环上自行运动樟脑粒子化学浓度波的精确解：一种新的势动力学观点
Exact solutions for chemical concentration waves of self-propelling camphor particles racing on a ring: A novel potential dynamics perspective
摘要：
发展了一种势动力学方法来确定漂浮在环形水槽上的自推进樟脑物体的周期性驻波和行波模式。导出了波型的精确解。半解析地导出了描述樟脑天体不动和自推进模式之间转变的分岔图。分叉是一个干草叉型，这是与早期的理论工作，其中自然边界条件已被认为是一致的。
英文摘要：
A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are derived. The bifurcation diagram describing the transition between the immobile and self-propelling modes of camphor objects is derived semi-analytically. The bifurcation is of a pitchfork type which is consistent with earlier theoretical work in which natural boundary conditions have been considered.
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