磁化颗粒在$S^{1}$上运行和翻滚
Magnetized granular particles running and tumbling on $S^{1}$
摘要：
研究表明，非振动磁性颗粒系统在交变磁场作用下，具有活性物质系统的大部分物理特性。在这项工作中，我们把我们的注意力集中在最简单的颗粒系统组成的一个单一的磁化球形粒子分配在一个准一维的圆形通道，从磁场水库接收能量，并将其转换成一个运行和翻滚运动。基于半径为R的圆上的奔跑和翻滚模型的理论分析预测了在奔跑和翻滚运动的特征持续长度为$\ell_{c} < R/2$时的不规则运动（无序相）与$\ell_{c}> R/2$时的持续运动（有序相）之间存在动力学相变。发现这些相的极限行为分别对应于圆周上的布朗运动和简单的匀速圆周运动。定性地表明，粒子的磁化强度越低，其余辉长度越大。至少在我们实验的有效性的实验限度内是这样的。我们的研究结果表明，理论和实验之间有很好的一致性。
英文摘要：
It has been shown that a nonvibrated magnetic granular system, when it is feeded by means an altenating magnetic field, behaves with most of the distinctive physical features of active matter systems. In this work we focus our attention on the simplest granular system composed by a single magnetized spherical particle allocated in a quasi one-dimensional circular channel that receives energy from a magnetic field reservoir and transduces it into a running and tumbling motion. The theoretical analysis based on the run and tumble model on a circle of radius R forecasts the existence of a dynamical phase transition between an erratic motion (disordered phase) when the characteristic persistence length of the run and tumble motion, $\ell_{c} < R/2$, to a persistent motion (ordered phase) when $\ell_{c}> R/2$. It is found that the limiting behaviours of these phases correspond to a Brownian motion on the circle and a simple uniform circular motion, respectively. It is qualitatively shown that the lower magnetization of a particle, the larger persistence lenght is. It is so at least within the experimental limit of validity of our experiments. Our results show a very good agreement between theory and experiment.
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