Abstract
We study cluster-cluster aggregation and fragmentation with a periodically
modulated binding rate. Using the Smoluchowski mean-field equations,
we derive exact solutions for the cluster size distribution for two
time courses of the binding rate: (i) harmonic modulations and (ii)
on-off switching of the binding rate with dwell times tau(b) and
tau(f). In both cases, the asymptotic cluster size distribution is
oscillatory in time. The formation of small-sized clusters is enhanced
compared to a constant binding rate below a critical cluster size
s(c). There is another critical cluster size s(p) close to which
the size distribution becomes quasistationary. We calculate analytically
the dependence of the critical points s(c) and s(p) on the relevant
system parameters for on-off switching of the binding rate. Our results
are relevant whenever clustering can be externally controlled.
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