Department of Mathematical Sciences MSc. in Modern Applications of Mathematics The Dynamics of Crowds

Crowds pose an interesting example of a complex system in which emergent behaviour is observed out of the interaction of many individual agents. This behaviour can be very important in the safe design of sports and other stadia, especially in the case of possible emergency situations. For this reason crowd dynamics is of great interest to architects. The purpose of this project is to review the current literature on crowd dynamics and to look at some simulations of different types of crowd behaviour in certain specific situations namely: the meeting of two crowds in a ’scramble crossing’, the motion of a crowd though an exit and the response of a crowd to an emergency (such as a fire). The student will implement a differential equation model of the crowd crossing problem. In particular, they will study the emergent behaviour that arises in the scramble crossing problem and see how this depends on various parameters relating to the individual actions of the members of the crowd. Declaration: I hereby certify that the work in this document is my own, unless otherwise referenced. Signed............................................................ Gareth Parry i Acknowledgements I would like to thank Professor Budd in particular for his help and input whilst writing this thesis. The lively debate and insightful questions raised in our meetings was one of the particularly enjoyable aspects of the project. I would also like to thank Dr Chris Williams and Odysseas Kontovourkis for their help in providing an Architects insight into pedestrian dynamics. Movies and Code Submitted along with this thesis are copies of several movies created by the simulator and converted to *.avi files. Also included on the CD are the final MATLAB script and function files (hard copies are in Appendix A) along with several *.mat files which are saved data from different simulations. The movie and *.mat files are named with the number of pedestrians simulated followed by the geometry the flow was simulated in. So if 500 pedestrians were modelled in a Scramble Crossing then the associated files would be