Abstract: Electron continement and its effect on the superconducting-to-normal phase transition driven by a magentic field and/or a current is studied in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We find that in a parallel magneitc field and/or in the presence of a supercurrent the transition from the superconducting to the normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magentic field exhibits quantum-size oscillations with pronounced resonant enhancements as a function of the wire radius.

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: Optical (atomic absorption spectroscopy, AAS; atomic emission spectroscopy, AES; atomic fluorescence spectroscopy, AFS; and optogalvanic spectroscopy) and mass spectrometric (magnetic sector, quadrupolemass 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 (5001500 V) is applied between an anode and a cathode. In most cases, the sample is also the cathode. A noble gas (e.g. Ar, Ne, and Xe) 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. 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. Unfortunately, the GD source functions optimally in a dry environment, making analysis of solutions more difficult. These sources also suffer from difficulties associated with analyzing nonconductingsamples. 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 samples. The requirements necessary to obtain optical information are addressed following the analytical applications. This section 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. GDsources provide analytically useful gas-phase species from solid samples. These sources can be interfaced with avariety of spectroscopic and spectrometric instruments for both quantitative and qualitative analysis.