论文标题
通过扩散回声提高搜索效率
Enhancing search efficiency through diffusive echo
论文作者
论文摘要
尽管已经研究了数十年，但第一次通过过程仍然是一个积极的研究领域。在此贡献中，我们检查了一个粒子在具有内部吸收边界和外反射边界的环中扩散的粒子。我们获得了以两个和三个维度的打击时间和击球角的关节分布的分析表达式。对于某些配置，我们观察到“扩散回波”，即在第一个通道时间分布中，两个定义明确的最大值，到吸收边界上有针对性位置。这种效果是由于起始位置和环境限制之间的相互作用而产生的，可能有助于通过在短时间内生成持续的通量来提高随机搜索的效率。最后，我们检查了相应的一维系统，没有明确的回声。
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We obtain analytic expressions for the joint distribution of the hitting time and the hitting angle in two and three dimensions. For certain configurations we observe a 'diffusive echo', i.e. two well-defined maxima in the first passage time distribution to a targeted position on the absorbing boundary. This effect, which results from the interplay between the starting location and the environmental constraints, may help to increase the efficiency of the random search by generating a sustained flux to the targeted position over a short period. Finally, we examine the corresponding one-dimensional system for which there is no well-defined echo.
