{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimal-mean-first-passage-time-of-a-brownian","title":"Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests","arxiv_id":"2106.09113","date":"2021-06-16","proceeding":null,"authors":["Felix Faisant","Benjamin Besga","Artyom Petrosyan","Sergio Ciliberto","Satya N. Majumdar"],"abstract":"We study experimentally, numerically and theoretically the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius $R_{\\text tol}$, a target at a distance $L$ from an initial position in the presence of resetting. The reset position is Gaussian distributed with width $\\sigma$. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period/rate for different target distances (values of the ratios $b=L/\\sigma$) and target size ($a=R_\\text{tol}/L$). We find an interesting phase transition at a critical value of $b$, both in one and two dimensions. The details of the calculations as well as experimental setup and limitations are discussed.","url_abs":"https://arxiv.org/abs/2106.09113v1","url_pdf":"https://arxiv.org/pdf/2106.09113v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"optimal-mean-first-passage-time-of-a-brownian","repo_url":"https://github.com/xif-fr/BrownianMotion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}