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Processes which propagate faster than exponentially
On Jan 21, 3:30*pm, jbriggs444 wrote:
Suppose you have 10 miles of oil in the Alaskan pipeline bearing down on a closed valve at a rate of one meter per second buffered by a 2 meter air bubble at 1 atmosphere directly adjacent to the valve. (Some idiot closed the valve abruptly) Assume that all relevant safety devices have been disabled and no other air bubbles exist. I think that the rate of increase of air pressure with respect to time and with respect to distance are both super-exponential (or are best modelled by a curve that is super-exponential) right up to the point where the pipe breaks. Yes, this is another example. One needs only to formulate the diff.eq. to see that this is super-exponential in the ideal case. If the oil has infinite motivating force and the pipe infinite strength, we have P = 1/(t'-t) where t' is when the bubble is crushed. This is equivalent to P' = P^2 which clearly grows faster than the exponential P' = P . Andrew Usher |
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