Fischer Andreas, Schmid Friederike, Speck Thomas
Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
Phys Rev E. 2020 Jan;101(1-1):012601. doi: 10.1103/PhysRevE.101.012601.
We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.
我们为通过自生成场相互作用的极性活性粒子发展了一种动态平均场理论，特别是通过发射化学信号产生的场。虽然这是一种趋化反应形式，但它与传统趋化作用不同，因为当局部浓度超过阈值时，粒子会不连续地改变其运动性。由此产生的密度和极化耦合方程是线性的，对于简单几何形状可以解析求解，从而产生非均匀密度分布。具体来说，这里我们考虑一个平面和圆形界面。因此，我们的理论解释了观察到的致密聚集体与活性气体的共存现象。然而，与基于自由能的更传统的液 - 气共存图景存在差异，最显著的是不存在临界点。我们通过对受限且通过体积排除相互作用的活性粒子进行数值模拟来证实我们的分析预测。通过一个有效的平移扩散系数实现了出色的定量一致性。我们最终表明，对化学梯度方向的额外响应足以诱导涡旋簇。我们的结果为设计运动响应铺平了道路，以便即使在不利条件下也能实现聚集和集体行为。
