2 resultados para Functions of a complex variable
em Repositório Científico da Universidade de Évora - Portugal
Resumo:
The Santa Eulalia plutonic complex (SEPC) is a late-Variscan granitic body placed in the Ossa-Morena Zone. The host rocks of the complex belong to metamorphic formations from Proterozoic to Lower Paleozoic. The SEPC is a ring massif (ca. 400 km2 area) composed by two main granitic facies with different colours and textures. From the rim to the core, there is (i) a peripheral pink medium- to coarse-grained granite (G0 group) involving large elongated masses of mafic and intermediate rocks, from gabbros to granodiorites (M group), and (ii) a central gray medium-grained granite (G1 group). The mafic to intermediate rocks (M group) are metaluminous and show wide compositions: 3.34–13.51 wt% MgO; 0.70–7.20 ppm Th; 0.84–1.06 (Eu/Eu*)N (Eu* calculated between Sm and Tb); 0.23–0.97 (Nb/Nb*)N (Nb* calculated between Th and La). Although involving the M-type bodies and forming the outer ring, the G0 granites are the most differentiated magmatic rocks of the SEPC, with a transitional character between metaluminous and peraluminous: 0.00–0.62 wt% MgO; 15.00–56.00 ppm Th; and 0.19–0.42 (Eu/Eu*)N ; 0.08–0.19 (Nb/Nb*)N [1][2]. The G1 group is composed by monzonitic granites with a dominant peraluminous character and represents the most homogeneous compositional group of the SEPC: 0.65–1.02 wt% MgO; 13.00–16.95 ppm Th; 0.57–0.70 (Eu/Eu*)N ; 0.14–0.16 (Nb/Nb*)N . According to the SiO2 vs. (Na2O+K2O–CaO) relationships, the M and G1 groups predominantly fall in the calc-alkaline field, while the G0 group is essencially alkali-calcic; on the basis of the SiO2 vs. FeOt/(FeOt+MgO) correlation, SEPC should be considered as a magnesian plutonic association [3]. New geochronological data (U-Pb on zircons) slightly correct the age of the SEPC, previously obtained by other methods (290 Ma, [4]). They provide ages of 306 2 Ma for the M group, 305 6 Ma for the G1 group, and 301 4 Ma for the G0 group, which confirm the late-Variscan character of the SEPC, indicating however a faintly older emplacement, during the Upper Carboniferous. Recent whole-rock isotopic data show that the Rb-Sr system suffered significant post-magmatic disturbance, but reveal a consistent set of Sm-Nd results valuable in the approach to the magmatic sources of this massif: M group (2.9 < Ndi < +1.8); G1 group (5.8 < Ndi < 4.6); G0 group (2.2 < Ndi < 0.8). These geochemical data suggest a petrogenetic model for the SEPC explained by a magmatic event developed in two stages. Initially, magmas derived from long-term depleted mantle sources (Ndi < +1.8 in M group) were extracted to the crust promoting its partial melting and extensive mixing and/or AFC magmatic evolution, thereby generating the G1 granites (Ndi < 4.6). Subsequently, a later extraction of similar primary magmas in the same place or nearby, could have caused partial melting of some intermediate facies (e.g. diorites) of the M group, followed by magmatic differentiation processes, mainly fractional crystallization, able to produce residual liquids compositionally close to the G0 granites (Ndi < 0.8). The kinetic energy associated with the structurally controlled (cauldron subsidence type?) motion of the G0 liquids to the periphery, would have been strong enough to drag up M group blocks as those occurring inside the G0 granitic ring.
Resumo:
Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10−10 in units of z2Ry. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.