 Myr and 8-10 Gyr, including pre-main sequence to zero-age main sequence spin up, prompt zero-age main sequence spin down, and early-main sequence convergence of the surface rotation rates. Fast rotators are found to have systematically shorter disk lifetimes than moderate and slow rotators, thus enabling dramatic pre-main sequence spin up. They also have shorter core-envelope coupling timescales, i.e., more uniform internal rotation. As to the mass dependence, lower mass stars require significantly longer core-envelope coupling timescale than solar-type ones, which results in strong differential rotation developing in the stellar interior on the early main sequence. Lower mass stars also require a weaker braking torque to account for their longer spin down timescale on the early main sequence, while they ultimately converge towards lower rotational velocities than solar-type stars on the longer term due to their reduced moment of inertia. We also find evidence that the mass-dependence of the wind braking efficiency may be related to a change of the magnetic topology in lower mass stars.Comment: 17 pages, 11 figures, accepted for publication in A&

Improved angular momentum evolution model for solar-like stars

We present new models for the rotational evolution of solar-like stars between 1 Myr and 10 Gyr with the aim to reproduce the distributions of rotational periods observed for star forming regions and young open clusters within this age range. The models include a new wind braking law based on recent numerical simulations of magnetized stellar winds and specific dynamo and mass-loss prescriptions are adopted to tie angular momentum loss to angular velocity. The model additionally assume constant angular velocity during the disk accretion phase and allow for decoupling between the radiative core and the convective envelope as soon as the former develops. We have developed rotational evolution models for slow, median and fast rotators with initial periods of 10, 7, and 1.4d, respectively. The models reproduce reasonably well the rotational behaviour of solar-type stars between 1 Myr and 4.5 Gyr, including PMS to ZAMS spin up, prompt ZAMS spin down, and the early-MS convergence of surface rotation rates. We find the model parameters accounting for the slow and median rotators are very similar to each other, with a disk lifetime of 5 Myr and a core-envelope coupling timescale of 28-30 Myr. In contrast, fast rotators have both shorter disk lifetime (2.5 Myr) and core-envelope coupling timescale (12 Myr). We emphasize that these results are highly dependent on the adopted braking law. We also report a tentative correlation between initial rotational period and disk lifetime, which suggests that protostellar spin-down by massive disks in the embedded phase is at the origin of the initial dispersion of rotation rates in young stars. We conclude that this class of semi-empirical models successfully grasp the main trends of the rotational behaviour of solar-type stars as they evolve and make specific predictions that may serve as a guide for further development.Comment: 16 pages, 5 figures, 4 table, accepted for publication by A&A. New version that include the linguistic correctio

Counting projections of rational curves

Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree of the curves and the dimensions of the two given ambient projective spaces, the number of curves and projections fulfilling the requirements is finite. Using standard techniques in intersection theory and the Bott residue formula, we compute this number.Comment: 27 page

The demand for alcohol: a meta-analysis of elasticities

Numerous studies have estimated elasticities of alcohol demand using different procedures. Because of widespread differences in demand estimates, however, it is difficult to synthesise the literature into coherent meaning. This study improves our understanding of alcohol demand by reporting results from a meta-analysis of 132 studies. Specifically, regressing estimated price, income and advertising elasticities of alcohol on variables accounting for study characteristics, we find alcohol elasticities to be particularly sensitive to demand specification, data issues and various estimation methods. Furthermore, compared to other alcoholic beverages, beer elasticities tend to be more inelastic.alcohol demand, elasticity, meta-analysis, Demand and Price Analysis,

Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2D, with no dependence along the vertical? We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number Rm << 1: we prove that the flow becomes exactly 2D asymptotically in time, regardless of the initial condition and provided the interaction parameter N is larger than a threshold value. We call this property "absolute two-dimensionalization": the attractor of the system is necessarily a (possibly turbulent) 2D flow. We then consider the full-magnetohydrodynamic equations and we prove that, for low enough Rm and large enough N, the flow becomes exactly two-dimensional in the long-time limit provided the initial vertically-dependent perturbations are infinitesimal. We call this phenomenon "linear two-dimensionalization": the (possibly turbulent) 2D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3D attractors may also exist and be attained for strong enough initial 3D perturbations. These results shed some light on the existence of a dissipation anomaly for magnetohydrodynamic flows subject to a strong external magnetic field.Comment: Journal of Fluid Mechanics, in pres