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Steady oscillations in aggregation-fragmentation processes.

N V Brilliantov1,2, W Otieno1, S A Matveev2

  • 1Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom.

Physical Review. E
|August 17, 2018
PubMed
Summary
This summary is machine-generated.

Steady oscillations were discovered in aggregation-fragmentation processes. For certain parameters, cluster size distributions exhibit stable, non-decaying oscillations, a surprising finding for closed systems.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Complex Systems

Background:

  • Aggregation-fragmentation processes are fundamental in various scientific fields.
  • Understanding the long-term behavior of these systems is crucial.
  • Previous models often assumed stable steady states.

Purpose of the Study:

  • To investigate the emergence of oscillations in aggregation-fragmentation dynamics.
  • To analyze the influence of aggregation and fragmentation kernels on system behavior.
  • To explore conditions leading to steady oscillations in cluster size distributions.

Main Methods:

  • Analytical solutions of Smoluchowski-like equations.
  • Analysis of aggregation kernels (K_{i,j}) and fragmentation kernels (F_{ij}).
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • Identified conditions for steady oscillations in cluster size distributions.
  • Demonstrated that for θ > 1, an attracting limit cycle can emerge for small fragmentation intensity (λ).
  • Observed that steady oscillations become prominent when θ is near 2 and λ is very small.

Conclusions:

  • The study reveals surprising steady oscillations in closed aggregation-fragmentation systems.
  • A critical transition to oscillatory behavior is identified for θ > 1.
  • The findings challenge the assumption of universally stable fixed points in such systems.