Reversible Clustering under the influence of a periodically modulated binding 
rate

Straube, R.; Falcke, M.

doi:10.1103/PhysRevE.76.010402

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Reversible Clustering under the influence of a periodically modulated binding rate

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Straube, R.
Systems Biology, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Citation

Straube, R., & Falcke, M. (2007). Reversible Clustering under the influence of a periodically modulated binding rate. Physical Review E, 76: 010402(R). doi:10.1103/PhysRevE.76.010402.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-97A7-9

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 τ_b and τ_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. ©2007 The American Physical Society [accessed 2013 June 13th]