Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Experimental lifetime determination in neutral praseodymium (Pr I) and neodymium (Nd I)

Radiative lifetime measurements have been performed, with a time-resolved laser-induced fluorescence technique, for 18 even-parity levels of Pr I and 15 odd-parity levels of Nd I. The new results are compared with the few experimental data available in the literature and good agreement is found. However, fragmentary knowledge of the spectra prevents reliable calculation of branching fractions and calls for additional laboratory efforts in order to provide the astrophysicists with reliable transition probabilities needed for investigating the magnetic fields in chemically peculiar stars