Canonical surfaces with big cotangent bundle

Surfaces of general type with positive second Segre number are known to have big cotangent bundle. We give a new criterion ensuring that a surface of general type with canonical singularities has a minimal resolution with big cotangent bundle. This provides many examples of surfaces with negative second Segre number and big cotangent bundle.Comment: 11 pages. Comments welcom

Mechanical properties of the elemental nanocomponents of nacre structure

Sheet nacre is a nanocomposite with a multiscale structure displaying a lamellar “bricks and mortar” microarchitecture. In this latter, the brick refer to aragonite platelets and the mortar to a soft organic biopolymer. However, it appears that each brick is also a nanocomposite constituted as CaCO3 nanoparticles reinforced organic composite material. What is the role of this “intracrystalline” organic phase in the deformation of platelet? How does this nanostructure control the mechanical behaviour of sheet nacre at the macroscale? To answer these questions, the mechanical properties of each nanocomponents are successively investigated and computed using spherical and sharp nanoindentation tests combined with a structural model of the organomineral platelets built from AFM investigations

On the hyperbolicity of surfaces of general type with small c12c_1 ^2

Surfaces of general type with positive second Segre number $s_2:=c_1^2-c_2>0$ are known by results of Bogomolov to be quasi-hyperbolic i.e. with finitely many rational and elliptic curves. These results were extended by McQuillan in his proof of the Green-Griffiths conjecture for entire curves on such surfaces. In this work, we study hyperbolic properties of minimal surfaces of general type with minimal $c_1^2$, known as Horikawa surfaces. In principle these surfaces should be the most difficult case for the above conjecture as illustrate the quintic surfaces in \bP^3. Using orbifold techniques, we exhibit infinitely many irreducible components of the moduli of Horikawa surfaces whose very generic member has no rational curves or even is algebraically hyperbolic. Moreover, we construct explicit examples of algebraically hyperbolic and (quasi-)hyperbolic orbifold Horikawa surfaces.Comment: 25 pages; final version to appear in J. Lond. Math. So

La Nacre, les biominéralisations et la pharmacopée

International audienceLa Nacre n'a rien de commun avec les pierres précieuses comme le diamant qui est forgé à des centaines de kilomètres au cœur de la Terre. Rien de commun non plus avec le rubis né des forces tectoniques qui font surgir les montagnes. Non ! La Nacre est une structure fascinante produite par le monde vivant. Comment l'Évolution biologique a-t-elle réussi à produire ce joyau ? Cet article nous montre qu'il s'agit de l'aboutissement d'un long processus qui a commencé il y a des milliards d'années sur Terre avec la vie elle-même ! Les chercheurs l'appellent biominéralisation c'est-à-dire le processus que la vie a élaboré et maîtrisé pour développer les tissus minéralisés comme les coquilles, les dents ou les os

Nano-Composite Structure of Nacre Biocrystal.

Pucon - ChiliIntermittent-Contact Atomic Force Microscopy with phase detection imaging reveals a nanostructure within the tablet (Pinctada maxima). A continuous organic framework divides each tablet into nanograins. Their mean extension is 45nm. Transmission electron microscopy performed in the darkfield mode evidences that intracrystalline matrix is highly crystallized and responds like a ‘single crystal'. The organic matrix is continuous inside the tablet, mineral phase is thus finely divided but behaves in the same time as a single crystal. It is proposed that each tablet results from the coherent aggregation of nanograins keeping strictly the same crystallographic orientation thanks to an hetero-epitaxy mechanism

Voronoi Growth Model of Sheet Nacre.

The aim of this work was to study the tiling mode of nacre tablets in the 'brick and mortar' array of sheet nacre. For that purpose, incipient shell nacre (Pinctada margaritifera) was analysed by electron microscopy (SEM) and Raman spectroscopy. Experimental observations pointed out the key role of the stairs-like growing front in sheet-like nacre not only for its long range ordering but also as controlling the hierarchy of local mechanisms. A morphogenesis sequence is proposed taking into account the dynamics of the environment. First, the mantel cells are organised to synthesise and discharge alternatively the extrapallial fluid as batches. Because of the stairs-like feature of the growth front, the extrapallial fluid organizes as successive 'biological films', each of them delayed from the underlying one by 10 to 15µm. Each film is a compartment to prefigure a nacre layer. Then, after individualisation, this film undergoes nucleation and crystallisation of tablets. Finally, the biological film transforms progressively as mature nacre following self assembly mechanisms. The resulting tablets have a shape which responds to a Voronoi growth model, this is shown for the first time: aggregation at the same speed in all directions around single growth centers. This is an efficient model to understand the growth mechanism and rationalise all the experimental observations we have obtained

Nacre biocrystal thermal behavior

International audienceThe thermal behaviour of Pinctada margaritifera nacre was studied at different temperatures by means of thermal gravimetric, thermo-mechanical and Rock-Eval analyses. From the mechanical point of view nacre exhibited a complete reversible behaviour up to 230 °C. The bio-aragonite allotrope was seen to be as stable as the abiotic aragonite up to 470–500 °C. It was also evidenced that the organic phase was keeping cracking oxygen functions at temperatures as high as 650 °C. Nacre thermal behaviour could be described following four distinctive stages and discussed in comparison with previous data obtained in oxidative conditions