Stochastic resetting is a protocol in which a process is returned to the origin repeatedly at random time intervals. Resetting processes are ubiquitous in nature and have been studied theoretically in the fields of physics, biology, chemistry, computer science, and even in queuing theory. Among other findings, it was demonstrated that stochastic resetting gives rise to a long series of non-equilibrium phenomena.
Diffusion with stochastic resetting serves as a paradigmatic model to study these phenomena, but the lack of a well-controlled platform by which this process can be studied experimentally has been a major impediment to research in the field. We have recently published the first experimental realization of such a process.
Our work verifies experimentally several fundamental predictions made for resetting processes, thus validating experimentally a large body of research. The experimental realization led us to explore the effect of realistic resetting protocols as opposed to the commonly considered instantaneous resetting protocols. Moreover, we studied experimentally the energetic cost of search and first-passage with resetting via two complementary approaches. First, we calculated the actual cost of resetting in our specific experiment. Then, we proceeded to identify factors limiting this cost in an idealized resetting process. We showed that there is an abrupt transition in the energetic cost of resetting and calculated a lower bound on this cost in first passage processes. We believe that these results will open a new topic of discussion in the field concerning energetic cost and optimization.
O. Tal-Friedman, A. Pal, A. Sekhon, S. Reuveni, and YR,
JPCL 11, https://arxiv.org/abs/2003.03096, 7350-7355 (2020).
Environmental memory facilitates search with home returns
Search processes in the natural world are often punctuated by home returns that reset the position of foraging animals, birds, and insects. Many theoretical, numerical, and experimental studies have now demonstrated that this strategy can drastically facilitate search, which could explain its prevalence. To further facilitate search, foragers also work as a group: modifying their surroundings in highly sophisticated ways, e.g., by leaving chemical scent trails that imprint the memory of previous excursions. Here, we design a controlled experiment to show that the benefit coming from such ``environmental memory'' is significant even for a single, non-intelligent, searcher that is limited to simple physical interactions with its surroundings. To this end, we employ a self-propelled bristle robot that moves randomly within an arena filled with obstacles that the robot can push around. To mimic home returns, we reset the bristle robot's position at constant time intervals. We show that trails created by the robot give rise to a form of environmental memory that facilitates search by increasing the effective diffusion coefficient. Numerical simulations, and theoretical estimates, designed to capture the essential physics of the experiment support our conclusions and indicate that these are not limited to the particular system studied herein.
Altshuler, Amy, Ofek Lauber Bonomo, Nicole Gorohovsky, Shany Marchini, Eran Rosen, Ofir Tal-Friedman, Shlomi Reuveni, and Yael Roichman.
"Environmental memory facilitates search with home returns." arXiv preprint arXiv:2306.12126 (2023).