Elements in the development of how the Great Doxologies were sung from the 18th to the 19th century

The main protagonist of the 19th century reformation, Chrysanthos, bishop of Madyta, as well as important 20th century scholars such as Constantinos Psachos and Gregorios Stathis, claimed that old Byzantine melodies transferred unchanged over the centuries through a process called “exegesis”. According to them, this was a kind of transcription of the melodies from a mainly stenographic to a more analytical version of the old Byzantine notation. Hence, the New Method system allowed these melodies to be notated in the most detailed and accurate way, so far. In our research, we question the validity of this theory at least concerning the way of singing Great Doxologies. On the one hand, we analyze different exegeses of the same old Doxologies, in which we find important variations regarding the interchangeability between syllabic and neumatic approach, the addition of extra melismata at the end of some phrases, and the choice of the point where “neumatization” starts. On the other hand, we compare two old Doxologies recorded in middle-18th century in five-line score with their exegeses made by Chourmouzios Chartofylax in early-19th century, where, in addition to the above-mentioned variations, we observe a differentiation in the whole texture of the two versions. Thus, we conclude that Old Method was partly ambiguous at least at the period before the New Method reformation, while we suspect that a semantic shifting of the term exegesis occurred at the same period. Furthermore, we present two ideas that may justify the development that took place, the one related to a redistribution of the tempo and the other to a possible rubato interpretation of Byzantine chants that gradually became mensuralistic

Electromagnetic low-frequency dipolar excitation of two metal spheres in a conductive medium

International audienceThis work concerns the low-frequency interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spheres embedded within a homogeneous conductive medium. In several applications, where two bodies are placed near one another, the 3-D bispherical geometry provides a good approximation. The particular physical problem is modeled by considering two solid impenetrable (metallic) obstacles, excited by a magnetic dipole, where the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers (ik) to the power n, where n ≥ 0 , k being the complex wave number of the exterior medium, for the incident, scattered and total electric and magnetic fields. We deal with the most important terms of the low-frequency expansions of the non-axisymmetric scattered electromagnetic fields, that is the static (for n=0) and the dynamic (n=1,2,3) terms, while for n≥4 the contribution of the additional terms is of minor significance. The calculation of the exact solutions, satisfying Laplace's and Poisson's differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. Thus, we obtain the electromagnetic fields in an analytically compact fashion as infinite series expansions of bispherical eigenfunctions. This particular electromagnetic scattering problem is then simulated in order to investigate the effect of the radii ratio, the relative position of the spheres and the position of the dipole on the real and imaginary parts of the calculated scattered magnetic field

Low-frequency electromagnetic scattering by two PEC spheres buried in conductive medium

ISSN 1559-9450International audienceAnalytical approaches of low-frequency electromagnetic scattering by perfectly conducting (PEC) bodies in conductive media involve expanding fields into positive integral powers of (jk), k wavenumber of the embedding medium at frequency ω, k = √jωσμ, σ conductivity, μ permeability, and calculating the real-valued vector coefficients at each power n: Rayleigh term n = 0, first dynamic ones n = 2, n = 3, the n = 1 term being trivial due to absence of primary field term for a magnetic dipole (current loop sources are employed, assimilated to dipoles). The magnetic field comprises an in-phase component (essentially from n = 0) and a quadrature component (from n = 2). In this contribution two simple bodies are modeled as spheres, of arbitrary radii and distance from one another (contact excepted), with limit case of one sphere collapsed to a plane, the magnetic dipole being of arbitrary location and orientation. The BVP is dealt with in the bispherical system of coordinates (attached to the spheres) and scalar/vector Laplace equations handled via harmonic eigenfunction expansions and using R-separability, + boundary conditions on the two surfaces. The main points of the analytical works carried out are sketched in the provided documents while numerical results obtained at low computational cost, even if the spheres almost touch one another, illustrate the investigation

Ionization wave propagation and cathode sheath formation due to surface dielectric-barrier discharge sustained in pulsed mode

