The heat kernel expansion for the electromagnetic field in a cavity

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite.Comment: 12 page

Homogenization and Scattering Analysis of Second-Harmonic Generation in Nonlinear Metasurfaces

We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time-domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces

Towards Self-Replicating Chemical Systems Based on Cytidylic and Guanylic Acids

This project is aimed towards a better understanding of template-directed reactions and, based on this, towards the development of efficient non-enzymatic RNA replicating systems. These systems could serve as models for the prebiotic synthesis of an RNA world. The major objectives of this project were: (a) To elucidate the mechanistic aspects of template-directed (TD) chemistry, (b) to identify the conditions, environmental and other, that favor "organized chemistry" and stereo selective polymerization of nucleotides and (c) to search and, hopefully, find catalysts that will improve the efficiency of these reactions. Enhanced efficiency is expected to facilitate the road towards a self-replicating chemical system based on all four nucleic acid bases. During the first nine months of the granting period from January 1997 to October 1997, we have made substantial progress towards the first two objectives. During this period our activities were directed towards (1) synthesizing activated nucleotides to be used as substrates, (2) using these substrates in order to determine the effect of the leaving group (imidazole (Im), 2-methylimidazole (2-MeIm), and 2,4-dimethylimidazole (2,4-diMeIm)) in the product distribution, (3) developing techniques for analysis of mixtures by LC/MS, (4) creating a protocol in order to obtain kinetic parameters of the dimerization reaction and (5) analyzing kinetic data obtained with the poly(C)/2-MeImpG system. With the exception of item (5), the experimental work for the projects (1) - (4) is still in progress. A list of publications and manuscripts resulted from this research is enclosed

Analisi dell’anisotropia microstrutturale in materiali compositi rinforzati con fibre corte

Synchrotron light microtomography has proved to be particularly efficient in order to analyze the microstructural characteristics in terms of reinforce fibre distribution and orientation in glass fibre reinforced composites. The spatial distribution of fibre within the polymeric matrix could be detected even in case of fibre characterized by a small diameter (10 micrometers average diameter). Differences in orientation distribution within a sample could be measured using the Mean Intercept Length (MIL) and the fabric tensor. The results presented herein refer to a sample of a 30% by weight glass fibre reinforced polyamide 6, extracted form a thin plate

Photoelasticity of sodium silicate glass from first principles

Based on density-functional perturbation theory we have computed the photoelastic tensor of a model of sodium silicate glass of composition (Na$_2$O)$_{0.25}$(SiO$_2$)$_{0.75}$ (NS3). The model (containig 84 atoms) is obtained by quenching from the melt in combined classical and Car-Parrinello molecular dynamics simulations. The calculated photoelastic coefficients are in good agreement with experimental data. In particular, the calculation reproduces quantitatively the decrease of the photoelastic response induced by the insertion of Na, as measured experimentally. The extension to NS3 of a phenomenological model developed in a previous work for pure a-SiO$_2$ indicates that the modulation upon strain of other structural parameters besides the SiOSi angles must be invoked to explain the change in the photoelstic response induced by Na