Publications

2015

• Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
  
  • Bethuel Fabrice
  • Gravejat Philippe
  • Smets Didier
  Annales Scientifiques de l'École Normale Supérieure, Gauthier-Villars ; Société mathématique de France, 2015, 48 (6), pp.1327-1381. We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the energy space. In particular, our results do not require smallness in some weighted spaces or a priori spectral assumptions. Our strategy is reminiscent of the one used by Martel and Merle in various works regarding generalized Korteweg-de Vries equations. The important feature of our contribution is related to the fact that while Korteweg-de Vries equations possess unidirectional dispersion, Schrödinger equations do not.
• Le presque, le non, l'anti et la rigueur
  
  • Paul Thierry
  , 2015. Diverses apparitions du "presque"en mathématiques sont envisagées dans une perspective philosophique.
• Countability properties of some Berkovich spaces
  
  • Favre Charles
  , 2015. We prove that any compact Berkovich space over the field of Laurent series over an arbitrary field is angelic. In particular, is it sequentially compact.
• Measuring a Cherenkov ring in the radio emission from air showers at 110–190MHz with LOFAR
  
  • Nelles A.
  • Schellart P.
  • Buitink S.
  • Corstanje A.
  • de Vries K.D.
  • Enriquez J.E.
  • Falcke H.
  • Frieswijk W.
  • Hörandel J.R.
  • Scholten O.
  • ter Veen S.
  • Thoudam S.
  • van den Akker M.
  • Anderson J.
  • Asgekar A.
  • Bell M.E.
  • Bentum M.J.
  • Bernardi G.
  • Best P.
  • Bregman J.
  • Breitling F.
  • Broderick J.
  • Brouw W.N.
  • Brüggen M.
  • Butcher H.R.
  • Ciardi B.
  • Deller A.
  • Duscha S.
  • Eislöffel J.
  • Fallows R.A.
  • Garrett M.A.
  • Gunst A.W.
  • Hassall T.E.
  • Heald G.
  • Horneffer A.
  • Iacobelli M.
  • Juette E.
  • Karastergiou A.
  • Kondratiev V.I.
  • Kramer M.
  • Kuniyoshi M.
  • Kuper G.
  • Maat P.
  • Mann G.
  • Mevius M.
  • Norden M.J.
  • Paas H.
  • Pandey-Pommier M.
  • Pietka G.
  • Pizzo R.
  • Polatidis A.G.
  • Reich W.
  • Röttgering H.
  • Scaife A.M.M.
  • Schwarz D.
  • Smirnov O.
  • Stappers B.W.
  • Steinmetz M.
  • Stewart A.
  • Tagger Michel
  • Tang Y.
  • Tasse C.
  • Vermeulen R.
  • Vocks C.
  • van Weeren R.J.
  • Wijnholds S.J.
  • Wucknitz O.
  • Yatawatta S.
  • Zarka P.
  Astroparticle Physics, Elsevier, 2015, 65, pp.11–21. Measuring radio emission from air showers offers a novel way to determine properties of the primary cosmic rays such as their mass and energy. Theory predicts that relativistic time compression effects lead to a ring of amplified emission which starts to dominate the emission pattern for frequencies above ∼100∼100 MHz. In this article we present the first detailed measurements of this structure. Ring structures in the radio emission of air showers are measured with the LOFAR radio telescope in the frequency range of 110–190 MHz. These data are well described by CoREAS simulations. They clearly confirm the importance of including the index of refraction of air as a function of height. Furthermore, the presence of the Cherenkov ring offers the possibility for a geometrical measurement of the depth of shower maximum, which in turn depends on the mass of the primary particle. (10.1016/j.astropartphys.2014.11.006)
  DOI : 10.1016/j.astropartphys.2014.11.006