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Mixing Problems with Many Tanks

Antonín Slavík
The American Mathematical Monthly
Vol. 120, No. 9 (November 2013), pp. 806-821
DOI: 10.4169/amer.math.monthly.120.09.806
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Page Count: 16
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Mixing Problems with Many Tanks
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Abstract We revisit the classical calculus problem of describing the flow of brine in a system of tanks connected by pipes. For various configurations involving an arbitrary number of tanks, we show that the corresponding linear system of differential equations can be solved analytically. Finally, we analyze the asymptotic behavior of solutions for a general closed system of tanks. It turns out that the problem is closely related to the study of Laplacian matrices for directed graphs.

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