Sur le problème de Plateau pour un quadrilatère variable qui peut acquérir un point double

Résumé Soit Γ un quadrilatère variable, dont deux c?tés opposés A₂A₃, A₁A₄ sont dans les plans x₃=c, x₃=−c. Quand c tend vers0, Γ tend vers un quadrilatèreΓ ⁰ présentant un point double, A⁰. Le travail étudie la représentation conforme sur le demi-plan R(ix)<0 (ou sur le cercle - unité) de la surface minimale ∑ passant par Γ. Il montre (§ I) que si les affixes x de A₁, A₂, A₄ sont 0, 1, ∞, l'affixe de A₃ sera ɛ⁻², où ɛ tend vers 0 avec c. Il étudie (§ II) l'allure pour ɛ tendant vers 0 des intégrales canoniques de l'équation linéaire du problème. La forme de la relation entre ɛ et c est indiquée au n^o 19; on montre que dans la région de striction ɛ |x| reste borné et que la surface ∑ y est assimilable à une surface minimale simple: la surface de vis à filet carré. La représentation conforme de l'une des deux régions de ∑ qui tendent à se séparer l'une de l'autre tend à envahir tout le demi-plan (ou tout le cercle-unité). Les représentations conformes de ∑ pour c>0 et c<0 ne sont pas analytiquement distinctes (n⁰ 20). A titre d'exemple, on étudie (n⁰ 21) le cas où ∑ possède un axe de symétrie. A M. Enrico Bompiani pour son Jubilé scientifique     

Facile preparation of single-crystalline nanowires of γMnOOH and βMnO2

A facile method has been developed to synthesize single-crystalline manganese (oxyhydr)oxide nanowires. A pure phase of single-crystalline MnOOH nanowires with the lengths of several hundred nanometres to several micrometers and the diameters of 5–40 nm was synthesized by hydrothermal transformation of commercial granular - or MnO₂ in water, and single-crystalline MnO₂ and polycrystalline Mn₂O₃ nanowires formed after subsequent calcination at 300 and 600 °C of the as-prepared MnOOH nanostructures, respectively. These low-dimensional nanostructured materials may find novel properties and provide more possible applications in lithium batteries and catalysis. PACS 81.07.-b; 81.10.Dn; 81.16.Be     

Accurate free energies of micelle formation

We determine the free energy of micelle formation for model surfactants in a Lennard-Jones solvent by employing a hybrid semi-grand Monte Carlo simulation scheme in combination with umbrella sampling and configurational bias techniques. Comparing the results to theoretical prediction, we obtain good agreement for large micellar sizes. We also study the effect of changing the surfactant headgroup size and tail length on the critical micelle concentration. The values of and the trends in the calculated critical micelle concentrations do agree with experimental observation for nonionic surfactants. The results open up the way for the calculation of critical micelle concentrations using realistic atomic force fields.     

Atomic-scale imaging of wall-by-wall breakdown and concurrent transport measurements in multiwall carbon nanotubes

We report the atomic-scale imaging with concurrent transport measurements of the breakdown of individual multiwall carbon nanotubes inside a transmission electron microscope equipped with a piezomanipulator. We found unexpectedly three distinct breakdown sequences: namely, from the outermost wall inward, from the innermost wall outward, and alternatively between the innermost and the outmost walls. Remarkably, a significant amount of current drop was observed when an innermost wall is broken, proving unambiguously that every wall is conducting. Moreover, the breakdown of each wall in any sequence initiates in the middle of the nanotube, not at the contact, proving that the transport is not ballistic.     

Evidence for strain glass in the ferroelastic-martensitic system Ti(50-x)Ni(50+x)

We report here "strain glass," a new glassy phenomenon in ferroelastic-martensitic system of Ni-rich intermetallic Ti(50-x)Ni(50+x) (x > 1), where local strain is frozen in disordered configuration below a critical temperature Tg. The ac elastic modulus shows a minimum at Tg, which exhibits logarithmic frequency dependence following Vogel-Fulcher relationship, and the corresponding internal friction shows a frequency-dependent peak located at a lower temperature. In situ high-resolution transmission electron microscopy observations reveal uncorrelated nanoclusters of martensiticlike phase, randomly frozen in the otherwise untransformed parentlike matrix. Being parallel to spin glass and relaxor, strain glass may shed new light on the fundamental physics of glass and lead to the discovery of novel properties.     

Nanoscale probing of adsorbed species by tip-enhanced Raman spectroscopy

Tip-enhanced Raman spectroscopy (TERS) is based on the optical excitation of localized surface plasmons in the tip-substrate cavity, which provides a large but local field enhancement near the tip apex. We report on TERS with smooth single crystalline surfaces as substrates. The adsorbates were CN- ions at Au(111) and malachite green isothiocyanate (MGITC) molecules at Au(111) and Pt(110) using either Au or Ir tips. The data analysis yields Raman enhancements of about 4 x 10(5) for CN- and up to 10(6) for MGITC at Au(111) with a Au tip, probing an area of less than 100 nm radius.     

A new direction in carbon-rich organometallic wires: diruthenium compounds bridged by E-hex-3-ene-1,5-diyn-diyl

New organometallic wires were obtained from two diruthenium units bridged by E-hex-3-ene-1,5-diyn-dyl.