Multi Phase Field Models for Cellular Structures on the Sphere

Research output: Types of thesis › Master thesis

Abstract

We present a multi phase field model for cellular structures on the sphere. This model is discretized with surface finite elements (SFEM) and implemented using the C++ library AMDiS. Our model shows important topological features of biological structures, like T1-transition and the occurrence of rosettes. Key properties of epithelial tissues, like the distribution of the aspect ratio, can be observed in our simulations. Furthermore we evaluate the behaviour of the model with a focus on neighbouring relationships. We show that for low activity the cells move to a stable state which is similar to the solution of the Thomson-Problem and study the transition between a solid and liquid state. Two different ways to incorporate inter-cellular forces are compared. On the one hand we investigate an interaction potential that takes only repulsion into account. On the other hand we examine the behaviour of an interaction potential with adhesion and repulsion. Additionally we investigate the occurrence of vortices in simulations with a high number of cells and high activity.

Details

Original languageEnglish
Qualification levelMaster of Science
Supervisors/Advisors
  • Voigt, Axel, Main supervisor
  • Schmidtchen, Markus, Reviewer
Defense Date (Date of certificate)3 Aug 2021
Publication statusPublished - 2021
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External IDs

ORCID /0000-0002-4525-9185/work/142253741