SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2737-2748, January 2020.
This article studies ordinary differential equations modeling incompressible flow in rigid pipes that connect two distensible vessels, one of which is periodically forced. The forcing controls either the pressure or the volume of the excited vessel and---in part of the period---can be replaced by free relaxation. The pressure losses at the junctions of the pipes and vessels are quadratic with or without switches according to the direction of the flow. Stability and net flow of the equilibria of the unforced systems is investigated. Pumping solutions are defined and proven to exist in case of nonlinear pressure losses at the junctions. In contrast to often-quoted literature, it is shown that “impedance defined” piecewise linear models can not produce net flow with continuous solutions. For partial forcing models numerical simulations are reported.

中文翻译：

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刚性管道回路中的流动模型抽水

SIAM应用动力系统杂志，第19卷，第4期，第2737-2748页，2020年1月。
本文研究了常态微分方程，该方程对连接两个可扩张容器的刚性管道中的不可压缩流动进行建模，其中之一周期性地受力。强制控制受激血管的压力或体积，并且-在部分周期中-可以由自由松弛代替。根据流动方向，在有或没有开关的情况下，管道和容器交界处的压力损失是平方的。研究了非受力系统平衡的稳定性和净流量。定义并证明了在交界处存在非线性压力损失的情况下存在抽水解决方案。与经常引用的文献相反，它表明“阻抗定义”的分段线性模型不能在连续解的情况下产生净流量。对于部分强迫模型，报告了数值模拟。