Kolloquium zur Masterarbeit: Tim Vogel

Studentischer Vortrag (Kolloquium zur Masterarbeit/Master's thesis defense)
Vortragender/Speaker: Tim Vogel
Ansprechpartner/Contact: Jun. Prof. Dr. Markus Schmidtchen

Titel/Title: 
Derivation and study of a non-confluent model for deformable cells

Zusammenfassung/Abstract:
This work provides an unified perspective on cell dynamics spanning rigid to deformable cell regimes in a non-confluent setting. Building upon the foundations laid in my Bachelor’s thesis significant improvements were made to the DF cell model, like reformulations of energies and according forces for stable large scale simulations (detailed in Section 2). Chapter 3 presents a rigorous validation by recreating the diffusion dynamics of the point particle and hard sphere models through extensive Monte Carlo simulations with varying hardness (0, 0.5, 1), representing soft, intermediate, and hard cell behaviours. The chapter further investigates shape deformation and highlights the dependence of cell diffusion and deformation on hardness and initial packing. Subsequently, Chapter 4 derives the macroscopic mean field description of the hard DF model. Starting from the vertex wise stochastic dynamics, partial differential equations governing the evolution of the mean field density are obtained, including explicit forms for shape preserving energies and the bounce overlap energy. A low-dimensional example illustrates the correspondence between first marginals of the empirical measure and the mean field limit, providing a bridge between microscopic and macroscopic descriptions. Finally, the thesis concludes with a summary of findings and an outlook on potential future extensions and applications of the DF model.