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: 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.

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: 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: This chapter lays out a conservation timeline, from past to future, for the Amsterdam version of Van Gogh's Sunflowers. It starts by considering the restoration history of the painting in order to assess its current physical state, and looks ahead to formulate an appropriate strategy for future conservation treatment and display. Due attention is paid to the two recorded episodes of restoration performed in 1927 and 1961 by the Dutch restorer, Jan Cornelis Traas. Based on physical and chemical investigation of Sunflowers we attempt to reconstruct what these former treatments (which are barely documented) entailed and consider the repercussions for the present condition of the painting. The former interventions by Traas also serve as a benchmark to reflect on current choices made, highlighting the extent to which ideas and methodologies have continued to evolve over the past century as conservation has moved further away from being a singularly craft-based activity to become an established historical and scientific discipline underpinned by ethical guidelines. Jan Cornelis Traas (1898–1984) As mentioned, the two main recorded interventions to the Amsterdam Sunflowers may be associated with the Dutch restorer, Jan Cornelis Traas, who treated the picture in 1927, close to the start of his career, and again in 1961, shortly before he retired. Traas was the first restorer to be appointed at the Mauritshuis in The Hague where he worked from 1931 to 1962 and treated hundreds of paintings, including iconic masterpieces such as Girl with a Pearl Earring by Johannes Vermeer. Yet despite the magnitude and importance of his restoration oeuvre, J.C. Traas (as he is usually referred to in surviving documents), has remained somewhat obscure. He is shown here in the only known surviving photograph of him at work, shortly before he retired (fig. 7.1). Unlike his illustrious contemporaries, A. Martin de Wild (1899–1969) and Helmut Ruhemann (1891–1973), for example, Traas did not publish anything, he appears to have kept no records of his work and no personal archive is known. However, the study of some newly discovered historical documents, combined with physical examination of Sunflowers and a large number of other works he treated, allows us to recover an idea of his working practices and approaches viewed within the context of his day.

Abstract: This chapter explains the materials and techniques employed in the Amsterdam Sunflowers, enabling a comparison with the London version described in chapter 3. Building upon the 2016 article published in the National Gallery Technical Bulletin, it incorporates the latest findings gained by computer-assisted methods used to characterize the canvas support, as well as in-situ campaigns of non-invasive investigation together with further analysis of microscopic paint samples. The chapter sequence follows the steps in Van Gogh's working practice. Starting with the canvas, automated analysis of the weave enables the provenance of the canvas to be traced back to a particular roll of linen ordered by Van Gogh. Combining technical evidence with knowledge of historical manufacturing techniques further allows us to reconstruct the way in which Van Gogh divided his canvas roll into pieces used for Sunflowers and other paintings. We go on to consider how, with the original painting at hand, he used charcoal to transfer the motif of the London Sunflowers onto his blank canvas. Despite careful planning of the composition, an adjustment was required late in the working process, when Van Gogh added a painted wooden strip to extend the background above the flower at the top edge of the canvas. The artist's process of working up the composition in paint is described, paying special attention to his use of colour. The pigments and pigment mixtures used in the Amsterdam Sunflowers have been comprehensively mapped and are compared with the London picture, with discussion of some similarities and differences that account for the distinctive colour scheme of each painting. This understanding of colour application in the Amsterdam Sunflowers lays the foundation for subsequent chapters that will go on to consider the impact of light-induced colour changes that have taken place over time, and the related need to define appropriate lighting guidelines for the future safe preservation of this painting and others made with similar materials (chapters 5 and 7).

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: Recent studies in which X-ray beams of (sub)micrometre to millimetre dimensions have been used for non-destructive analysis and characterization of pigments, minute paint samples and/or entire paintings from fifteenth to twentieth century artists are discussed. 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 with X-ray diffraction (XRD). Microscopic XRF (μ-XRF) is a variant of the XRF method able to visualize the elemental distribution of key elements, mostly metals, on the scale from 1 μm to 100 μm present inside multi-layered micro samples taken from paintings. In the context of the characterization of artists’ pigments subjected to natural degradation, in many cases the use of methods limited to elemental analysis or imaging does not suffice to elucidate the chemical transformations that have taken place. However, at synchrotron facilities, combinations of μ-XRF with related methods such as μ-XAS (microscopic X-ray absorption spectroscopy) and μ-XRD have proven themselves to be very suitable for such studies. Since microscopic investigation of a relatively limited number of minute paint samples may not yield representative information about the complete artefact they were taken from, several methods for macroscopic, non-invasive imaging have recently been developed. Combined macroscopic XRF/XRD scanning is able to provide a fairly complete overview of the inorganic pigments employed to create a work of art, to answer questions about ongoing degradation phenomena and about its authenticity. As such these newly developed non-invasive and highly specific imaging methods are of interest for many cultural heritage stakeholders.