Random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food. In this paper we take a target-centric viewpoint, by analyzing the accumulation of resources in a set of targets due to multiple rounds of search-and-capture events; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position (resetting after capture). The searcher is then resupplied with cargo and a new search process is initiated after a random delay. Assuming that the accumulation of resources is counterbalanced by degradation, one can derive general expressions for the moments of the resource distribution. We develop the theory by considering diffusive search in two distinct geometric configurations. First, we determine the mean and Fano factor of the distribution of resources between pair of concentric spherical targets, and explore how these depend on the initial location of the searcher, the dimension d, the degradation rate and the distribution of delays. Second, we use asymptotic analysis to determine the mean number of resources in each of N small interior targets within a three-dimensional bounded domain. In particular, we show that the mean number of resources in a target is proportional to its effective `` shape capacitance. '' Finally, we extend the analysis to the case of diffusive search with stochastic resetting before  capture.
 In this paper we use asymptotic analysis to determine the steady-state mean number of resources in each of N small interior targets within a three-dimensional bounded domain. The accumulation of resources is based on multiple rounds of search-and-capture events; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position (resetting after capture). The searcher is then resupplied with cargo and a new search process is initiated after a random delay. Assuming that the accumulation of resources is counterbalanced by degradation, one can derive general expressions for the moments of the resource distribution. We use this to show that the mean number of resources in a target is proportional to its effective " shape capacitance. " We then extend the analysis to the case of diffusive search with stochastic resetting before capture, where the position of the searcher is reset to its initial position at a random sequence of times that is statistically independent of the ongoing search process, in contrast to the sequence of resetting times after capture.
D
Random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on the first passage time (FTP) problem to find a target. This single search-and-capture event then triggers a downstream process or provides the searcher with some resource such as food.
R
take a target-centric viewpoint, by analyzing the accumulation
use asymptotic analysis to determine the steady-state mean number
R
a set of targets due to
each of N small interior targets within a three-dimensional bounded domain. The accumulation of resources is based on
R
develop the theory by considering diffusive search in two distinct geometric configurations. First, we determine the mean and Fano factor of the distribution of resources between pair of concentric spherical targets, and explore how these depend on the initial location of the searcher, the dimension d, the degradation rate and the distribution of delays. Second, we use asymptotic analysis to determine the mean number of resources in each of N small interior targets within a three-dimensional bounded domain. In particular, we
use this to
R
``
"
R
'' Finally, we
" We then
A
capture, where the position of the searcher is reset to its initial position at a random sequence of times that is statistically independent of the ongoing search process, in contrast to the sequence of resetting times after