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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 28, 2012
- Source ID
- 10.1063/1.4772598
Entities
People
- Maria R D'Orsogna
- Romain Yvinec
- Tom Chou
Organizations
- Army Research Office
- California State University, Northridge
- National Science Foundation
- University of California, Los Angeles
- University of Lyon