Abstract: <script type='text/javascript'>document.write(unpmarked('Single-walled carbon nanotubes (SWCNTs) possessing a confined inner space protected by chemically resistant shells are promising for delivery, storage, and desorption of various compounds, as well as carrying out specific reactions. Here, we show that SWCNTs interact with molten mercury dichloride (HgCl2) and guide its transformation into dimercury dichloride (Hg2Cl2) in the cavity. The chemical state of host SWCNTs remains almost unchanged except for a small p-doping from the guest Hg2Cl2 nanocrystals. The density functional theory calculations reveal that the encapsulated HgCl2 molecules become negatively charged and start interacting via chlorine bridges when local concentration increases. This reduces the bonding strength in HgCl2, which facilitates removal of chlorine, finally leading to formation of Hg2Cl2 species. The present work demonstrates that SWCNTs not only serve as a template for growing nanocrystals but also behave as an electron-transfer catalyst in the spatially confined redox reaction by donation of electron density for temporary use by the guests.'));

Abstract: The European Synchrotron Radiation Facility (ESRF) has recently commissioned the new Extremely Brilliant Source (EBS). The gain in brightness as well as the continuous development of beamline instruments boosts the beamline performances, in particular in terms of accelerated data acquisition. This has motivated the development of new access modes as an alternative to standard proposals for access to beamtime, in particular via the “block allocation group” (BAG) mode. Here, we present the recently implemented “historical materials BAG”: a community proposal giving to 10 European institutes the opportunity for guaranteed beamtime at two X-ray powder diffraction (XRPD) beamlines-ID13, for 2D high lateral resolution XRPD mapping, and ID22 for high angular resolution XRPD bulk analyses-with a particular focus on applications to cultural heritage. The capabilities offered by these instruments, the specific hardware and software developments to facilitate and speed-up data acquisition and data processing are detailed, and the first results from this new access are illustrated with recent applications to pigments, paintings, ceramics and wood.

Abstract: The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.

Abstract: The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.

Abstract: A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections