Bøger af Amandine Aftalion

Why do you lean in a bend? Why does a sprinter slow down before the finish line? Why do golf balls have dimples? Why do you swim better slightly underwater? Why, on a bike, the faster you go, the more stable you are? Why shouldn¿t you rely on doping tests too much? Is there a law of evolution of records?These are some of the 40 questions that Amandine Aftalion answers in this book using simple physics and mathematics, and some humor. Not only will it allow you to improve yourself in sports, but it will also but it will also give way to understanding how champions do.An easy book to read and the must to have if you are a sports addict or if you watch sports on TV and ask yourself ¿why?¿.Amandine Aftalion is a French mathematician. She is a CNRS senior scientist and graduated from École normale supérieure in Paris. She has given talks all over the world, as a specialist of models coming from low temperature physics. She has written a book on vortices in Bose¿Einstein condensates. More recently, she has used energy minimization to study an optimal control problem coming from human energy: optimizing running. She has written papers on sports aimed at coaches. Part of her latest results have inspired the first chapter of this book. She is the producer and director of a French YouTube channel for the popularization of mathematics, Videodimath, elected as one of the 5 best French YouTube channels for popular mathematics.

Since the first experimental achievement of Bose-Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling of some specific experiments which display vortices and to a rigorous analysis of features emerging experimentally.In contrast to a classical fluid, a quantum fluid such as a Bose-Einstein condensate can rotate only through the nucleation of quantized vortices beyond some critical velocity. There are two interesting regimes: one close to the critical velocity, where there is only one vortex that has a very special shape; and another one at high rotation values, for which a dense lattice is observed. One of the key features related to superfluidity is the existence of these vortices. We address this issue mathematically and derive information on their shape, number, and location. In the dilute limit of these experiments, the condensate is well described by a mean field theory and a macroscopic wave function solving the so-called Gross-Pitaevskii equation. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. We prove existence of solutions that have properties consistent with the experimental observations. Open problems related to recent experiments are presented. The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum fluids, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments.