Un processus effectif de détermination des systoles pour les surfaces hyperboliques

We give an effective process to discribe explicitly the systols of an hyperbolic surface depending on his Fenchel-Nielsen coordinates.      

Modelling Unsaturated Moisture Transport in Heterogeneous Limestone

The influence of macro-scale heterogeneities on the imbibition process is investigated for Savonnières, a French layered limestone. Free uptake experiments are performed both parallel and perpendicular to the bedding. It is found that the position of the different layers, and the exact material properties inside each layer can significantly influence the imbibition process. The experimental results are compared with numerical simulations. For the flow simulations, moisture permeability of the different layers is obtained with the upscaling technique presented in Part 1. Good agreement between simulations and experiments validate the proposed upscaling from meso to macroscopic scale.     

Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions

The rheological behavior of a cetylpyridinium chloride 100 mmol l^–1/sodium salicylate 60 mmol l^–1 aqueous solution was studied in this work under homogeneous (cone and plate) and non-homogeneous flow conditions (vane-bob and capillary rheometers), respectively. Instabilities consistent with non-monotonic flow curves were observed in all cases and the solution exhibited similar behavior under the different flow conditions. Hysteresis and the sigmoidal flow curve suggested as characteristic of systems that show constitutive instabilities were observed when running cycles of increasing and decreasing stress or shear rate, respectively. This information, together with a detailed determination of steady states at shear stresses close to the onset of the instabilities, allowed one to show unequivocally that "top and bottom jumping" are the mechanisms to trigger the instabilities in this micellar system. It is shown in addition that there is not a true plateau region in between the "top and bottom jumping". Finally, the flow behavior beyond the upturn seemed to be unstable and was found accompanied by an apparent violation of the no-slip boundary condition.     

Radiation degradation of methyl α-chloroacrylate–methacrylonitrile copolymers

The radiation degradation behavior of methyl α-chloroacrylate (MCA) and methacrylonitrile (MCN) copolymers has been investigated as part of a program to develop high-sensitivity polymeric resists for integrated circuit manufacture. High-molecular-weight copolymers were prepared by emulsion techniques. Several different copolymer compositions were prepared varying from 19 to 68 mole % MCA. These copolymers were fractionated and then subjected to γ irradiation from a ⁶⁰Co Source. The G_s - G_s, G_s - 4G_s values were determined from M?;F>n_k^?1 and G_u^?1 versus dose plots, and the G_fs and G_s Values were then calculated. Molecular weights of both unirradiated and irradiated polymers were analyzed by membrane osmometry and gel permeation chromatography. All copolymers exhibited higher degradation susceptibilities than that of poly(methyl methacrylate) (PPMA), which has G_x = 1.3. The individual G_x and G_x values of the copolymers were found to fall between those of the two homopolymers, poly(methyl α-chloroacrylate) (G_x = 6.0) and polymethacrylonitrile (G_x ～ 3.1). The dependence of G_x and G_x values on molecular weight was minor. The crosslinking susceptibility of the poly(methyl α-chloroacrylate) (G_x ～ 0.8), was greatly decreased by copolymerization with MCN. Relatively small amounts of MCN caused a large drop in G_x, i.e., G_x ～ 0.15 at 32% MCN and G_x ～ 0.03 at 51% MCN. The observation could be attributed to the decreasing probability that crosslinking sites, in the MCA monomer units on adjacent chains, would lie in close proximity.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

The Estimation of Multiple Light Scattering in Turbid Colloidal Suspensions using a 2-Probe Detector

This paper describes a detector for the direct measurement of multiple scattering in moderately turbid colloidal suspensions. The detector uses two optical fibers aligned so that one of the fibers measures the total signal (single and multiple scattering) and the other measures multiple scattering only. We report the results of preliminary investigations, and show how such a detector can be used to aid both static and dynamic light scattering investigations. In the former case we show how this information can be used to correct for low level multiple scattering. The utility and limitations of the technique are discussed.     

The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is {1+\sqrt{2}}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is ${\mu=\sqrt{2+\sqrt{2}}}$ . A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with ${n\in [-2,2]}$ (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface fugacity y associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov’s identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be ${y_{\rm c}=1+2/\sqrt{2-n}}$ . This value plays a crucial role in our generalized identity, just as the value of the growth constant did in Smirnov’s identity. For the case n = 0, corresponding to self-avoiding walks interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height T, taken at its critical point 1/μ, tends to 0 as T increases, as predicted from SLE theory.     

Coarsening-resistant Ag nanoparticles stabilized on amorphous TiO<Subscript>x</Subscript> nanoparticles

Bare Ag nanoparticles (～10 nm) and Ag nanoparticles (1–20 nm) on the surfaces of larger TiO_x nanoparticles were prepared by laser ablation of microparticle aerosols (LAMA). The behaviors of the nanoparticles during high temperature annealing were then studied with ex situ and in situ transmission electron microscopy. For the ex situ heating experiments, Ag and Ag-on-TiO_x NPs were collected onto gold TEM grids and subjected to annealing treatments at 500 °C in argon, vacuum, and air. At this temperature, bare Ag NPs on carbon TEM supports coarsened rapidly in both air and argon atmospheres. In contrast, Ag-on-TiO_x NPs that were heated to 500 °C in flowing argon or in a vacuum did not coarsen significantly and were remarkably stable. Ag-on-TiO_x NPs that were heated to 500 °C in air, however, behaved quite differently. The TiO_x crystallized upon heating and a significant loss of Ag were observed from the surfaces of the TiO_x, likely due to sublimation. These results demonstrate that the surface defect structure and chemistry of the oxide support strongly influence the thermal stability of Ag NPs produced by LAMA.     

A study of the Immune Epitope Database for some fungi species using network topological indices

In the last years, the encryption of system structure information with different network topological indices has been a very active field of research. In the present study, we assembled for the first time a complex network using data obtained from the Immune Epitope Database for fungi species, and we then considered the general topology, the node degree distribution, and the local structure of this network. We also calculated eight node centrality measures for the observed network and compared it with three theoretical models. In view of the results obtained, we may expect that the present approach can become a valuable tool to explore the complexity of this database, as well as for the storage, manipulation, comparison, and retrieval of information contained therein.