Formation and Ageing of Biological Cells: Bulk-Surface Partial Differential Equations

Project description

In this project, we will propose a novel mathematical framework rooted in continuum theory to investigate the mechanical behavior of materials undergoing deformation and phase segregation, focusing on the interplay between bulk and surface dynamics. Our approach will involve establishing a principle of virtual powers tailored to accommodate scenarios where boundaries may lose smoothness, allowing for discontinuities in the normal field at edges.

The resultant set of equations resembles a hybrid formulation reminiscent of the Navier–Stokes–Cahn–Hilliard equation, addressing both bulk and surface dynamics. Beyond a systematic treatment involving a specialized version of the virtual power principle and considerations of free-energy imbalances within bulk-surface theories, our research incorporates two crucial elements: phase segregation to emulate the formation process of cells' internal organelles and the correlation between out-of-equilibrium thermodynamics with ageing.