Rational Development of Remote C−H Functionalization of Biphenyl: Experimental and Computational Studies

A simple and efficient nitrile-directed meta-C−H olefination, acetoxylation, and iodination of biaryl compounds is reported. Compared to the previous approach of installing a complex U-shaped template to achieve a molecular U-turn and assemble the large-sized cyclophane transition state for the remote C−H activation, a synthetically useful phenyl nitrile functional group could also direct remote meta-C−H activation. This reaction provides a useful method for the modification of biaryl compounds because the nitrile group can be readily converted to amines, acids, amides, or other heterocycles. Notably, the remote meta-selectivity of biphenylnitriles could not be expected from previous results with a macrocyclophane nitrile template. DFT computational studies show that a ligand-containing Pd–Ag heterodimeric transition state (TS) favors the desired remote meta-selectivity. Control experiments demonstrate the directing effect of the nitrile group and exclude the possibility of non-directed meta-C−H activation. Substituted 2-pyridone ligands were found to be key in assisting the cleavage of the meta-C−H bond in the concerted metalation–deprotonation (CMD) process.     

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

The aim of this work is to propose an accurate and efficient numerical approximation for high frequency diffraction of electromagnetic waves. In the context of the boundary integral equations presented in F. Collino and B. Després, to be published in J. Comput. Appl. Math., the strategy we propose combines the microlocal discretization (T. Abboud et al., in: Third International Conference on Mathematical Aspects of Wave Propagation Phenomena, SIAM, 1995, pp. 178–187) and the multilevel fast multipole method (J.M. Song, W.C. Chew, Microw. Opt. Tech. Lett. 10 (1) (1995) 14–19). This leads to a numerical method with a reduced complexity, of order O(N^4/3ln(N)+N_iterN^2/3), instead of the complexity O(N_iterN²) for a classical numerical iterative solution of integral equations. Computations on an academic geometry show that the new method improves the efficiency, for a solution with a good level of accuracy. To cite this article: A. Bachelot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

The double duals and gauges of the Lanczos tensor

It is shown that: i) the Weyl tensor can be expressed in terms of the sum of a tensor and its double dual, where the tensor is constructed from the covariant derivatives of the Lanczos tensor, ii) a similar expression does not exist for the Riemann tensor in electromagnetic theory, iii) the electromagnetic field cannot be identified with the differential gauge freedom of the Lanczos tensor, iv) the symmetries of Einstein Maxwell theory and the Lanczos tensor do not prohibit the identification of the electromagnetic field with the algebraic gauge freedom of the Lanczos tensor, these symmetries require a differential equation relating the electromagnetic field tensor to the algebraic gauge vector and this is given.     

Resonant-cavity-enhanced photodetectors and LEDs in the mid-infrared

In this paper we outline the use of resonant-cavity enhancement for increasing the exterior coupling efficiency of photodetectors and light-emitting diodes (LEDs) in the mid-infrared (MIR) spectral region. This method is potentially very important in the MIR because encapsulation is not presently feasible due to the lack of suitable materials. Among other potential applications, resonant-cavity-enhanced (RCE) photodetectors and LEDs could be particularly suitable for greenhouse gas detection because of their ‘pre-tunable’ spectrally narrowed resonantly enhanced peaks. We also present the optical characterization of an InAs RCE photodetector aimed at the detection of methane gas (λ≈3.3 μm), and an InAs/InAs_0.91Sb_0.09 resonant-cavity LED (RCLED) aimed at carbon dioxide gas (λ≈4.2 μm). The high peak responsivity of the RCE photodetector was 34.7 A/W at λ=3.14 μm, and the RCLED peaked at λ=3.96 μm. These are among the longest operating wavelengths for III–V RCE photodetectors and RCLEDs reported in the literature.     

Galactic Metrics

The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and this requirement places a restricting equation on the spacetime metric. This equation has a non-unique spherically symmetric solution that in the Newtonian limit has a logarithmic potential. It also can be solved in terms of a conformal factor. In particular it has solutions which are conformal to the vacuum-Einstein solutions and such spacetimes are solutions to the vacuum-Bach equations. Therefore it is suggested that the Bach equations describe dynamics on galactic length scales.     

Contemplating Criteria for Science Education Reform: The Case of the Olympia School District

Proposals for current reform in science education elaborate national standards and a plethora of state-level interpretations commonly labeled as curriculum or learning frameworks. The purpose of this case study was to examine the dynamics of the science curriculum reform process in one of the first school districts to use the Georgia Framework for Learning Mathematics and Science as a basis for their reform initiative. The paper describes the ways in which members of the Olympia School District's Science Curriculum Committee participated in the science curriculum reform process, as well as their personal beliefs about the criteria needed for reform to take place. The results highlight the nature of metaphors guiding reform efforts; the influence of social, historical, economic, and political forces on the reform process; the use of local and professional languages as discourses for communicating about reform; and the complex power relations that influence the micropolitics of reform in the Olympia School District. This study has important implications for other teachers and school districts engaged in standards-based science curriculum reform. It points to the need for reform to include reflection and analysis of the role of teachers in the reform process and consideration of the purpose of science education reform in society.     

Thick grids with circular apertures: A comparison of theoretical and experimental performance

In this paper a comparison between a rigorous electromagnetic model for transmission through a hexagonal array of circular waveguides in a series of thick, metallic screens and experimental measurements in the far infrared is made. It is found that there is excellent agreement between theory and experiment when the frequency is below that where any diffracted orders propagate. The agreement is still very good above this frequency. Below a frequency approximately equal to the cut-off frequency of the circular waveguides little power is transmitted. As the thickness of the screen is increased, this decrease in transmission becomes more abrupt. Also, for thick screens, resonances appear in the transmission spectrum which are analogous to those which appear in the spectra of two grids separated by a distance comparable to the wavelength of the radiation being used.