Christophe Brun

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This article presents the formal design of a functional algorithm which computes the convex hull of a finite set of points incrementally. This algorithm, specified in Coq, is then automatically extracted into an OCaml-program which can be plugged into an interface for data input (point selection) and graphical visualization of the output. A formal proof of(More)
The energy gap Delta of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Delta was found to decrease from its bulk value as a function of inverse island thickness. Corresponding T_{c} values, estimated using bulk gap-to-T_{c} ratio, are in quantitative agreement(More)
Electrical contacts between nanoengineered systems are expected to constitute the basic building blocks of future nanoscale electronics. However, the accurate characterization and understanding of electrical contacts at the nanoscale is an experimentally challenging task. Here, we employ low-temperature scanning tunneling spectroscopy to investigate the(More)
The two charge-density wave (CDW) transitions in NbSe3 were investigated by scanning tunneling microscopy (STM) on an in situ cleaved (b, c) plane. The temperature dependence of first-order CDW satellite spots, obtained from the Fourier transform of the STM images, was measured between 5 and 140 K to extract the surface critical temperatures (T{s}). The(More)
We report on scanning-tunneling microscopy experiments in a charge-density wave (CDW) system allowing visually capturing and studying in detail the individual solitons corresponding to the self-trapping of just one electron. This "Amplitude Soliton" is marked by vanishing of the CDW amplitude and by the π shift of its phase. It might be the realization of(More)
This article deals with a method to build programs in computational geometry from their specifications. It focuses on a case study namely computing incrementally the convex hull of a set of points in the plane using hypermaps. Our program to compute convex hulls is specified and proved correct using the Coq proof assistant. A concrete implementation in(More)
1 Faculté des Sciences de Base, Ecole Polytechnique Fédérale de Lausanne, Institut de Physique de la Matière Condensée, Lausanne, Switzerland 2 Key Laboratory for Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing, China 3 Institut des Nanosciences de Paris, Université Pierre et Marie Curie and CNRS-UMR 7588,(More)
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