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: The anticipated development of decentralized electricity generation is expected to strengthen the opportunities of prosumers in the residential areas of cities, in line with the predicted establishment of renewable energy generation and storage. Based on academic research and on successful case studies, the opportunity for residential prosumers to organize in microgrids emerges as a viable and promising solution. This paper focuses on microgrids that are planned to generate electricity with a PV unit and use a shared storage system, and that opt to have a connection with the main grid. However, the point of common coupling needs to be agreed first between the microgrid operator and the network operator, and this agreement is determined by several factors and conditions beyond the basic technical and regulatory requirements. A survey of academic literature on the determinant factors for such an agreement exposes the fact that current research either focuses on the integration of individual prosumers in the main grid, or regards the point of common coupling as a given component of microgrids. We argue that neither of the two approaches is helpful in the case of microgrids vs. main grid, seeing as the agreement is not self-evident under just any circumstances, nor can the microgrid be equated to a single, large prosumer. Therefore this short paper compiles a set of determinant factors for the microgrid integration, as they emerge from academic literature, with the aim to document further research needs and support the discussion on microgrid integration.

Abstract: This chapter provides a description of colour changes in the Amsterdam Sunflowers due to chemical alteration of pigments, with a focus on geranium lakes and chrome yellows. The brilliant and forceful colours of these and other late nineteenth-century synthetic materials offered artists such as Vincent van Gogh new means of artistic expression that exploited a range of contrasting hues and tints. However, geranium lakes have a strong tendency to fade and chrome yellows to darken under the influence of light. Van Gogh, like other artists of his day, was aware of this drawback, yet he continued to favour the use of both pigments up until his death in July 1890 due to the unparalleled effects they gave. In April 1888, Vincent wrote to his brother Theo: Van Gogh's use of unstable colours opens a series of questions regarding the extent to which colour change affects the way his paintings look today, as discussed here in relation to the Amsterdam Sunflowers. Furthermore, given the frequency with which geranium lakes and chrome yellows occur in Van Gogh's paintings of the period 1888–90 and the predominance of chrome yellows in Sunflowers, it becomes important to understand the factors that can drive these processes of deterioration in order to develop appropriate strategies for conserving the artist's works.

Abstract: The formation and distribution of metal soaps produced as a result of the reactivity and aging of the materials in a fifteenth-century egg tempera and oil paintings on wood are presented. The painting technique involves the application of several paint layers over a ground using, sometimes in the same paint layer sequence, drying oil and egg yolk binders. We show, with a selection of examples, how the use of thin sections and a combination of various micro-sensitive analytical techniques is adequate to obtain the high-quality data necessary for the unambiguous identification of metal soaps and metal oxalates as well as their distribution in the paint layers. The techniques include micro infrared spectroscopy (μSR-FTIR) and micro X-ray diffraction (μSR-XRD) with synchrotron radiation, optical microscopy (OM), and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDS). The data obtained sheds light about the underlying reaction and aging mechanisms happening in each paint layer and among them. This helps to define the state of conservation of the artworks.

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: We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).

Abstract: Atomic Spectroscopy Optical (atomic absorption spectroscopy, AAS; atomic emission spectroscopy, AES; atomic fluorescence spectroscopy, AFS; and optogalvanic spectroscopy) and mass spectrometric (magnetic sector, quadrupole mass analyzer, QMA; quadrupole ion trap, QIT; Fourier transform ion cyclotron resonance, FTICR; and time-of-flight, TOF) instrumentation are well suited for coupling to the glow discharge (GD). The GD is a relatively simple device. A potential gradient (500–1500 V) is applied between an anode and a cathode. In most cases, the sample is also the cathode. A noble gas (mostly Ar) is introduced into the discharge region before power initiation. When a potential is applied, electrons are accelerated toward the anode. As these electrons accelerate, they collide with gas atoms. A fraction of these collisions are of sufficient energy to remove an electron from a support gas atom, forming an ion. These ions are, in turn, accelerated toward the cathode. These ions impinge on the surface of the cathode, sputtering sample atoms from the surface. Sputtered atoms that do not redeposit on the surface diffuse into the excitation/ionization regions of the plasma where they can undergo excitation and/or ionization via a number of collisional processes, and the photons or ions created in this way can be detected with optical emission spectroscopy or mass spectrometry. GD sources offer a number of distinct advantages that make them well suited for specific types of analyses. These sources afford direct analysis of solid samples, thus minimizing the sample preparation required for analysis. The nature of the plasma also provides mutually exclusive atomization and excitation processes that help to minimize the matrix effects that plague so many other elemental techniques. In recent years, there is also increasing interest for using GD sources for liquid and gas analyses. In this article, first, the principles of operation of the GD plasma are reviewed, with an emphasis on how those principles relate to optical spectroscopy and mass spectrometry. Basic applications of the GD techniques are considered next. These include bulk analysis, surface analysis, and the analysis of solution and gaseous samples. The requirements necessary to obtain optical information are addressed following the analytical applications. This article focuses on the instrumentation needed to make optical measurements using the GD as an atomization/excitation source. Finally, mass spectrometric instrumentation and interfaces are addressed as they pertain to the use of a GD plasma as an ion source. GD sources provide analytically useful gas-phase species from solid samples. These sources can be interfaced with a variety of spectroscopic and spectrometric instruments for both quantitative and qualitative analyses.