Mathematical Sciences Department
Analysis and PDE Seminar
Speaker: Martine Ben Amar, Sorbonne Université and Ecole Normale Supérieure
Monday, February 13, 2023
11:00 am - 12:00 pm
Salisbury Labs 411
Title: Morpho-elasticity of living systems by examples: leaves and embryonic C.elegans
Abstract: During morphogenesis and embryogenesis, the shape of living species results from growth, stress relaxation and remodeling. When the growth does not generate any stress, the body shape only reflects the growth density. In two dimensions, we show that stress free configurations are simply determined by the time evolution of a conformal mapping which concerns not only the boundary but also the displacement field during an arbitrary period of time inside the sample. We apply our model to fresh planar leaves: they have no elastic stress, almost no weight, and their shape can be easily represented by holomorphic functions. The growth factor, isotropic or anisotropic, is related to the metrics between the initial and current conformal maps. By adjusting the mathematical shape function, main characteristics such as tips (convex or concave or sharp-pointed), undulating borders and veins, can be mathematically recovered, which are in good agreement with observations.
For embryogenesis study, we focus of the elongation of the C-elegans embryo just before hatching. In three hours, the length of the embryo becomes more than three times the initial length due to four axial muscles. As muscles are contractile, the interpretation of this strong elongation is not intuitive. Our model predicts this elongation by active stresses working both circumferentially and axially.