Core Concepts
The core message of this article is to investigate the impact of a constant external input on the dynamics and steady-state behavior of irreversible aggregation processes, focusing on the emergence of gelation transitions and the resulting cluster mass distributions.
Abstract
The article examines the dynamics of input-driven aggregation processes, where a constant source of small mass clusters drives the system. It considers both binary and ternary aggregation models, analyzing the evolution of the cluster mass distribution over time.
Key highlights:
- For input-driven binary aggregation with mass-independent rates, the system reaches a stationary state with a power-law tail in the cluster mass distribution.
- The input-driven binary aggregation with product kernel (proportional to the product of cluster masses) undergoes a gelation transition, where a giant component rapidly engulfs the entire system.
- The authors derive exact parametric representations for the generating function and the mass of the giant component in the post-gelation phase.
- For input-driven ternary aggregation with product kernel, the authors analyze the emergence of a non-trivial stationary mass distribution using the Stockmayer approach, in contrast to the Flory approach which predicts the vanishing of all finite cluster concentrations.
- The article emphasizes the importance of efficient numerical methods for integrating the large systems of nonlinear kinetic equations governing the aggregation dynamics, especially in the context of gelling systems.
Stats
The article does not contain any key metrics or important figures that directly support the author's main arguments. The analysis relies more on analytical derivations and qualitative descriptions of the aggregation dynamics.