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Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests
Ist Teil von
Journal of statistical mechanics, 2021-11, Vol.2021 (11), p.113203
Ort / Verlag
IOP Publishing and SISSA
Erscheinungsjahr
2021
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Abstract
We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius
R
tol
, a target at a distance
L
from an initial position in the presence of resetting. The reset position is Gaussian distributed with width
σ
. 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
/
σ
) and target size (
a
=
R
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 the experimental setup and limitations are discussed.