lew@ihuxr.UUCP (09/19/83)
In spite of my inability to make sense of Jim Stekas's "closed orbit" arguments, he struck a chord with me when he mentioned that the cross section of the trapezoidal holes must be the same in either direction. Of course, Alan Wendt was making the specific assertion that the cross section was different (to the tune of a factor of 3) in opposite directions, so that Jim's surprise that this was "overlooked" is a little puzzling, but I think Jim may have the last laugh here. I tried calculating the 2-d cross section of a trapezoidal hole (in 3-d this would be a long slit with trapezoidal "cross section" (different meaning here) ). It turned out to be the same in either direction. I got 1 = 1 + (cos - sin) - (cos - sin). This makes me think that Alan might have made a mistake in the set-up of his simulation. Reversibility of paths isn't sufficient in itself to enforce this. We can imagine, for example, a narrow range of angles being fanned out into a wide range, so that a greater flux is being intercepted on one side. However, I think it comes out in the wash that a narrowing of angular distribution entails a broadening of cross sectional area over those angles, so that the same flux will be sampled. I think this may be related to the conservation of phase space volume (Liouville's Theorem). If this is the case, my suggested resolution invoking thermal interaction with the walls is moot. I think you should be able to model a gas as hard spheres with smooth elastic walls ... and no quantum mechanics! Lew Mammel, Jr. ihnp4!ihuxr!lew