Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

TL;DR

This paper introduces a Monte Carlo method to analyze temperature-dependent Smoluchowski equations, revealing novel aggregation regimes like permanent temperature growth and density separation, and suggests the absence of gelation.

Contribution

The paper develops a new Monte Carlo technique based on low-rank approximation to study temperature-dependent aggregation equations, uncovering unexpected regimes and classifying kernels.

Findings

Identification of anomalous aggregation regimes

Discovery of permanent temperature growth and density separation

Conjecture of no gelation in the system

Abstract

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities with constant rate coefficients, the temperature-dependent equations describe both -- the evolution of the densities as well as cluster temperatures, which determine the aggregation rates. To solve these equations, we develop a novel Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation", with a large gap in the size distribution for middle-size clusters. We perform classification of the aggregation kernels for the temperature-dependent equations and conjecture the lack of gelation. The results of our scaling analysis agree well with the simulation data.