Sharp exponent of acceleration in general nonlocal equations with a weak Allee effect

We study an acceleration phenomenon arising in monostable integro-differential equations with a weak Allee effect. Previous works have shown its occurrence and have given correct upper bounds on the rate of expansion in some particular cases, but precise lower bounds were still missing. In this paper, we provide a sharp lower bound for this acceleration rate, valid for a large class of dispersion operators. Our results manage to cover fractional Laplace operators and standard convolutions in a unified way, which is new in the literature. A first very important result of the paper is a general flattening estimate of independent interest: this phenomenon appears regularly in acceleration situations, but getting quantitative estimates is most of the time open. This estimate at hand, we construct a very subtle sub-solution that captures the expected dynamics of the accelerating solution (rates of expansion and flattening) and identifies several various regimes that appear in the dynamics depending on the parameters of the problem

A model of bubble-induced turbulence based on large-scale wake interactions

Navier–Stokes simulations of the agitation generated by a homogeneous swarm of high-Reynolds-number rising bubbles are performed. The bubbles are modelled by fixed momentum sources of finite size randomly distributed in a uniform flow. The mesh grid is regular with a spacing close to the bubble size. This allows us to simulate a swarm of a few thousand bubbles in a computational domain of a hundred bubble diameters, which corresponds to a gas volume fraction α from 0.6% to 4%. The small-scale disturbances close to the bubbles are not resolved but the wakes are correctly described from a distance of a few diameters. This simple model reproduces well all the statistical properties of the vertical velocity fluctuations measured in previous experiments: scaling as α0.4, self-similar probability density functions and power spectral density including a subrange evolving as the power −3 of the wavenumber k. It can therefore be concluded that bubble-induced agitation mainly results from wake interactions. Considering the flow in a frame that is fixed relative to the bubbles, the combined use of both time and spatial averaging makes it possible to distinguish two contributions to the liquid fluctuations. The first is the spatial fluctuations that are the consequence of the bubble mean wakes. The second corresponds to the temporal fluctuations that are the result of the development of a flow instability. Note that the latter is not due to the destabilization of individual bubble wakes, since a computation with a single bubble leads to a steady flow. It is a collective instability of the randomly distributed bubble wakes. The spectrum of the time fluctuations shows a peak around a frequency fcwi, which is independent of α. From the present results it is possible to determine the origin of the overall properties of the total fluctuations observed in the experiments. The scaling of the velocity fluctuation as α^0.4 is a combination of the scalings of the spatial and temporal fluctuations, which are different from each other. As the time fluctuations are symmetric in the vertical direction, the asymmetry of the probability density function of the vertical velocity comes from that of the spatial fluctuations. Both contributions exhibit a k−3 spectral behaviour around the same range of wavenumbers, which explains why it is observed regardless of the nature of the dominant contribution

Multiple-Table Data in R with the multitable Package

Data frames are integral to R. They provide a standard format for passing data to model-fitting and plotting functions, and this standard makes it easier for experienced users to learn new functions that accept data as a single data frame. Still, many data sets do not easily fit into a single data frame; data sets in ecology with a so-called fourth- corner problem provide important examples. Manipulating such inherently multiple-table data using several data frames can result in long and difficult-to-read workflows. We introduce the R multitable package to provide new data storage objects called data.list objects, which extend the data.frame concept to explicitly multiple-table settings. Like data frames, data lists are lists of variables stored as vectors; what is new is that these vectors have dimension attributes that make accessing and manipulating them easier. As data.list objects can be coerced to data.frame objects, they can be used with all R functions that accept an object that is coercible to a data.frame

Etude du regret après stérilisation tubaire par dispositif ESSURE ®

Introduction : Les techniques de stérilisation sont irréversibles. Les femmes choisissant cette contraception peuvent donc regretter leur décision. Depuis 2002, le nombre de stérilisations tubaires réalisées par voie hystéroscopique par la technique Essure® augmente. Sa simplicité, son faible risque opératoire et l absence d anesthésie en font la première technique de stérilisation tubaire en France. Les médecins de soins primaires, acteurs essentiels dans la contraception, doivent pouvoir informer sur cette technique. Le taux de regret après stérilisation par Essure ® n a jamais été évalué. C est le but de cette étude. Méthodes : Toutes les patientes ayant bénéficié d une stérilisation par Essure ® dans les hôpitaux Bicêtre et Béclère entre juin 2005 et décembre 2011 ont été inclues. Celles ayant une indication médicale de stérilisation ainsi que les obturations d hydrosalpinx ont été exclues. Un questionnaire a été envoyé à toutes. Résultats : Durant la période de l étude, 452 patientes ont bénéficié d une stérilisation par Essure ®. 306 (67,7 %) ont répondu. L âge moyen lors de la stérilisation était de 41,1 ans. Le recul moyen après stérilisation était de 3,58 ans. 17 patientes (5,5 %) ont exprimé un sentiment de regret après stérilisation. 7 (2,3 %) ont consulté pour envisager une nouvelle grossesse. Aucune n a encore réalisé ce projet. Les patientes n ayant pas parlé de la stérilisation avec leur conjoint et celles ayant des problèmes conjugaux à ce moment-là semblent plus à risque de regretter. Conclusion : Le regret après stérilisation tubaire par hystéroscopie est un évènement peu fréquent. Chez la patiente désireuse d une telle contraception, le médecin doit ainsi savoir identifier les potentiels facteurs de risque de regret afin de l accompagner au mieux dans son choixPARIS12-Bib. électronique (940280011) / SudocSudocFranceF

Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

The time discretization of gradient flows in metric spaces uses variants of the celebrated implicit Euler-type scheme of Jordan, Kinderlehrer and Otto. We propose in this Note a different approach which allows to construct two second order in time numerical schemes. We show that these schemes are well defined and prove (theoretically and numerically) the convergence for a gradient flow in the Wasserstein space corresponding to a Fokker–Planck equation