Preventive work in environments with large crowds can contribute to increased safety. In her dissertation, Thoa Thieu examines active-passive dynamics in pedestrians.
You have defended your dissertation with "Models for linked active-passive population dynamics: Mathematical analysis and simulation". Tell us about your research.
- The motivation of my research is based on studying models in the real life. There are several reasons for this. Firstly, I am passionate about working with PDEs and SDEs, especially on applying them to real world situations. Secondly, nowadays, stochastic tools are widely used and applied in many branches of sciences, techniques and finance, especially in biology, medicine, social dynamics, life science applications and insurance etc. I took the inspiration from the models of crowds of pedestrians for my research.
The topic of escape evacuation and social human behaviour are interesting. In an emergency situation, building occupants require information about surrounding environment and social interactions in order to evacuate successfully.
My PhD dissertation focused on mathematical analysis and simulation of models for couped active-passive pedestrian dynamics. I presented conceptually three different crowd dynamics models that describe the joint evolution of active-passive populations. This work comes in three main parts, in which I adopt distinct perspectives and conceptually different tools from lattice gas models, partial differential equations, and stochastic differential equations, respectively.
In what way will your research contribute and to which area?
- My research has many applications in society. In fact, the dynamics of crowds of pedestrians has attracted the interest of the scientific community. The modeling of pedestrian flows offers many challenging questions to the science and technology in general. The unpredictability of pedestrian trajectories makes the dynamics of crowds difficult to model. However, from essential human benifits which give more motivation to the studies of pedestrian dynamics. Safety is a primary issue and important aspect need to be studied carefully.
Many accidents occurred over the years in dense crowd regimes, would have been avoided by the prediction supported by mathematical tools.
A deep understanding of pedestrian motion would allow for intelligent environments featuring, for instance, efficient illumination systems and smart evacuation signaling systems.
In the literature, many models have been proposed to describe pedestrian dynamics in different scenarios. Some researchers consider macroscopic models, where the density and speed of the flow are accounted for, while others study microscopic models in which each individual is represented separately as a moving particle, hence, systems of interacting particles are considered. Pedestrians have a complex psychologic and sociologic behavior which is often only considered in simplified ways in the various approaches. My dissertation focuses on studying three different pedestrian models from three different perspectives: lattice gas models, a fluid-like driven system and stochastic differential equations.
Will you continue to study this subject?
- Yes, I will continue to study group dynamics and related problems. My research interests are mainly concentrated on developing mathematical models that describe the common development in pedestrian group dynamics and social dynamics in general.
I examine three different descriptions:
• A continuous one with deterministic dynamics (i.e. a PDE system coupling fast-slow flows in porous media via Forchheimer-like equations coupled with diffusion via non-linear interaction terms)
• A discrete one with Monte Carlo stochastic dynamics (i.e. a gas dynamics formalism involving two species driven by different dynamics competing via simple exclusion processes for the same lattice)
• Systems of Stochastic Differential Equations and/or the coupled systems between SDEs and PDEs that described social dynamics, life science applications
You are about to move to Canada – what will be your job there?
- I got a postdoctoral position at Wilfrid Laurier University in Waterloo, Canada. I will work with the research project "Modeling for Complex Systems in Data-Driven Environments with a focus on multiscale hybrid models based on deterministic and stochastic mathematical models with applications in brain research and social networks".
I believe that the service will give me good opportunities to expand my knowledge of complex systems and networks in the social dynamics, the interplay between social and biological factors and uncertainty quantification for multi-scale application.
Watch a film that describes the group dynamics in larger collections of pedestrians
Models for coupled active-passive population dynamics: Mathematical analysis and simulation
