Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First passage times in homogeneous nucleation and self-assembly   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.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat