Abstract
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels homogeneous in masses and of merging clusters and fragmentation kernels, , with parameter quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when . For , however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small , they become steady if is close to 2 and is very small. Simulation results lead to a conjecture that for the system has a stable fixed point, corresponding to the steady-state density distribution, while for any there exists a critical value , such that for , the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.
5 More- Received 2 March 2018
- Revised 14 May 2018
DOI:https://doi.org/10.1103/PhysRevE.98.012109
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