SICs and Algebraic Number Theory

We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.     

A comparative study of fluorine substituents for enhanced stability of flexible and ITO‐free high‐performance polymer solar cells

Two low‐band gap polymer series based on benzo[1,2‐b:4,5‐b′]dithiophene (BDT) and dithienylbenzothiadiazole, with different numbers of fluorine substituents on the 2,3,1‐benzothiadiazole unit, have been synthesized and explored in a comparative study of the photochemical stability and operational lifetime in flexible large area roll‐coated bulk heterojunction solar cells. The two polymer series have different side chains on the BDT unit, namely 2‐hexyldecyloxy (BDT_HDO) ( P1–P3 ) or 2‐hexyldecylthiophene (BDT_THD) ( P4–P6 ). The photochemical stability clearly shows that the stability enhances along with the number of fluorine atoms incorporated on the polymer backbone. Fabrication of the polymer solar cells based on the materials was carried out in ambient atmosphere on a roll coating/printing machine employing flexible and indium‐tin‐oxide‐free plastic substrates. Solar cells based on the P4–P6 series showed the best performance, reaching efficiencies up to 3.8% for an active area of 1 cm², due to an enhanced current compared to P1–P3 . Lifetime measurements, carried out according to international summit on OPV stability (ISOS), of encapsulated devices reveals an initial fast decay for P1–P6 in the performance followed by a much slower decay rate, still retaining 40–55% of their initial performance after 250 h of testing under ISOS‐L‐1 conditions. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 893–899     

Theoretical prediction of the damping of a railway wheel with sandwich-type dampers

This paper presents a procedure for predicting the damping added to a railway wheel when sandwich-type dampers are installed. Although there are different ways to reduce the noise generated by a railway wheel, most devices are based on the mechanism of increasing wheel damping. This is why modal damping ratios are a clear indicator of the efficiency of the damping device and essential when a vibro-acoustic study of a railway wheel is carried out. Based on a number of output variables extracted from the wheel and damper models, the strategy explained herein provides the final damping ratios of the damped wheel. Several different configurations are designed and experimentally tested. Theoretical and experimental results agree adequately, and it is demonstrated that this procedure is a good tool for qualitative comparison between different solutions in the design stages.     

Aryl vinyl cyclopropane Cope rearrangements

While the divinyl cyclopropane Cope rearrangement is well-known, and has been broadly applied in synthesis, examples of the aryl vinyl cyclopropane Cope rearrangement are less common and generally limited in scope or reaction yield. The aryl vinyl cyclopropane Cope rearrangement gives access to the benzocycloheptene scaffold, which is present in a variety of naturally occurring and medicinally relevant products. Herein we report a method to obtain either of two regioisomeric benzocycloheptene products via an aryl vinyl cyclopropane Cope rearrangement, featuring additive-controlled regioselectivity. Mechanistic studies indicate a dynamic equilibration of cyclopropane stereoisomers, followed by rearrangement of the cis diastereomer.     

Rational Design of a Uranyl Metal–Organic Framework for the Capture and Colorimetric Detection of Organic Dyes

A new uranyl containing metal–organic framework, RPL-1 : [(UO₂)₂(C₂₈H₁₈O₈)] ^. H₂O (RPL for Radiochemical Processing Laboratory), was prepared, structurally characterized, and the solid-state photoluminescence properties explored. Single crystal X-ray diffraction data reveals the structure of RPL - 1 consists of two crystallographically unique three dimensional, interpenetrating nets with a 4,3-connected tbo topology. Each net contains large pores with an average width of 22.8 Å and is formed from monomeric, hexagonal bipyramidal uranyl nodes that are linked via 1,2,4,5-tetrakis(4-carboxyphenyl)benzene (TCPB) ligands. The thermal and photophysical properties of RPL-1 were investigated using thermogravimetric analysis and absorbance, fluorescence, and lifetime spectroscopies. The material displays excellent thermal stability and temperature dependent uranyl and TCPB luminescence. The framework is stable in aqueous media and due to the large void space (constituting 76 % of the unit cell by volume) can sequester organic dyes, the uptake of which induces a visible change to the color of the material.