Aggregation Dynamics of Heterogeneous Systems
Open AccessIrreversible aggregation is a widespread natural process observed across various systems and scales. Recent technological advancements have enabled the study of complex systems exhibiting clustering and group formation on a larger scale. In particular, living systems, like social networks, have diverse populations of agents with inherent heterogeneity, shaping interactions based on individual differences. While traditional research has focused on physical and chemical systems, there is a growing interest in developing generalized modeling frameworks that consider population diversity and interactions among heterogeneous agents.In the first part of the thesis, we introduce a versatile toy model of a heterogeneous dynamic random network, where the link formation mechanism depends on node heterogeneity. We analyze the cluster size distribution using two distinct approaches: (1) stochastic simulation with the Gillespie direct method, accurately accounting for inherent randomness, and (2) mean-field approximations based on a generalized Smolukhowski-type analytical model. This combination allows for a thorough investigation of system properties, gaining a deeper understanding of its dynamics and identifying mean-field modeling limitations. The framework's versatility enables its application to various systems.In the subsequent part of the thesis, we apply the framework to different types of systems, inspired by online social systems, to study the effect of heterogeneity and showcase analysis methods and generalizations. Specifically, we investigate a scenario with homophily, representing like-like interactions, where the impact of heterogeneity is controlled by a tuning parameter. Through numerical simulations and analytical approximations on small and large networks with varying levels of heterogeneity, we assess the validity of the mean-field model and explore the effects of heterogeneity on the system's dynamics. Our investigations reveal that heterogeneity induces a shift in the system's dynamical behavior, leading to observable changes in the cluster size distribution. This highlights the significant role of heterogeneity in shaping the dynamics of the system. Additionally, we extend the basic framework to accommodate modifications related to the influx of monomers and system volume, revealing non-trivial effects on the dynamics and the evolution of the giant connected component. Finally, we examine how the framework captures dynamics in systems with changing population properties, including cases of consensus and polarization. The mean-field approach remains effective in these scenarios, highlighting its versatility and applicability.Overall, this thesis provides valuable insights into the dynamics of many-body systems with heterogeneous components, shedding light on irreversible aggregation processes. The research opens new avenues for understanding phenomena in diverse fields, from chemical reactions and biological networks to social interactions and information spreading.
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