Research


My current research focuses on a qualitiative analysis of advection-diffusion-reaction PDE equations with main applications in the following models:

The first scenario for evacuation of a panicked population during a catastrophic event: the population is concentrated in a single group in the center of the space domain. The exit is located in the center of the right side wall (where we can see congestion at the end).


Second scenario for evacuation of a panicked population during a catastrophic event: the population is divided into three groups inside the space domain. The exit is located in the center of the right side wall. We can observe that evacuation is fluent than in the first scenario (eventually less congestion at the exit).


Third scenario for evacuating a panicked population during a catastrophic event: an obstacle is located between the exit and the population, which is concentrated in a single group in the space domain. The exit is always located in the center of the right side wall. We can see that evacuation is smoother than in the first two scenarios, so perhaps we can say here that the role of the obstacle is to facilitate access to the exit.


For more details on the study that led to the above simulation videos, please refer to the recently accepted article in the journal M3AS "Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event"  on the publications list page.