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Dynamics of attracting Brownian particles

García, Adrián (Supervisors: Cristóbal López and Emilio Hernández)
Master Thesis , (2017)

We have studied the properties of an assembly of Brownian particles interacting via an attractive soft-core GEM-α potential in 1d. Through numerical simulations we show that the particles tend to aggregate in clusters that collapse at extremely long times. We determine the diffusion coefficient of the cluster formed and its dependencies. We perform a linear stability analysis of the system, finding the conditions that lead to a cluster formation. Also, by the study of the deterministic part of the equation for the macroscopic density we propose a relationship between the size of the cluster and the parameters of the potential and the particles. Through numerical simulations we check these results.