Free boundary skin current magnetohydrodynamic equilibria
Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.
In the footsteps of our previous work \cite{RamatonBoschi} we generalize the Stefan-Boltzmann and Wien's displacement laws for the $ \textrm{AdS}_5 \times {\cal S}^5 $ spacetime, the background of the AdS/CFT correspondence foremost realization. Our results take into account the $ \textrm{AdS}_5 \times {\cal S}^5 $ full dimensionality in the electromagnetic field $A^{\mu}$ wave equation, which yields the higher-dimensional blackbody characteristic features suggested in literature. In particular, the total radiated power and the spectral radiancy match the original Stefan-Boltzmann and Wien's displacement laws in the low-energy regime up to available experimental data.