论文标题
当两者都回家时
Capture of a diffusing lamb by a diffusing lion when both return home
论文作者
论文摘要
当允许他们两者间歇性地回到家园时，散布的狮子会追求散布的羔羊。通过一对恶性随机步行者识别系统，我们在泊松和尖锐的重置下研究了它们的动态。在没有任何重置的情况下，两个步行者的交集位置遵循凯奇的分布。在存在重置的情况下，歼灭位置的分布由两个部分组成：一个部分交叉而不重置（中心），而另一部分至少重置一次轨迹，然后再重置一次，然后它们相互交叉（尾巴）。我们发现，对于两个重置协议，尾部部分呈指数衰减。另一方面，分布的中心部分取决于重新启动方案的性质，库奇（Cauchy）用于泊松重置和高斯（Gaussian）进行清晰的重置。我们发现分析结果与数值计算的良好一致性。
A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting. In absence of any resets, the location of intersection of the two walkers follows a Cauchy distribution. In presence of resetting, the distribution of the location of annihilation is composed of two parts: one in which the trajectories cross without being reset (center) and the other where trajectories are reset at least once before they cross each other (tails). We find that the tail part decays exponentially for both the resetting protocols. The central part of the distribution, on the other hand, depends on the nature of the restart protocol, with Cauchy for Poisson resetting and Gaussian for sharp resetting. We find good agreement of the analytical results with numerical calculations.