International audienceThis work deals with the experimental study of a surface dielectric-barrier discharge (DBD), as a part of the ongoing interest in the control of plasma induced electro-fluid dynamic effects (e.g., plasma actuators). The discharge is generated using a plasma reactor consisting of a fused silica plate which is sandwiched between two printed circuit boards where the electrodes are developed. The reactor is driven by narrow high voltage square pulses of asymmetric rising (25 ns) and falling (2.5 μs) parts, while the discharge evolution is con-sidered in a temporarily and spatially resolved manner over these pulses. That is, conventional electrical and optical emission analyses are combined with high resolution optical emission spectroscopy and ns-resolved imaging, unveiling main characteristics of the discharge with a special focus on its propagation along the dielectric-barrier surface. The voltage rising part leads to cathode-directed ionization waves, which propagate with a speed up to 10^5 m s−1. The voltage falling part leads to cathode sheath formation on the driven electrode. Τhe polarization of the dielectric barrier appears critical for the discharge dynamics

Computational Approach of Charging and Discharging Phases in a Novel Compact Solar Collector with Integrated Thermal Energy Storage Tank: Study of Different Phase Change Materials

A numerical study was carried out to investigate charging and discharging processes of different phase change materials (PCMs) used for thermal storage in an innovative solar collector, targeting domestic hot water (DHW) requirements. The aim was to study PCMs that meet all application requirements, considering their thermal performance in terms of stored and retrieved energy, outlet temperatures, and water flow rate. Work was carried out for three flat-plate solar panels of different sizes. For each panel, a PCM tank with a heat exchanger was attached on the back plate. Simulations were conducted on a 2D domain using the enthalpy–porosity technique. Three paraffin-based PCMs were studied, two (A53, P53) with phase-change temperatures of approximately 53 °C and one of approximately 58 °C (A58H). Results showed that, during charging, A58H can store the most energy and A53 the least (12.30 kWh and 10.54 kWh, respectively, for the biggest unit). However, the biggest unit, A58H, takes the most time to be fully charged, i.e., 6.43 h for the fastest feed rate, while the A53 unit charges the fastest, at 4.25 h. The behavior of P53 lies in between A53 and A58H, considering stored energy and charging time. During discharging, all PCMs could provide an adequate DHW amount, even in the worst case, that is, a small unit with a high hot water consumption rate. The A58H unit provides hot water above 40 °C for 10 min, P53 for 11 min, and A53 for 12 min. The DHW production duration increased if a bigger unit was used or if the consumption rate was lower

Computational Approach of Charging and Discharging Phases in a Novel Compact Solar Collector with Integrated Thermal Energy Storage Tank: Study of Different Phase Change Materials

A numerical study was carried out to investigate charging and discharging processes of different phase change materials (PCMs) used for thermal storage in an innovative solar collector, targeting domestic hot water (DHW) requirements. The aim was to study PCMs that meet all application requirements, considering their thermal performance in terms of stored and retrieved energy, outlet temperatures, and water flow rate. Work was carried out for three flat-plate solar panels of different sizes. For each panel, a PCM tank with a heat exchanger was attached on the back plate. Simulations were conducted on a 2D domain using the enthalpy–porosity technique. Three paraffin-based PCMs were studied, two (A53, P53) with phase-change temperatures of approximately 53 °C and one of approximately 58 °C (A58H). Results showed that, during charging, A58H can store the most energy and A53 the least (12.30 kWh and 10.54 kWh, respectively, for the biggest unit). However, the biggest unit, A58H, takes the most time to be fully charged, i.e., 6.43 h for the fastest feed rate, while the A53 unit charges the fastest, at 4.25 h. The behavior of P53 lies in between A53 and A58H, considering stored energy and charging time. During discharging, all PCMs could provide an adequate DHW amount, even in the worst case, that is, a small unit with a high hot water consumption rate. The A58H unit provides hot water above 40 °C for 10 min, P53 for 11 min, and A53 for 12 min. The DHW production duration increased if a bigger unit was used or if the consumption rate was lower