Cover Picture: Turning Spiroketals Inside Out: A Rearrangement Triggered by an Enol Ether Epoxidation (ChemistryOpen 5/2015)

Invited for this month''s cover picture is the group of Professor Mark Peczuh at the University of Connecticut. The cover picture compares the rearrangement of a small molecule to the process of turning a stuffed animal inside out. The recycled, inside-out stuffed animals are both artistic and philosophically provocative. They capture the essence of the rearrangement reaction because the compounds themselves turn inside out over the course of the reaction, extending the diversity of products that can arise from simple starting materials. Small molecules often have functional groups with latent reactivity; under the appropriate conditions, those groups can react with other compounds (e.g., reagents) and also with other groups in the same molecule in an intramolecular reaction. The research team found that the epoxidation of some highly functionalized spiroketal compounds promoted rearrangements of their structures that turned them inside out. Some of the features of the products led them to use X-ray crystallography or a combination of computer-assisted structure elucidation, computation, and a new version of the 1,1-ADEQUATE NMR experiment to determine their structures. For more details, see the Communication on p. 577 ff.     

Exploring Network Formation of Tough and Biocompatible Thiol‐yne Based Photopolymers

This work deals with the in‐depth investigation of thiol‐yne based network formation and its effect on thermomechanical properties and impact strength. The results show that the bifunctional alkyne monomer di(but‐1‐yne‐4‐yl)carbonate ( DBC ) provides significantly lower cytotoxicity than the comparable acrylate, 1,4‐butanediol diacrylate ( BDA ). Real‐time near infrared photorheology measurements reveal that gel formation is shifted to higher conversions for DBC /thiol resins leading to lower shrinkage stress and higher overall monomer conversion than BDA . Glass transition temperature (T_g), shrinkage stress, as well as network density determined by double quantum solid state NMR, increase proportionally with the thiol functionality. Most importantly, highly cross‐linked DBC /dipentaerythritol hexa(3‐mercaptopropionate) networks (T_g ≈ 61 °C) provide a 5.3 times higher impact strength than BDA , which is explained by the unique network homogeneity of thiol‐yne photopolymers.

     

A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.     

Energy and hole transfer between dyes attached to titania in cosensitized dye-sensitized solar cells

Cosensitization of broadly absorbing ruthenium metal complex dyes with highly absorptive near-infrared (NIR) organic dyes is a clear pathway to increase near-infrared light harvesting in liquid-based dye-sensitized solar cells (DSCs). In cosensitized DSCs, dyes are intimately mixed, and intermolecular charge and energy transfer processes play an important role in device performance. Here, we demonstrate that an organic NIR dye incapable of hole regeneration is able to produce photocurrent via intermolecular energy transfer with an average excitation transfer efficiency of over 25% when cosensitized with a metal complex sensitizing dye (SD). We also show that intermolecular hole transfer from the SD to NIR dye is a competitive process with dye regeneration, reducing the internal quantum efficiency and the electron lifetime of the DSC. This work demonstrates the general feasibility of using energy transfer to boost light harvesting from 700 to 800 nm and also highlights a key challenge for developing highly efficient cosensitized dye-sensitized solar cells.     

Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg–Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.     

A survey of Sylvester's problem and its generalizations

Summary LetP be a finite set of three or more noncollinear points in the plane. A line which contains two or more points ofP is called aconnecting line (determined byP), and we call a connecting lineordinary if it contains precisely two points ofP. Almost a century ago, Sylvester posed the disarmingly simple question:Must every set P determine at least one ordinary line? No solution was offered at that time and the problem seemed to have been forgotten. Forty years later it was independently rediscovered by Erdös, and solved by Gallai. In 1943 Erdös proposed the problem in the American Mathematical Monthly, still unaware that it had been asked fifty years earlier, and the following year Gallai's solution appeared in print. Since then there has appeared a substantial literature on the problem and its generalizations.In this survey we review, in the first two sections, Sylvester's problem and its generalization to higher dimension. Then we gather results about the connecting lines, that is, the lines containing two or more of the points. Following this we look at the generalization to finite collections of sets of points. Finally, the points will be colored and the search will be for monochromatic connecting lines.     

Polarization-selective grating mirrors used in the generation of radial polarization

Two novel methods to control the polarization of laser radiation are presented. The discrimination between different polarization distributions isperformed with a corrugation grating in the top high-index layer of a multilayer mirror, which couples the undesired polarization into a lossy waveguidemode of the multilayer. The generation of radially polarized radiation in a laser resonator is presented as a practical verification of the principle.This revised version was published online in May 2005. The Article Category was removed.This revised version was published online in August 2005 with a corrected cover date.     

Dynamical systems — Past and present

Plenary lecture at the International Congress of Mathematicians (Berlin 1998, August 18–27). Reprinted from Doc. Math. J., DMV, Extra Volume ICM I, 1998, pp. 381–402. ©J.Moser, 1998.