The math of faucet-fiddling to get a constantly warm shower

Charles Betz says:
Christina Matzke at the University of Bonn in Germany and Damien Challet of the Institute for Scientific Interchange in Turin, Italy, used a mathematical model to show that shower temperature becomes increasingly sensitive to small changes in hot-water flow as the number of users increases. Thus in a youth hostel, for example, the showers often fluctuate between scalding hot and ice cold during heavy use.
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