随机搜索中的死亡率、冗余度和多样性
Mortality, Redundancy, and Diversity in Stochastic Search
摘要：
我们调查了一个随机搜索过程中的死亡率，冗余度和多样性的搜索者的竞争作用下的一维。这张图片是一个精子使卵母细胞受精的玩具模型。$N$独立的和致命的扩散搜索者的群体都从$x=L$开始，并试图到达$x=0$的目标。当死亡率不相关时，检索时间尺度为$\ln N\gg 1$的$τ_D/\ln N$，其中$τ_D\sim L^2/D$是扩散时间尺度。相反，当搜索者的死亡率$μ$足够大时，搜索时间缩放为$\sqrt{τ_D/μ}$，独立于$N$。当搜索者有不同的和高的死亡率，一个非平凡的最佳扩散率的子群体是最有可能达到目标。我们还讨论了趋化性对搜索时间及其波动的影响。
英文摘要：
We investigate a stochastic search process in one dimension under the competing roles of mortality, redundancy, and diversity of the searchers. This picture represents a toy model for the fertilization of an oocyte by sperm. A population of $N$ independent and mortal diffusing searchers all start at $x=L$ and attempt to reach the target at $x=0$. When mortality is irrelevant, the search time scales as $τ_D/\ln N$ for $\ln N\gg 1$, where $τ_D\sim L^2/D$ is the diffusive time scale. Conversely, when the mortality rate $μ$ of the searchers is sufficiently large, the search time scales as $\sqrt{τ_D/μ}$, independent of $N$. When searchers have distinct and high mortalities, a subpopulation with a non-trivial optimal diffusivity are most likely to reach the target. We also discuss the effect of chemotaxis on the search time and its fluctuations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
