通过排列和体积排除相互作用的自推进盘的多层模型
A multi-layer model for self-propelled disks interacting through alignment and volume exclusion
摘要：
我们提出了一个基于个人的模型，描述平行平面内移动的圆盘状自推进粒子。磁盘的运动方向遵循每层内部的对齐规则。此外，磁盘受到与那些相邻层的体积排除约束所引起的相互作用。这些相互作用影响盘相对于运动平面的倾角。我们正式推导了一个宏观模型，该模型由描述质量输运和圆盘在每个平面中的平均运动方向的演化的平面自组织流体动力学（SOH）模型组成，并补充了平均圆盘倾角的输运方程。这些平面模型由于与相邻平面的相互作用而耦合。基于个人和宏观模型之间的数值比较进行。例如，这些模型可以用于描述精子细胞的集体动力学。
英文摘要：
We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow alignment rules inside each layer. Additionally, the disks are subject to interactions with those of the neighboring layers arising from volume exclusion constraints. These interactions affect the disk inclinations with respect to the plane of motion. We formally de-rive a macroscopic model composed of planar Self-Organized Hydrodynamic (SOH) models describing the transport of mass and evolution of mean direction of motion of the disks in each plane, supplemented with transport equations for the mean disk inclination. These planar models are coupled due to the interactions with the neighboring planes. Numerical comparisons between the individual-based and macroscopic models are carried out. These models could be applicable, for instance, to describe sperm-cell collective dynamics.
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