Subextension of plurisubharmonic functions with weak singularities

We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball \B \sub \C^n with its relative logarithmic capacity in \C^n with respect to the same ball \B. An analoguous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of \C^n is also proved. Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of \psh lemniscates associated to the Lelong class of \psh functions of logarithmic singularities at infinity on \C^n as well as the Cegrell class of \psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W \Sub \C^n. Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of \psh functions.Comment: 25 page

Effect of catalyst layer defects on local membrane degradation in polymer electrolyte fuel cells

© 2016 Elsevier B.V. All rights reserved. Aiming at durability issues of fuel cells, this research is dedicated to a novel experimental approach in the analysis of local membrane degradation phenomena in polymer electrolyte fuel cells, shedding light on the potential effects of manufacturing imperfections on this process. With a comprehensive review on historical failure analysis data from field operated fuel cells, local sources of iron oxide contaminants, catalyst layer cracks, and catalyst layer delamination are considered as potential candidates for initiating or accelerating the local membrane degradation phenomena. Customized membrane electrode assemblies with artificial defects are designed, fabricated, and subjected to membrane accelerated stress tests followed by extensive post-mortem analysis. The results reveal a significant accelerating effect of iron oxide contamination on the global chemical degradation of the membrane, but dismiss local traces of iron oxide as a potential stressor for local membrane degradation. Anode and cathode catalyst layer cracks are observed to have negligible impact on the membrane degradation phenomena. Notably however, distinct evidence is found that anode catalyst layer delamination can accelerate local membrane thinning, while cathode delamination has no apparent effect. Moreover, a substantial mitigating effect for platinum residuals on the site of delamination is observed

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules

Color flows for the process gg --> Bc + c + b-bar

The contributions of different color flows into the gluonic Bc-meson production cross section has been calculated. This study is essential to simulate Bc-meson production with the help of Pythia program. The essence of matter is that in the frame work of the Lund model used by Pythia the hadronization way of the final partons and hadronic remnants depends on the color flow type. The modified method for calculation of the color flow contributions has been proposed.Comment: 16 pages, 5 figures, RevTeX

Non-factorizable photonic corrections to ee->WW->4fermions

We study the non-factorizable corrections to W-pair-mediated four-fermion production in ee annihilation in double-pole approximation. We show how these corrections can be combined with the known corrections to the production and the decay of on-shell W-boson pairs, and how the full off-shell Coulomb singularity is included. Moreover, we find that the actual form of the real non-factorizable corrections depends on the parametrization of phase space, more precisely, on the definition of the invariant masses of the resonant W bosons. For the usual parametrization the full analytical results for the non-factorizable corrections are presented. Our analytical and numerical results for the non-factorizable corrections agree with a recent calculation, which was found to differ from a previous one. The detailed numerical discussion covers the invariant-mass distribution, various angular distributions, and the lepton-energy distribution for leptonic final states.Comment: 46 pages, latex, 13 eps figures, incorrect remarks concerning the universality of non-factorizable corrections to pure invariant-mass distributions discarde