My Math Forum Cube with spheres bumping within

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 August 20th, 2017, 08:54 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 464 Thanks: 29 Math Focus: Number theory Cube with spheres bumping within Take a cubic box of edge E, wherein two spheres of like diameter and mass bounce elastically. Will the box move randomly or not?
 August 20th, 2017, 09:17 PM #2 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 You miss several physical info: For example if you shake the box to move the balls, or you just launch them etc... The most simple case is if you have an open box, wide enough, and you just live vertically falling the two (separate) perfectly spherical (of mechanical known characteristic) balls from a fixed eight that is less than the height of the box, and they bump on a perfectly plane (rigid or not) bottom surface... etc... in this case is deterministic, else the problem can becomes non deterministic, for example if you shake the box, than you stop it looking the balls bumping....
August 20th, 2017, 09:32 PM   #3
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Quote:
 For example if you shake the box to move the balls, or you just launch them etc.
Perhaps the result is the same for each regarding randomness/determinism.

I was trying to minimise the parameters of the problem and preserve its basis.

August 28th, 2017, 07:19 AM   #4
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Quote:
 Originally Posted by Loren Take a cubic box of edge E, wherein two spheres of like diameter and mass bounce elastically. Will the box move randomly or not?
In reality, gases inside boxes exert equal pressure on the six faces of the box and the magnitude of statistical fluctuations for pressure inside the box are so small relative to the force required to overcome friction that no movement occurs. If the box is in a vacuum sitting on a frictionless surface with a gas trapped inside it, statistical variations in pressure can occur, but the acceleration caused by the fluctuations is so tiny that any macroscopic motion is virtually undetectable.

However, statistical dynamics of gases can become very important in some studies. For example, one of the ways of cooling gases down to very low temperatures (e.g. whilst studying Bose-Einstein condensates and the like) is to take a small sample of very-low energy particles and let the ones with the greatest energy out of them all (i.e. those at the top end of the Maxwell-Boltzmann distribution) leave. The net effect on the whole sample is a cooling effect that's somewhat similar to macroscopic evaporative cooling

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