Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série LPTMS
Domaines cond-mat.stat-mech
Date Mardi 3 Octobre 2023
Heure 11:00
Institut LPTMS
Salle Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530
Nom de l'orateur Boyer
Prenom de l'orateur Denis
Addresse email de l'orateur
Institution de l'orateur Universidad Nacional Autónoma de México
Titre Optimising the random search of a target with finite lifetime
Résumé Random searches find applications in a broad range of problems in biology, chemistry or everyday life. In a typical set-up, a searcher follows a random motion and reacts with a fixed target site upon first encounter. In many situations, however, the target has a finite lifetime after which it becomes inactive, lost or no longer available for reaction. To be successful, the searcher must therefore find the target site before the latter becomes inactive. We present exact results on a minimal model, namely, a one-dimensional searcher performing a discrete time random walk or Lévy flight, while the target has an exponentially distributed lifetime. In contrast with the case of a permanent target, it is possible to optimise the capture probability and the conditional mean first passage time at the target. The optimal Lévy index takes a non-trivial value, even by taking the infinite lifetime limit, and exhibits a "phase transition" as the initial distance to the target site is varied. This transition can be discontinuous or continuous depending on the target lifetime. We outline connections between this problem and search processes based on resetting.
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