4,120 research outputs found
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
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