Kruk Nikita, Carrillo José A, Koeppl Heinz
Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, Rundeturmstrasse 12, 64283 Darmstadt, Germany.
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Phys Rev E. 2020 Aug;102(2-1):022604. doi: 10.1103/PhysRevE.102.022604.
We consider stochastic dynamics of self-propelled particles with nonlocal normalized alignment interactions subject to phase lag. The role of the lag is to indirectly generate chirality into particle motion. To understand large-scale behavior, we derive a continuum description of an active Brownian particle flow with macroscopic scaling in the form of a partial differential equation for a one-particle probability density function. Due to indirect chirality, we find a spatially homogeneous nonstationary analytic solution for this class of equations. Our development of kinetic and hydrodynamic theories towards such a solution reveals the existence of a wide variety of spatially nonhomogeneous patterns reminiscent of traveling bands, clouds, and vortical structures of linear active matter. Our model may thereby serve as the basis for understanding the nature of chiral active media and designing multiagent swarms with designated behavior.
我们考虑具有非局部归一化对齐相互作用且存在相位滞后的自驱动粒子的随机动力学。滞后的作用是间接在粒子运动中产生手性。为了理解大规模行为，我们以单粒子概率密度函数的偏微分方程形式，推导出具有宏观尺度的活性布朗粒子流的连续描述。由于间接手性，我们找到了这类方程的空间均匀非平稳解析解。我们针对此类解发展的动力学和流体动力学理论揭示了存在多种空间非均匀模式，这些模式让人联想到线性活性物质的行波带、云团和涡旋结构。因此，我们的模型可作为理解手性活性介质本质以及设计具有指定行为的多智能体群体的基础。
