We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length $L<L^{*}$ and for high tumbling rates $\lambda >{\lambda }^{*}$, with threshold values $L^{*}$ and ${\lambda }^{*}$ which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs.

中文翻译：

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微通道中主动流动的晶格模型

我们引入一维晶格模型来研究连接有限储层的窄通道中的活性颗粒。该模型描述了相互作用的奔跑游泳者在相邻粒子上施加推力，从而允许在通道内形成长的活动簇。我们的模型能够重现在自推进细菌的完整分子动力学模拟中观察到的新兴振荡动力学[Paoluzzi等。，物理 牧师 115，188303（2015）]，并允许我们以简单的方式将分析扩展到广泛的系统参数（框长，游泳者数量），同时考虑到不同的物理条件（存在或不存在翻滚，不同形式的进入渠道的可能性）。我们发现，对于短通道长度，振荡行为受到抑制$\mathrm{大号}<{\mathrm{大号}}^{*}$ 高翻滚率 $\lambda >{\lambda }^{*}$，具有阈值 ${\mathrm{大号}}^{*}$ 和 ${\lambda }^{*}$通常取决于物理参数。此外，我们发现，通过使用不同的进入概率，振荡仍会持续，但是，这会影响振荡特性和储层的充注动力学。