Optimal transportation with traffic congestion and Wardrop equilibria

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant taking into account congestion. This leads to an optimization problem posed on a set of probability measures on a suitable paths space. We establish existence of minimizers and give a characterization. As an application, we obtain existence and variational characterization of equilibria of Wardrop type in a continuous space setting

Accurate fundamental parameters for Lower Main Sequence Stars

We derive an empirical effective temperature and bolometric luminosity calibration for G and K dwarfs, by applying our own implementation of the InfraRed Flux Method to multi-band photometry. Our study is based on 104 stars for which we have excellent BVRIJHK photometry, excellent parallaxes and good metallicities. Colours computed from the most recent synthetic libraries (ATLAS9 and MARCS) are found to be in good agreement with the empirical colours in the optical bands, but some discrepancies still remain in the infrared. Synthetic and empirical bolometric corrections also show fair agreement. A careful comparison to temperatures, luminosities and angular diameters obtained with other methods in literature shows that systematic effects still exist in the calibrations at the level of a few percent. Our InfraRed Flux Method temperature scale is 100K hotter than recent analogous determinations in the literature, but is in agreement with spectroscopically calibrated temperature scales and fits well the colours of the Sun. Our angular diameters are typically 3% smaller when compared to other (indirect) determinations of angular diameter for such stars, but are consistent with the limb-darkening corrected predictions of the latest 3D model atmospheres and also with the results of asteroseismology. Very tight empirical relations are derived for bolometric luminosity, effective temperature and angular diameter from photometric indices. We find that much of the discrepancy with other temperature scales and the uncertainties in the infrared synthetic colours arise from the uncertainties in the use of Vega as the flux calibrator. Angular diameter measurements for a well chosen set of G and K dwarfs would go a long way to addressing this problem.Comment: 34 pages, 20 figures. Accepted by MNRAS. Landscape table available online at http://users.utu.fi/luccas/IRFM