Abstract: The interaction of diatoms with sunlight is fundamental in order to deeply understand their role in terrestrial ecology and biogeochemistry, essentially due to their massive contribution to global primary production through photosynthesis and its e↵ect on carbon, oxygen and silicon cycles. Following the journey of light through natural waters, its propagation through the intricate frustule micro- and nano-structure and, finally, its fate inside the photosynthetic machinery of the living cell requires several mathematical and computational models in order to accurately describe all the involved phenomena taking place at di↵erent space scales and physical regimes. In this chapter, we review the main analytical models describing the underwater optical field, the essential numerical algorithms for the study of photonic properties of the diatom frustule seen as a natural metamaterial, as well as the principal models describing photon harvesting in diatom plastids and methods for complex EM propagation problems and wave propagation in dispersive materials with multiple relaxation times. These mathematical methods will be integrated in a unifying geometric perspective.

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: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.

Abstract: Recent studies in which X-ray beams of macroscopic to (sub) microscopic dimensions were used for non-destructive analysis and characterization of pigments, paint micro samples and/or entire paintings by Vincent van Gogh are concisely reviewed. The overview presented encompasses the use of laboratory and synchrotron radiation-based instrumentation and deals with the use of several variants of X-ray fluorescence (XRF) as a method of elemental analysis and imaging as well as with the combined use of X-ray diffraction (XRD) and X-ray absorption spectroscopy (XAS). Microscopic and macroscopic XRF are variants of the method that are well suited to visualize the elemental distribution of key elements, mostly metals, present in paint multi layers, either on the length scale from 1–100 μm inside micro samples taken from paintings or on the 1–100 cm length scale when the (subsurface) distribution of specific pigments in entire paintings is concerned. In the context of the characterization of van Gogh's pigments subject to natural degradation, the use of methods limited to elemental analysis or imaging usually is not sufficient to elucidate the chemical transformations that have taken place. However, at synchrotron facilities, combinations of μ-XRF with related methods such as μ-XAS and μ-XRD have proven themselves to be very suitable for such studies. Their use is often combined with microscopic Fourier transform infra-red (μ-FTIR) spectroscopy since this method delivers complementary information at more or less the same length scale as the X-ray microprobe techniques. Also in the context of macroscopic imaging of works of art, the complementary use of X-ray based and infra-red based imaging appears very promising; some recent developments are discussed.

Abstract: Dalle de verre windows, created from 19301940 onwards, consist of glass pieces with a thickness of approximately 2 to 5 cm, set in a matrix of (reinforced) concrete. Besides the degradation of the concrete, the windows suffer mainly from a complex three-dimensional form of cracking of the glass elements. The cracks need to be consolidated in order to ensure stability and improve transparency. A selection of possible adhesives was evaluated: Araldite® 2020, Hxtal NYL-1, Fynebond, Paraloid® B-72, LV740, A18 and OR-G®. An attempt has been made to objectively compare these adhesives using a bench-marking system. None of the adhesives appears to be suitable for in situ application; sufficient penetration of the adhesives can only be realised with the help of vacuum techniques.

Abstract: In 2008, Museum M in Louvain (Flanders, Belgium) acquired a panel depicting The Anointing at Bethany that is believed once to have adorned the citys former Charterhouse. The panel required conservation treatment, which was preceded by a thorough art-historical and technical examination. It emerged that comparable panels are kept at the Metropolitan Museum of Art and the Riverside Church in New York. Chemical analyses show most of the glass in the panel to have a typical 16th century high-limelow-alkali composition. The conservation treatment was based on the evaluation of these findings and focused very strongly on enhancing the aesthetic balance for an improved reading of the panel.

Abstract: In the past years, and also within the framework of this CRP, we have used a combination of several nuclear and non-nuclear techniques in fundamental research and especially in various applications. Most work has been done with energy-dispersive X ray fluorescence in combination with electron probe X ray microanalysis, but several other more common analysis techniques have been used as well. The applications have included mostly preventive conservation (e.g. characterisation of damaging atmospheric particles in many museums) and environmental monitoring (e.g. for atmospheric particles in relation to their health effects in outdoor and especially indoor environments). Fundamental aspects have been in the optimising of interfaced electron microprobe and Raman microprobe analysis and the evaluation of the potential of such an instrument for atmospheric aerosols; quite a few unexpected and unpredicted problems have appeared in the latter study.