Anomalous aggregation regimes of temperature-dependent Smoluchowski equations

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.