The black-body radiation is considered in a theory with noncommutative electromagnetic fields; that is noncommutativity is introduced in field space, rather than in real space. A direct implication of the result on Cosmic Microwave Background map is argued.

Including loop corrections, black-body radiation in noncommutative space is anisotropic. A direct implication of possible space noncommutativity on the Cosmic Microwave Background map is argued.

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young–Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

A new set of mathematical identities is presented for axi-symmetric sessile drops on flat and curved substrates. The geometrical parameters, including the apex curvature and height, and the contact radius, are related by the identities. The validity of the identities are checked by various numerical solutions both for flat and curved substrates.

The problem of black-body radiation is considered in the Born-Infeld theory of electrodynamics. In particular, at 2-loop order the deviation from the Planck expression due to the self-interaction of photons is calculated. It is seen that the system of interacting photons of the theory, opposed to its non-Abelian counterpart, has higher internal energy at this order of perturbation. Possible implications of the result on the evolution of very hight temperature systems, including various stellar media and the early universe, are briefly discussed.