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Gelation in input-driven aggregation.

P L Krapivsky1,2, S A Matveev3,4

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Summary
This summary is machine-generated.

This study examines irreversible aggregation of small clusters. Depending on the model used, a percolation transition leads to either system-wide engulfment or a stable mass distribution.

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Area of Science:

  • Physical Chemistry
  • Chemical Engineering
  • Statistical Mechanics

Background:

  • Irreversible aggregation processes are fundamental in various scientific domains.
  • Understanding cluster mass distribution dynamics is crucial for predicting system behavior.

Purpose of the Study:

  • To investigate irreversible aggregation driven by small mass clusters.
  • To analyze the cluster mass distribution in the long-time limit.
  • To explore the percolation transition in input-driven aggregation.

Main Methods:

  • Analytical and numerical examination of an infinite system of nonlinear ordinary differential equations.
  • Focus on truncated systems with finite equations for numerical integration.
  • Comparison of the Flory and Stockmayer approaches post-percolation.

Main Results:

  • Input-driven aggregation exhibits a percolation transition.
  • Two distinct behaviors emerge after the transition: system-wide engulfment (Flory) or a stationary mass distribution (Stockmayer).
  • The choice of theoretical or numerical approach influences the observed dynamics.

Conclusions:

  • The long-time behavior of aggregation systems is highly dependent on the chosen theoretical framework.
  • The study highlights the critical role of percolation in aggregation processes.
  • A generalization to ternary aggregation is proposed.