Speaker: Marina Amado Ferreira

Title:
Particle-based models with volume-exclusion constraints and 
applications to biology

Particle systems are widely found in biology, for example, in cell
tissues, flocks of birds or herds of sheep.
In this talk I will present a particle-based modelling framework 
which relies on simple behavioural rules, such as, 1) two particles 
cannot overlap with each other and 2) the particles seek 
a minimum of a given confining potential at all times. 
The dynamics is driven by the evolution of the confining potential
and changes in particle characteristics, such as size. 
The model involves a non-convex minimization problem which will 
be tackled with the recently proposed damped Arrow-Hurwicz algorithm. 
The derivation and convergence analysis in 1D of this algorithm will 
be presented. Finally, these tools will be used to simulate ballistic 
aggregation in a torus and the evolution of a packed cell tissue.