论文标题
分支运行颗粒的极端价值统计数据
Extreme value statistics for branching run-and-tumble particles
论文作者
论文摘要
主动物质的极端价值统计数据为其独特的特性提供了重要的见解。最近在分支跑步颗粒的模型中报道了相变，描述了一维活性物质不断发展的菌落的空间扩散。在“持续”阶段，颗粒形成宏观的稳健簇，在“间歇性”相中，整个弹道传播，而是隔离粒子。我们将研究重点放在最右边位置的波动上，$ x _ {\ max}（t）$按时间$ t $为此型号而言。长期以来，随着殖民地逐渐入侵未开发的区域，$ x _ {\ max}（t）$的累积概率被旅行的前沿描述。过渡对这一方面产生了显着影响。在间歇性阶段，它在质量上与满足Fisher-KPP方程的前部相似，该方程式著名地描述了非活动性分支布朗尼运动的极值统计。在持续的阶段出现了截然不同的行为，在这种阶段中，活动赋予了我们准确地计算出意外和异常特征的前部。
The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an evolving colony of active matter in one-dimension. In a "persistent" phase, the particles form macroscopic robust clusters that ballistically propagate as a whole while in an "intermittent" phase, particles are isolated instead. We focus our study on the fluctuations of the rightmost position $x_{\max}(t)$ reached by time $t$ for this model. At long time, as the colony progressively invades the unexplored region, the cumulative probability of $x_{\max}(t)$ is described by a travelling front. The transition has a remarkable impact on this front. In the intermittent phase it is qualitatively similar to the front satisfying the Fisher-KPP equation, which famously describes the extreme value statistics of the non-active branching Brownian motion. A dramatically different behaviour appears in the persistent phase, where activity imparts the front with unexpected and unusual features which we compute exactly.
