Pattern formation in active particle systems

Recently, understanding pedestrians’ behaviours in real-life phenomena have become a focal point of researchers. The mathematical simulation model has been suggested as an effective approach to address the complexity of the dynamic nature of pedestrians’ behaviours. In particular, addressing different patterns of pedestrians’ movement have become a primary concern in mathematical research. Based on the social force model, this thesis aims to numerically model different patterns of pedestrians’ movement in crowded narrow places using active particles. To achieve this aim, we presented three novel concepts namely chirality, colored noise, and rescue team, and modelled them in relation to pedestrians’ movement. Chapter 1 presents an introduction and literature review for the thesis. Chapter 2 investigated the impact of chirality force on the patterns of active particles moving in multiple lanes. The main findings showed a phase transition of pedestrians moving from multiple lanes to two lanes in opposite directions. Chapter 3 investigated the impact of colored noise on the patterns of pedestrians’ movement in crowded narrow places. The results primarily indicated a phase transition of pedestrians’ movement from several or two lanes to chaotic cases that cause panic in emergency situations. Chapter 4 investigated the impact of the rescue team concept on the management of a huge flux. The results indicated that different sizes of rescue team members were able to segregate and manage a huge flux into two fluxes moving in the same direction. Chapter 5 gives a conclusion for overall findings and their possible theoretical and practical implications. The findings of this research suggest that understanding and managing different patterns of pedestrians’ behaviours have important implications for the safety, transportation, and management of urban areas.