Resetting-mediated navigation of an active Brownian searcher in a homogeneous topography.

Abstract

Designing navigation strategies for search-time optimization remains of interest in various interdisciplinary branches in science. Herein, we focus on active Brownian walkers in noisy and confined environments, which are mediated by one such autonomous strategy, namely stochastic resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently. The resetting clock is operated externally without any influence from the searchers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple governing laws of motion, it shows a significant ramification for the search-time statistics, in contrast to the search process conducted by the underlying reset-free dynamics. Using extensive numerical simulations, we show that the resetting-driven protocols enhance the performance of these active searchers. This, however, depends robustly on the inherent search-time fluctuations, measured by the coefficient of variation of the underlying reset-free process. We also explore the effects of different boundaries and rotational diffusion constants on the search-time fluctuations in the presence of resetting. Notably, for the annealed condition, resetting is always found to expedite the search process. These features, as well as their applicability to more general optimization problems from queuing systems, computer science and randomized numerical algorithms, to active living systems such as enzyme turnover and backtracking recovery of RNA polymerases in gene expression, make resetting-based strategies universally promising.