Dr Gomes’s research lies at the intersection between Mathematics and Social Sciences as she works to apply the fundamentals of complex models to a variety of real-life situations.
This proposal is a natural continuation of her previous work on estimation models for pedestrian dynamics. She aims to investigate the behaviour and dynamics of crowd control in order to improve the safety and management of high volume areas. With this information, Dr Gomes hopes to apply it to a range of building and infrastructure designs in order to better place obstacles and minimise evacuation time.
As she further explains, “Models for crowds allow for a simplification in the sense that they can describe the crowd as one entity, and model its dynamics using a partial differential equation (PDE)”. With her innovative approach, Dr Gomes is able to transform a system of finite equations into an infinite-dimensional one. This facilitates the application of a broader range of analytical tools in order to quantify uncertain behaviours and predict the outcome of various scenarios.
This framework provides a mathematical foundation to quantify uncertainty in these estimates using pedestrian trajectory data. This is the first of its kind in the transportation literature. By further exploring models surrounding pedestrian dynamics, Dr Gomes wants to understand how crowd behaviour can be controlled safely. With already promising results, this research is incredibly promising, as it will lead to important novel inter- and intra-disciplinary developments at the interface of applied mathematics and transportation research