Wave

The wave theory foundations of today's radio occultation techniquesForty years ago, the premier radio occultation problem was how to profile the atmosphere and radius of Mars using signals sent by the Mariner 4 spacecraft. Researchers then could rely on ray theory-based techniques for accurate analysis of the thin, uniform Martian atmosphere. Today's radio occultation challenges mostly involve communications platforms-and related data, instrument systems, and applications-in the Earth's own atmosphere.

Wave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric $g$. By Noether's theorem, symmetries of the Lagrangian imply conservation laws for wave maps, such as conservation of energy.