title: First passage times in homogeneous nucleation and self-assembly.
abstract: Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE, we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.
authors.affiliation: Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 Blvd. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France.
authors.forename: Romain
authors.initials: R
authors.lastname: Yvinec
authors.forename: Maria R
authors.initials: MR
authors.lastname: D'Orsogna
authors.forename: Tom
authors.initials: T
authors.lastname: Chou