论文标题
无武力互惠的堆积物的拓扑状态和连续模型
Topological states and continuum model for swarmalators without force reciprocity
论文作者
论文摘要
堆积物是既是自propelled颗粒又是振荡器的代理系统。每个粒子都有一个相位调节其与其他颗粒的相互作用力的相。作为回报，相对位置调节相互作用粒子之间的相位同步。在当前模型中，没有力量互惠：当粒子吸引另一个粒子时，后者会排斥前者。这导致追求行为。在本文中，我们得出了该伴侣系统的流体动力模型，并表明它在两个空间维度中具有显式的双周期旅行波解决方案。这些特殊的解决方案享有通过一个时期沿相位矢量索引量化的非平凡拓扑结构。通过研究模型的双波利度条件来研究这些溶液的稳定性。显示了粒子和流体动力模型的数值解。他们证实了流体动力模型与粒子的一致性，对于小时或大相位，但在小相位噪声的情况下也揭示了有趣的模式的出现。
Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In return, relative positions modulate phase synchronization between interacting particles. In the present model, there is no force reciprocity: when a particle attracts another one, the latter repels the former. This results in a pursuit behavior. In this paper, we derive a hydrodynamic model of this swarmalator system and show that it has explicit doubly-periodic travelling-wave solutions in two space dimensions. These special solutions enjoy non-trivial topology quantified by the index of the phase vector along a period in either dimension. Stability of these solutions is studied by investigating the conditions for hyperbolicity of the model. Numerical solutions of both the particle and hydrodynamic models are shown. They confirm the consistency of the hydrodynamic model with the particle one for small times or large phase-noise but also reveal the emergence of intriguing patterns in the case of small phase-noise.
