Abstract:
This paper deals with self-assembly of segments (this problem having arisen in attempts to model the self-assembly of viruses). In this problem, a segment $[1,n]$ is formed from individual particles $1,\dots,n$ (the particles are assumed to be different). This occurs as follows: adjacent particles collide and form two-particle units; adjacent units collide and form larger units, until the segment $[1,n]$ is generated. The appropriate system of differential equations is written; it turns out that its solutions have an extremely simple form. The paper determines how the number of segments $[1,n]$ increases and considers some generalizations of the problem.
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