Asymptotic behaviour of disconnection and non-intersection exponents

Summary. We study the asymptotic behaviour of disconnection and non-intersection exponents for planar Brownian motionwhen the number of considered paths tends to infinity. In particular, if η _n (respectively ξ (n, p)) denotes the disconnection exponent for n paths (respectively the non-intersection exponent for n paths versus p paths), then we show that lim _{n →∞} η _n /n = 1 2 and that for a > 0 and b > 0,lim _{n →∞} ξ ([na],[nb])/n = (√ a + √ b) ² /2. Received: 28 February 1996 / In revised form: 3 September 1996     

SLEs as boundaries of clusters of Brownian loops

In this research announcement, we show that SLE curves can in fact be viewed as boundaries of certain clusters of Brownian loops (of the clusters in a Brownian loop soup). For small densities c of loops, we show that the outer boundaries of the clusters created by the Brownian loop soup are SLE_κ-type curves where κ∈(8/3,4] and c related by the usual relation c=(3κ?8)(6?κ)/2κ (i.e., c corresponds to the central charge of the model). This gives (for any Riemann surface) a simple construction of a natural countable family of random disjoint SLE_κ loops, that behaves “nicely” under perturbation of the surface and is related to various aspects of conformal field theory and representation theory. To cite this article: W. Werner, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Stuck walks

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the neighbourhood of their current position. We prove that in a range of the relevant parameter of the model such random walkers can be eventually confined to a finite interval of length depending on the parameter value. The phenomenon arises as a result of competing self-attracting and self-repelling effects where in the named parameter range the former wins.     

Über geschlossene Laplace-Ketten ungerader Periodenzahl

Ohne Zusammenfassung     

Conformal restriction: The chordal case

We characterize and describe all random subsets of a given simply connected planar domain (the upper half-plane , say) which satisfy the ``conformal restriction' property, i.e., connects two fixed boundary points ( and , say) and the law of conditioned to remain in a simply connected open subset of is identical to that of , where is a conformal map from onto with and . The construction of this family relies on the stochastic Loewner evolution processes with parameter and on their distortion under conformal maps. We show in particular that SLE is the only random simple curve satisfying conformal restriction and we relate it to the outer boundaries of planar Brownian motion and SLE.     

Highly sensitive optical detection of humidity on polymer/metal nanoparticle hybrid films

Porous metal films for optical humidity sensing were prepared from copper nanoparticles protected by a 2-3 nm carbon coating, a silicon tenside, and a polymeric wetting agent. Exposure to water or solvent vapor revealed an exceptional sensitivity with optical shifts in the visible light range of up to 50 nm for a change of 1% in relative humidity. These properties could be attributed to a combination of surface plasmon resonance effects at low humidity and thin film interference at higher water or solvent concentration in the surrounding air. The simple concept and use of ultra-low-cost materials suggests application of such porous metal-film-based optical humidity sensors in large-scale applications for food handling, storage, and transport.     

Preparation of Functionalized Carbon-Coated Cobalt Nanoparticles with Sulfonated Arene Derivatives,a Study on Surface Functionalization and Stability

The functionalization of magnetic nanoparticles has been an important field in the last decade due to the versatile applications in catalysis and biomedicine. Generally, a high degree of functionalities on the surface of the nanoparticles is desired. In this study, covalent functionalization of various aromatic sulfonic acids on carbon-coated cobalt nanoparticles are investigated on surface functionalization yield and stability. The nanoparticles are prepared via covalent linkage of an in situ generated diazonium on the graphene-like surface. Adsorption and wash experiments were performed to confirm a covalent bonding of the naphthalene derivatives on the nanoparticle surface. With an increased number of sulfonic acid groups on the aromatic compound a significantly lower loading is observed on the corresponding functionalized nanoparticles. This can be counteracted by a change of nitrite species. With this method, nanoparticles with a high number of sulfonic acid groups can be produced.     

Glass and bioglass nanopowders by flame synthesis

The preparation of amorphous nanopowders by flame synthesis opens access to common soda-lime, metal-doped glasses or bioglasses in the range of 20-80 nm and offers an alternative to conventional wet-phase preparation, solid state reactions or melting.