The Brazil Nut Problem, imaged with MRI. Why do the large nuts rise to the top in a shaken can of mixed nuts? This work shows that it is NOT because the small nuts squeeze under the big ones, with a net upward movement of the big ones bouncing on top. Instead, this shows that a convective flow develops and that ALL nuts move upward, while only the smaller ones are able to enter the corresponding downward flow (visible along the sides of the second image). See a nice review of theory and experiment.
This is still a very active area of research, and corresponding to the title, the results can not yet be explained based on first principles. This is an emergent property of nuts, people, and (often) beer.
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