Conformally self-dual spaces and Maxwell's equations

The nonlinear system of partial differential equations generalizing Plebanski's ω-equation is given for conformally self-dual spaces. It is then shown that solving this system is equivalent to the problem that the induced connection in a certain distinguished line bundle hasa self-dual curvature and self-dual “involuted” curvature.     

Reduced Dynamics of the Non-holonomic Whipple Bicycle

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.     

An Oxygen Paradox: Catalytic Use of Oxygen in Radical Photopolymerization

A peculiar radical polymerization reaction is presented in which oxygen serves as a cocatalyst, alongside triethylamine, to provide activation with light in the far‐red (690 nm, 3 mW cm^?2) of the PET‐RAFT process in the presence of zinc(II) (2,3,7,8,12,13,17,18‐octaethyl‐5,10,15,20‐tetraphenylporphyrin) as photocatalyst. Apart from the ability to exert temporal control by switching the light on or off, this system possesses the exciting capability of inducing temporal control by removal or reintroduction of oxygen. Furthermore, this multicomponent catalytic system was typified by controlled polymerizations of various acrylate and acrylamide monomers, which all resulted in well‐defined polymers with low dispersity (<1.2). The process displayed excellent living characteristics that were demonstrated through chain extensions and a range of degrees of polymerization (200–1600).     

Violation of the Cauchy-Schwarz inequality in the macroscopic regime

We have observed a violation of the Cauchy-Schwarz inequality in the macroscopic regime by more than 8 standard deviations. The violation has been obtained while filtering out only the low-frequency noise of the quantum-correlated beams that results from the technical noise of the laser used to generate them. We use bright intensity-difference squeezed beams produced by four-wave mixing as the source of the correlated fields. We also demonstrate that squeezing does not necessarily imply a violation of the Cauchy-Schwarz inequality.     

The low-temperature specific heat of PTFE (Teflon) at pressures to 5.2 kbar

The specific heat of PTFE (Teflon) has been measured between 0.3 and 20 K at zero pressure, and between 1 and 20 K at five other pressures ranging up to 5.2 kbar. The specific heat anomalies typical of amorphous materials were observed. The linear term is smaller than for other organic polymers and is closer in magnitude to those of high purity glassy insulators. At zero pressure the T³ term in the specific heat exceeds that calculated from the sound velocities by 24%. The evolution with pressure of the T³ term and of the maximum in C/T³ are very similar, suggesting a close relation between the vibrational modes that contribute to these features in the specific heat. This result and the relatively simple structure of Teflon rule out independent localized oscillators as the source of the maximum in C/T³.     

Crystal structure of 5-(p-methoxyphenylamino)indane and AM1 calculations on N-arylamines derivatives, precursors of phenothiazine drugs

The structural determination by X-ray crystallography of the titled N-arylamine 4a, as well as AM₁ calculations on a series of derivatives (4b–c, 5a–c), are reported. The compound 4a is monoclinic P2₁/c with a = 7.656(3), b = 23.655(5), c = 7.686(9) Å, = 112.59(6)°, V = 1285.2(2) ų and Z = 4. This structure has been used as a template for the building of some others derivatives used for AM₁ calculations. The results show that the cyclization position on the aromatic rings, which can lead to two regioisomers, depends on the nature of the benzylic substituants.     

Synthesis of natural products from the Indian neem tree Azadirachta indica

The synthesis of five natural products (3, 6, 7, 10, and 14), isolated from the Indian neem tree Azadirachta indica, is reported from a common intermediate (2). The judicious choice of transacetalization conditions allows efficient access to both the azadirachtinin (9 and 10) and the azadirachtin (3, 6, 7, and 14) skeletons.     

Oxidative coupling of acridinones: Synthesis of new C2‐symmetry atropisomers

The preparation of symmetric 2,2′‐dimethoxy‐10,10′‐biacridinyl‐9,9′‐dione atropisomers were obtained by the oxidative coupling of 9(10H)‐acridinone with 1,3‐dibromo‐5,5‐dimethyl‐imidazolidine‐2,4‐dione