Abstract
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 flow1,2. 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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References
Brass, D. Unternehmensforschung 12, 258–268 (1968).
Cohen, J. E. Am. Scient. 76, 576–583 (1988).
Horowitz, P. & Hill, W. The Art of Electronics 2nd Edn 304; 335–341; 1054–1055 (Cambridge University Press, New York, 1989).
Cohn, R. M. Proc. Am. math. Soc. 1, 316–324 (1950).
Bott, R. & Duffin, R. J. Trans. Am. math. Soc. 74, 99–109 (1953).
Duffin, R. J. in Studies in Graph Theory Vol. 1 (ed. Fulkerson, D. R.) 94–138 (Mathematical Association of America, Providence, 1975).
Landau, L. D. & Lifshitz, E. M. Fluid Mechanics (Pergamon, London, 1959).
Carslaw, H. S. & Jaeger, J. C. Conduction of Heat in Solids 2nd edn (Oxford University Press, 1959).
Steinberg, R. & Zangwill, W. I. Transportation Sci. 17, 301–318 (1983).
Dafermos, S. & Nagurney, A. Transportation Res. B 18, 101–110 (1984); Math. Programming 28, 174–184 (1984).
Cohen, J. E. & Kelly, F. P. J. appl. Probability 27, 730–734 (1990).
Dubey, P. Maths Ops Res. 11, 1–8 (1986).
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Cohen, J., Horowitz, P. Paradoxical behaviour of mechanical and electrical networks. Nature 352, 699–701 (1991). https://doi.org/10.1038/352699a0
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DOI: https://doi.org/10.1038/352699a0
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