Department of Mathematics, Duke University, Durham, USA.
Bull Math Biol. 2022 Jun 1;84(7):71. doi: 10.1007/s11538-022-01024-4.
In this paper, we consider the dynamics of a 2D target-searching agent performing Brownian motion under the influence of fluid shear flow and chemical attraction. The analysis is motivated by numerous situations in biology where these effects are present, such as broadcast spawning of marine animals and other reproduction processes or workings of the immune systems. We rigorously characterize the limit of the expected hit time in the large flow amplitude limit as corresponding to the effective one-dimensional problem. We also perform numerical computations to characterize the finer properties of the expected duration of the search. The numerical experiments show many interesting features of the process and in particular existence of the optimal value of the shear flow that minimizes the expected target hit time and outperforms the large flow limit.
在本文中，我们考虑了在流体切变流和化学吸引力的影响下，执行布朗运动的二维目标搜索代理的动力学。这种分析的动机来自生物学中存在这些效应的许多情况，例如海洋动物的广播产卵和其他繁殖过程或免疫系统的工作原理。我们严格地描述了在大流动幅度极限下的预期命中时间的极限，对应于有效的一维问题。我们还进行了数值计算，以描述搜索的预期持续时间的更精细特性。数值实验展示了该过程的许多有趣特征，特别是切变流的最优值的存在，该值最小化了预期的目标命中时间，并优于大流动极限。
