Determining cluster-cluster aggregation rate kernals using inverse methods

TL;DR: In this article, the authors investigate the potential of inverse methods for retrieving adequate information about the rate kernel functions of cluster-cluster aggregation processes from mass density distribution data, and propose a new nonlinear inverse method, based upon a novel factorisation of homogeneous kernels, whose properties are assessed in respect of both stationary and scaling mass distribution data inputs.

Abstract: We investigate the potential of inverse methods for retrieving adequate information about the rate kernel functions of cluster-cluster aggregation processes from mass density distribution data. Since many of the classical physical kernels have fractional order exponents the ability of an inverse method to appropriately represent such functions is a key concern. In early chapters, the properties of the Smoluchowski Coagulation Equation and its simulation using Monte Carlo techniques are introduced. Two key discoveries made using the Monte Carlo simulations are briefly reported. First, that for a range of nonlocal solutions of finite mass spectrum aggregation systems with a source of mass injection, collective oscillations of the solution can persist indefinitely despite the presence of significant noise. Second, that for similar finite mass spectrum systems with (deterministic) stable, but sensitive, nonlocal stationary solutions, the presence of noise in the system can give rise to behaviour indicative of phase-remembering, noise-driven quasicycles. The main research material on inverse methods is then presented in two subsequent chapters. The first of these chapters investigates the capacity of an existing inverse method in respect of the concerns about fractional order exponents in homogeneous kernels. The second chapter then introduces a new more powerful nonlinear inverse method, based upon a novel factorisation of homogeneous kernels, whose properties are assessed in respect of both stationary and scaling mass distribution data inputs.