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Mixing Problems with Many Tanks
The American Mathematical Monthly
Vol. 120, No. 9 (November 2013), pp. 806-821
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.09.806
Page Count: 16
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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.
Copyright the Mathematical Association of America 2013