Kolloquium zur Masterarbeit: Griseldis Oberschelp

Studentischer Vortrag (Kolloquium zur Masterarbeit/Master's thesis defense)
Vortragender/Speaker: Griseldis Oberschelp
Ansprechpartner/Contact: Prof. Dr. Axel Voigt, Dr. Rainer Backofen
Übertragung/Streaming: https://tud.link/fgtqt9

Titel/Title: Quantifying the shape of cells – from Minkowski tensors to p-atic order

Zusammenfassung/Abstract:
The rank-p shape tensor provides the most recent basis for determining p-atic orders. The latter represent a promising concept for deciphering collective cell dynamics in multicellular systems and assess the cell symmetries under rotation by 2\pi/p with p an integer. The rank-p shape tensor entails an essential simplification: cells are assumed to be polygonal. To overcome this limitation, we introduce a Minkowski tensor-based method, which similarly allows the regularity and orientation of these symmetries to be quantified. We provide an implementation that can be seamlessly connected to e.g. multiphase field models and preserves their entire information content with respect to the cell shape. Based on an active vertex and multiphase field model, we assess the fundamental regularity behaviour in p-atic orders as consistent with the literature. Contrary to the literature, we argue that no assumption can be made about the dominance of certain p-atic orders at different length scales. We find evidence that especially the nematic and hexatic orders are reversed in terms of their regularity when considering a solid-liquid transition. Starting from the cell orientations determined by the Minkowski tensor-based method, we establish a methodology for the identification of topological defects in arbitrary p-atic orders. It allows for the correct identification of the topological charge of the defects in almost all of our test cases. We document basic findings based on this methodology.