OSCILLATIONS IN A BECKER-DO?RING MODEL WITH INJECTION AND DEPLETION

We study the Becker-Do center dot ring bubblelator, a variant of the Becker-Do center dot ring coagulation -fragmentation system that models the growth of clusters by gain or loss of monomers. Motivated by models of gas evolution oscillators from physical chemistry, we incorporate the injection of monomers and depletion of large clusters. For a wide range of physical rates, the Becker-Do center dot ring system itself exhibits a dynamic phase transition as mass density increases past a critical value. We connect the Becker-Do center dot ring bubblelator to a transport equation coupled with an integrodifferential equation for the excess monomer density by formal asymptotics in the near-critical regime. For suitable injec-tion/depletion rates, we argue that time-periodic solutions appear via a Hopf bifurcation. Numerics confirm that the generation and removal of large clusters can become desynchronized, leading to temporal oscillations associated with bursts of large-cluster nucleation.

Automated summary

This study focuses on the Becker-Do center dot ring bubblelator, a system that models the growth of clusters by gain or loss of monomers. The research incorporates the injection of monomers and depletion of large clusters and finds that the system exhibits a dynamic phase transition at certain physical rates. Numerical simulations confirm that the generation and removal of large clusters can become desynchronized.