Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative

We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this setting.Comment: 33 pages, no figures, third version, to appear in Ast\'erisqu

Financing the Response to AIDS in Low- and Middle-Income Countries: International Assistance From the G8, European Commission and Other Donor Governments, 2008

Summarizes 2008 data on international AIDS assistance from donor governments. Presents trends by donor country, by funding channel, on aid as percentages of GDP, and on the gaps between needs and resources and between commitments and disbursements

Phase-field simulation of core-annular pipe flow

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.Comment: Paper accepted for publication in International Journal of Multiphase Flo