Asymptotic preserving numerical schemes for a non‐classical radiation transport model for atmospheric clouds

We present numerical schemes for the P1‐moment and M1‐moment approximations of a non‐classical transport equation modeling radiative transfer in atmospheric clouds. In contrast to classical radiative transfer, the photon path‐length is introduced as an additional variable and serves as pseudo‐time in this model. Because clouds may have optically thick regions, we introduce a diffusive scaling and show that the diffusion limits of the moment models and the original equations agree. Furthermore, we show that the numerical schemes also preserve the diffusion asymptotics as well as the set of admissible and realizable states, both for the explicit and the implicit discretization of the pseudo‐time variable. A source iteration‐like method is proposed, and we observe that it converges slowly in the optical thick case, but a suitable initialization can help to overcome this problem. We validate our method in 1D and present simulation results in the 2D‐case for real cloud data. Copyright © 2013 John Wiley & Sons, Ltd.     

The Accumulated Persistence Function,a New Useful Functional Summary Statistic for Topological Data Analysis,With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples.     

The generalized Krawtchouk polynomials and the fifth Painlevé equation

We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painlevé equation when viewed as functions of one of the parameters in the weight.     

Recycling of carbon and silicon wastes: room temperature formylation of N-H bonds using carbon dioxide and polymethylhydrosiloxane

A highly active organocatalytic system based on N-heterocyclic carbenes has been designed for the formylation of N-H bonds in a large variety of nitrogen molecules and heterocycles, using two chemical wastes: CO(2) and polymethylhydrosiloxane (PMHS).     

Functionalized orthoesters as powerful building blocks for the efficient preparation of heteroaromatic bicycles

By combining substituted anilines with functionalized orthoesters, an efficient and connective methodology for the preparation of benzoxazole, benzothiazole, and benzimidazole derivatives has been established. The versatility of this approach enables the development of new libraries of heterocycles containing multifunctional sites.     

Gold(I)-catalysed cycloisomerisation of 1,6-cyclopropene-enes

The gold(I)-catalysed cycloisomerisation of appropriately substituted 1,6-cyclopropene-enes proceeds through regioselective electrophilic ring opening of the three-membered ring to generate an alkenyl gold carbenoid that achieves the intramolecular cyclopropanation of the remote olefin. This strategy allows straightforward, highly efficient and diastereoselective access to a variety of substituted 3-oxa- and 3-azabicyclo[4.1.0]heptanes, as well as to bicyclo[4.1.0]heptan-3-ol derivatives. Since the isopropylidene group in the resulting cycloisomerisation products can be subjected to ozonolysis, 3,3-dimethylcyclopropenes behave as interesting surrogates for α-diazoketones.     

VUV synchrotron radiation: a new activation technique for tandem mass spectrometry

A novel experimental technique for tandem mass spectrometry and ion spectroscopy of electrosprayed ions using vacuum‐ultraviolet (VUV) synchrotron radiation is presented. Photon activation of trapped precursor ions has been performed by coupling a commercial linear quadrupole ion trap (Thermo scientific LTQ XL), equipped with the electrosprayed ions source, to the DESIRS beamline at the SOLEIL synchrotron radiation facility. The obtained results include, for the first time on biopolymers, photodetachment spectroscopy using monochromated synchrotron radiation of multi‐charged anions and the single photon ionization of large charge‐selected polycations. The high efficiency and signal‐to‐noise ratio achieved by the present set‐up open up possibilities of using synchrotron light as a new controllable activation method in tandem mass spectrometry of biopolymers and VUV‐photon spectroscopy of large biological ions.     

Charge collection in amorphous silicon solar cells: Cell analysis and simulation of high-efficiency pin devices

The drift length L_drift = μτE within the i layer of a-Si:H solar cells is a crucial parameter for charge collection and efficiency. It is strongly reduced not only by light-induced reduction of μτ, but also by electric field deformation ΔE by charges near the p–i and i–n interfaces. Here, a simple model is presented to estimate contributions of free carriers, charges trapped in band tails and charged dangling bonds to ΔE. It is shown that the model reproduces correctly trends observed experimentally and by ASA simulations: charged dangling bonds contribute most to ΔE of meta-stable cells. Electrons trapped in the conduction band tail near the i–n interface lead to the strongest field deformation in the initial state, while positively charged dangling bonds near the p–i interface get more important with degradation under AM1.5g spectrum. The measurable parameter V_coll is proposed as an indirect parameter to estimate the electric field, and an experimental technique is presented that could enable the distinction of defects near the p–i and the i–n interfaces.     

Large velocities in a collisionless plasma

We consider smooth compactly supported solution to the classical three-dimensional Vlasov–Poisson system. The radius of the support in the velocity variable is shown to grow at most like the power 2/3 of the time variable.     

Mixed molecular and atomic phase of dense hydrogen

We used Raman and visible transmission spectroscopy to investigate dense hydrogen (deuterium) up to 315 (275) GPa at 300 K. At around 200 GPa, we observe the phase transformation, which we attribute to phase III, previously observed only at low temperatures. This is succeeded at 220 GPa by a reversible transformation to a new phase, IV, characterized by the simultaneous appearance of the second vibrational fundamental and new low-frequency phonon excitations and a dramatic softening and broadening of the first vibrational fundamental mode. The optical transmission spectra of phase IV show an overall increase of absorption and a closing band gap which reaches 1.8 eV at 315 GPa. Analysis of the Raman spectra suggests that phase IV is a mixture of graphenelike layers, consisting of elongated H2 dimers experiencing large pairing fluctuations, and unbound H2 molecules.