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: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non-local, dispersive, and space-time multiphysics model based on Maxwell's and asymptotic Smoluchowski's equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi-relaxation Debye-based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non-dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331-342. (c) 2019 Wiley Periodicals, Inc.

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