The Regularity of Optimal Irrigation Patterns

A branched structure is observable in draining and irrigation systems, in electric power supply systems, and in natural objects like blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s ^α with 0 < α < 1. The aim of this paper is to prove the regularity of paths (rivers, branches,...) when the irrigated measure is the Lebesgue density on a smooth open set and the irrigating measure is a single source. In that case we prove that all branches of optimal irrigation trees satisfy an elliptic equation and that their curvature is a bounded measure. In consequence all branching points in the network have a tangent cone made of a finite number of segments, and all other points have a tangent. An explicit counterexample disproves these regularity properties for non-Lebesgue irrigated measures.     

In Process Citation

Metal phosphorothioates are titrated in acetone, acetonitrile and dimethylformamide with potassium hydroxide, with potentiometric detection. They can be titrated in the presence of the corresponding phosphorothioic acids in the dimethylformamide.     

Sur la synthese d'isosteres thiopheniques des flavones,thioflavones et xanthones

Synthesis of 5-aryl[3,2-b]thieno-7-pyranones or thiopyranones and [3,2-b]thieno-9-chromenones from 3-methoxy or 3-thiomethoxy thiophenes is described, involving the use of pyridinium chlorhydrate as a cyclising and demethylating agent.     

Gluon identification in planar e+e− events

A method is proposed to identify gluon jets in the planar hadronic events recently found in e⁺e^? annihilation. If a fast hadron is detected at a given angle θ_h ? 30° with respect to the axis opposite to the thrust axis, it is most probably a quark (or antiquark) fragment. An explicit formula then predicts the angle and energy of the unbiased accompanying gluon.     

Roughness analysis of the cracked surfaces of a face centered cubic alloy

Intergranular and transgranular fracture surfaces obtained in a face centered cubic alloy are studied using 3D maps reconstructed by scanning electron microscopy stereo imaging. The roughness exponents measured in the intergranular and transgranular surfaces, respectively, zeta = 0.83 +/- 0.05 and zeta = 0.75 +/- 0.05, are in agreement with the universal roughness value of 3D fractures. However, the slightly smaller value related to the transgranular surface could be a consequence of crystallographic transgranular zones disseminated on the surface whose roughness exponent zeta = 0.65 +/- 0.07 is close to the one usually measured on 2D fractures.     

Novel microscopic mechanism of intermixing during growth on soft metallic substrates

Generic computer simulations using empiric interatomic potentials suggest a new, collective mechanism that could be responsible for mixing at heteroepitaxial interfaces. Even if single adsorbate atoms diffuse by hopping on the substrate surface and do not mix at the terraces, two-dimensional islands formed by nucleation may become unstable above a certain critical size and explode upwards forming clusters of several atomic layers. This process is accompanied by strong distortions of the underlying atomic layers, and on soft materials it can result in surface etching and incorporation of substrate atoms into the islands.     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Crosslinking and ageing of C labelled polyisoprene part 1: Synthesis and polymerisation of 4-C-isoprene

4-¹³C-isoprene was prepared by the Wittig reaction. All reaction steps were optimised using unlabelled compounds. By reaction with triphenyl phosphine, ¹³C labelled methyl iodide afforded labelled methyl-triphenyl phosphine iodide in 84% yield. This reacted with meth acrolein with production of 4-¹³C-isoprene in 64% yield. Labelled polyisoprene was prepared by anionic polymerisation initiated by t-butyl lithium. Based on ¹³CH₃I the overall yield is ca 30%. The polymer was characterized by ¹H and ¹³C NMR spectroscopy. The contribution of each microstructure was [cis 1-4, 72%]; [trans 1-4, 10%]; [3-4, 18%].     

Comparison of several models for multi-size bubbly flows on an adiabatic experiment

This paper deals with the modelling and numerical simulation of isothermal bubbly flows with multi-size bubbles. The study of isothermal bubbly flows without phase change is a first step towards the more general study of boiling bubbly flows. Here, we are interested in taking into account the features of such isothermal flow associated to the multiple sizes of the different bubbles simultaneously present inside the flow. With this aim, several approaches have been developed. In this paper, two of these approaches are described and their results are compared to experimental data, as well as to those of an older approach assuming a single average size of bubbles. These two approaches are (i) the moment density approach for which two different expressions for the bubble diameter distribution function are proposed and (ii) the multi-field approach. All the models are implemented into the NEPTUNE_CFD code and are compared to a test performed on the MTLOOP facility. These comparisons show their respective merits and shortcomings in their available state of development.