Nature 352, 699 - 701 (22 August 1991); doi:10.1038/352699a0

Paradoxical behaviour of mechanical and electrical networks

Joel E. Cohen^*† & Paul Horowitz^‡

^†Rockefeller University, 1230 York Avenue, Box 20, New York, New York 10021-6399, USA
^‡Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
^*To whom correspondence should be addressed.

WE describe here a network of strings and springs in which cutting a string that supports a weight results in a rise of the weight at equilibrium. In an analogous electronic circuit of passive two-terminal devices (resistors and Zener diodes), adding a current-carrying path increases the voltage drop across the circuit. These systems are mechanical and electrical analogues of a paradox of congested traffic flow^1,2. Along with similar hydraulic and thermal analogues, they show how non-intuitive equilibrium behaviour can arise in physical networks made up of classical components.

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