On the Estimation of Bivariate Return Curves for Extreme Values

In the multivariate setting, defining extremal risk measures is important in many contexts, such as finance, environmental planning and structural engineering. In this paper, we review the literature on extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level, and propose new estimation methods based on multivariate extreme value models that can account for both asymptotic dependence and asymptotic independence. We identify gaps in the existing literature and propose novel tools for testing and validating return curves and comparing estimates from a range of multivariate models. These tools are then used to compare a selection of models through simulation and case studies. We conclude with a discussion and list some of the challenges.Comment: 41 pages (without supplementary), 11 figures, 2 table

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, this framework is only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK

Low-surface energy surfactants with branched hydrocarbon architectures

International audienceSurface tensiometry and small-angle neutron scattering have been used to characterize a new class of low-surface energy surfactants (LSESs), "hedgehog" surfactants. These surfactants are based on highly branched hydrocarbon (HC) chains as replacements for environmentally hazardous fluorocarbon surfactants and polymers. Tensiometric analyses indicate that a subtle structural modification in the tails and headgroup results in significant effects on limiting surface tensions γcmc at the critical micelle concentration: a higher level of branching and an increased counterion size promote an effective reduction of surface tension to low values for HC surfactants (γcmc 24 mN m-1). These LSESs present a new class of potentially very important materials, which form lamellar aggregates in aqueous solutions independent of dilution

The effects of counterion exchange on charge stabilization for anionic surfactants in nonpolar solvents.

HYPOTHESIS: Sodium dioctylsulfosuccinate (Aerosol OT or NaAOT) is a well-studied charging agent for model poly(methyl methacrylate) (PMMA) latexes dispersed in nonpolar alkane solvents. Despite this, few controlled variations have been made to the molecular structure. A series of counterion-exchanged analogs of NaAOT with other alkali metals (lithium, potassium, rubidium, and cesium) were prepared, and it was expected that this should influence the stabilization of charge on PMMA latexes and the properties of the inverse micelles. EXPERIMENTS: The electrophoretic mobilities of PMMA latexes were measured for all the counterion-exchanged AOT analogs, and these values were used to calculate the electrokinetic or ζ potentials. This enabled a comparison of the efficacy of the different surfactants as charging agents. Small-angle scattering measurements (using neutrons and X-rays) were performed to determine the structure of the inverse micelles, and electrical conductivity measurements were performed to determine the ionized fractions and Debye lengths. FINDINGS: Sodium AOT is a much more effective charging agent than any of the other alkali metal AOTs. Despite this, the inverse micelle size and electrical conductivity of NaAOT are unremarkable. This shows a significant non-periodicity in the charging efficiency of these surfactants, and it emphasizes that charging particles in nonpolar solvents is a complex phenomenon

Structural studies of thermally stable, combustion-resistant polymer composites

Composites of the industrially important polymer, poly(methyl methacrylate) (PMMA), were prepared by free-radical polymerization of MMA with varying amounts (1–30 wt. %) of sodium dioctylsulfosuccinate (Aerosol OT or AOT) surfactant added to the reaction mixture. The composites with AOT incorporated show enhanced resistance to thermal degradation compared to pure PMMA homopolymer, and micro-cone combustion calorimetry measurements also show that the composites are combustion-resistant. The physical properties of the polymers, particularly at low concentrations of surfactant, are not significantly modified by the incorporation of AOT, whereas the degradation is modified considerably for even the smallest concentration of AOT (1 wt. %). Structural analyses over very different lengthscales were performed. X-ray scattering was used to determine nm-scale structure, and scanning electron microscopy was used to determine μm-scale structure. Two self-assembled species were observed: large phase-separated regions of AOT using electron microscopy and regions of hexagonally packed rods of AOT using X-ray scattering. Therefore, the combustion resistance is observed whenever AOT self-assembles. These results demonstrate a promising method of physically incorporating a small organic molecule to obtain a highly thermally stable and combustion-resistant material without significantly changing the properties of the polymer

Coherent Random Lasing Realized in Polymer Vesicles

We have demonstrated the realization of a coherent vesicle random lasing (VRL) from the dye doped azobenzene polymer vesicles self-assembled in the tetrahydrofuran-water system, which contains a double-walled structure: a hydrophilic and hydrophobic part. The effect of the dye and azobenzene polymer concentration on the threshold of random laser has been researched. The threshold of random laser decreases with an increase in the concentration of the pyrromethene 597 (PM597) laser and azobenzene polymer. Moreover, the scattering of small size group vesicles is attributed to providing a loop to boost the coherent random laser through the Fourier transform analysis. Due to the vesicles having the similar structure with the cell, the generation of coherent random lasers from vesicles expand random lasers to the biomedicine filed