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Double Bubble Trouble?

April 8, 2013
storymaker-weirdest-mars-craters-1112305-514x268

Strange Mars Crater

Besides the fact that these do not really look like impact craters at all, I can think of no way ordinary matter can make that pattern through an impact with such a straight line between the two craters. A force is trying to minimize area for the volumes, which I believe is gravity. I also believe those are sinkholes and not craters.  I believe the ionizing radiation and gravity is causing the sinkhole.

The isoperimetric problem, in an n-dimensional Riemannian manifold, is to enclose a region of a given (n-dimensional) volume v using a hypersurface of the smallest possible “area” (n-1 dimensional volume). For example, in Euclidean space, a classical theorem asserts that the unique area-minimizer is a sphere. The “soap bubble problem” is a generalization in which the problem is to enclose and separate m regions of prescribed volumes v_1, …, v_m, using a (singular) hypersurface of minimal area. In many cases there is a natural conjecture for the area-minimizer, but proving it can be extremely difficult. For example, the Double Bubble Conjecture in R^3 was proved only recently. This conjecture, or now theorem, asserts that the least-area enclosure of two prescribed volumes in R^3 is the “standard double bubble”, consisting of three pieces of spheres meeting along a circle at 120 degree angles. There is one such shape for each pair of volumes; if the two volumes are equal, the middle “sphere” is a flat disc. The standard double bubble looks like this:

double bubbleGodspeed

 

From → Astrophysics

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