Asymptotics of an optimal compliance-location problem

We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the minimization problem, after properly scaling the functionals involved, and to the limit distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.Comment: 20 pages with 2 figures; final accepted version (minor changes, some extra details on the positivity assumption on $f$

Graphene on the C-terminated SiC (000 1ˉ\bar{1}) surface: An ab initio study

The atomic and electronic structures of a graphene layer on top of the $(2\times2)$ reconstruction of the SiC (000$\bar{1}$) surface are studied from ab initio calculations. At variance with the (0001) face, no C bufferlayer is found here. Si adatoms passivate the substrate surface so that the very first C layer presents a linear dispersion characteristic of graphene. A small graphene-substrate interaction remains in agreement with scanning tunneling experiments (F.Hiebel et al. {\it Phys. Rev. B} {\bf 78} 153412 (2008)). The stacking geometry has little influence on the interaction which explains the rotational disorder observed on this face.Comment: 4 pages, 3 figures, additional materia

Conception d'un épandeur de fumures organiques pour les exploitations à traction animale d'Afrique

Design of an Animal-drawn Manure Spreader for Small Farms in Africa. Les bilans azotés des farines d'asticots de 2 jours séchés pendant 12, 24 et 48 heures à 70 °C ont été étudiés. Parmi elles, la farine dérivée d'asticots séchés durant 24 heures a le meilleur bilan azoté, du reste inférieur à celui de la caséine. Toutefois, au regard de la valeur de leurs bilans azotés, ces farines d'asticots séchés apparaissent globalement comme une source potentielle de protéine pour l'alimentation animale

Electron states of mono- and bilayer graphene on SiC probed by STM

We present a scanning tunneling microscopy (STM) study of a gently-graphitized 6H-SiC(0001) surface in ultra high vacuum. From an analysis of atomic scale images, we identify two different kinds of terraces, which we unambiguously attribute to mono- and bilayer graphene capping a C-rich interface. At low temperature, both terraces show $(\sqrt{3}\times \sqrt{3})$ quantum interferences generated by static impurities. Such interferences are a fingerprint of $\pi$-like states close to the Fermi level. We conclude that the metallic states of the first graphene layer are almost unperturbed by the underlying interface, in agreement with recent photoemission experiments (A. Bostwick et al., Nature Physics 3, 36 (2007))Comment: 4 pages, 3 figures submitte

Quasiparticle Chirality in Epitaxial Graphene Probed at the Nanometer Scale

Graphene exhibits unconventional two-dimensional electronic properties resulting from the symmetry of its quasiparticles, which leads to the concepts of pseudospin and electronic chirality. Here we report that scanning tunneling microscopy can be used to probe these unique symmetry properties at the nanometer scale. They are reflected in the quantum interference pattern resulting from elastic scattering off impurities, and they can be directly read from its fast Fourier transform. Our data, complemented by theoretical calculations, demonstrate that the pseudospin and the electronic chirality in epitaxial graphene on SiC(0001) correspond to the ones predicted for ideal graphene.Comment: 4 pages, 3 figures, minor change

Quantum Transport in Chemically-modified Two-Dimensional Graphene: From Minimal Conductivity to Anderson Localization

An efficient computational methodology is used to explore charge transport properties in chemically-modified (and randomly disordered) graphene-based materials. The Hamiltonians of various complex forms of graphene are constructed using tight-binding models enriched by first-principles calculations. These atomistic models are further implemented into a real-space order-N Kubo-Greenwood approach, giving access to the main transport length scales (mean free paths, localization lengths) as a function of defect density and charge carrier energy. An extensive investigation is performed for epoxide impurities with specific discussions on both the existence of a minimum semi-classical conductivity and a crossover between weak to strong localization regime. The 2D generalization of the Thouless relationship linking transport length scales is here illustrated based on a realistic disorder model.Comment: 14 pages, 18 figures, submitte

Screening and interlayer coupling in multilayer graphene field-effect transistors

With the motivation of improving the performance and reliability of aggressively scaled nano-patterned graphene field-effect transistors, we present the first systematic experimental study on charge and current distribution in multilayer graphene field-effect transistors. We find a very particular thickness dependence for Ion, Ioff, and the Ion/Ioff ratio, and propose a resistor network model including screening and interlayer coupling to explain the experimental findings. In particular, our model does not invoke modification of the linear energy-band structure of graphene for the multilayer case. Noise reduction in nano-scale few-layer graphene transistors is experimentally demonstrated and can be understood within this model as well.Comment: 13 pages, 4 figures, 20 reference

Localization of Dirac electrons by Moire patterns in graphene bilayers

We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.Comment: 4 pages, 5 figure