2381/44416
NV Brilliantov
NV
Brilliantov
W Otieno
W
Otieno
SA Matveev
SA
Matveev
AP Smirnov
AP
Smirnov
EE Tyrtyshnikov
EE
Tyrtyshnikov
PL Krapivsky
PL
Krapivsky
Steady oscillations in aggregation-fragmentation processes
University of Leicester
2019
Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
POPULATION BALANCE MODELS
COALESCENCE INTEGRALS
SIZE DISTRIBUTION
DUST COAGULATION
BEHAVIOR
EQUATION
KINETICS
GELATION
RINGS
2019-06-14 13:10:09
Journal contribution
https://figshare.le.ac.uk/articles/journal_contribution/Steady_oscillations_in_aggregation-fragmentation_processes/10235213
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are
observed for the class of aggregation kernels Ki,j = iν jμ + j ν iμ homogeneous in masses i and j of merging
clusters and fragmentation kernels, Fij = λKij , with parameter λ 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 θ ≡ ν − μ < 1. For
θ = ν − μ > 1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very
small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for
θ < 1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any
θ > 1 there exists a critical value λc, such that for λ<λc, 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.