%0 Publication
%T First passage times in homogeneous nucleation and self-assembly
%A D'Orsogna, Maria-Rita R.; Chou, Tom; Yvinec, Romain
%I AIP Publishing
%U doi.org/10.1063/1.4772598
%R http://localhost/files/9593tx648
%X 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.
%G en
%9 Article
%~ ScholarWorks
%W Cal State