Caustic Sheet Waveforms in Non-Euclidean Geometries: Relevance to Spacetime Phase-Transition Geometries at Pacific-Atoll Detonations

In Figure 6, on p. 23, of this article [Frittelli and Petters, 2002: (http://arxiv.org/PS_cache/astro-ph/pdf/0208/0208135v1.pdf)], the authors show the kind of three-dimensional caustic sheet waveforms that can be viewed as being waveforms that would accompany the presence of a two-dimensional, "M-shaped" shock-front shape. An M-shaped shock front is, as I'll try to show in some diagrams, soon, in its simplest incarnation, a kind of "triad" of Rayleigh-Taylor instability surfaces, with one surface existing as a central peak and the other two (or four or many, in a ring or spiral around the central peak) being pushed down to the sides or to the circumference or perimeter (or whatever) of the ring or other region that surrounds the central peak.

Anyway, the waveforms shown in that article don't really capture the geometry one would expect to see for the central "peak" of an X-wave that a mushroom cloud can be viewed as constituting So-called "M-shaped" shock waves or caustic waveforms can be seen trailing behind (and at the front of) some airplanes, when the airplanes are flying at supersonic speeds. The authors weren't trying to show shock wave geometries, but some of those waveforms could be regarded as being approximations for the types of replication geometries or, more precisely, "replication-directing, phase-transition-boundary-surface-geometries" one might see, in my view, if one mapped out or simulated the geometries of the phase-transition surfaces at some of the nuclear detonations at Pacific atoll sites (sites that exhibit, in many cases, M-shaped geometries). Some ground-based gravitational wave detectors also exhibit M-shaped, "cross-like" geometries.

Everything surrounding this stuff is so terrible and so terribly sad.