Path coalescence transition and its applications.
Path coalescence transition and its applications.
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路径合并转变及其应用。
DOI：
10.1103/physreve.68.040101
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Bernhard Mehlig
中科院分区：
文献类型：
--
作者：
Michael Wilkinson;Bernhard Mehlig
我们分析了一个系统的粒子受到随机力波动在空间和时间，并经历粘性阻尼的运动。当阻尼超过某个阈值时，系统会发生相变;粒子轨迹会合并。我们通过将其映射到我们精确解决的Kramers问题来分析这种转变。在弱随机力的限制下，我们通过计算焦散线交叉的速率和聚结相中粒子密度的统计来表征动力学。最后但并非最不重要的是，我们描述了可能实现的效果，从雨滴的轨迹有机玻璃表面的动物迁徙模式。
We analyze the motion of a system of particles subjected to a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition; the particle trajectories coalesce. We analyze this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterize the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realizations of the effect, ranging from trajectories of raindrops on perspex surfaces to animal migration patterns.