I doubt that a proof is possible without more assumptions, e.g. about the contact friction and the shape of the container. But the problem has been studied and given a name "the museli effect" for the larger objects tending to the top. https://en.wikipedia.org/wiki/Granular_convection Brent On 12/10/2018 9:16 AM, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
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