Some mathematical problems in shape formation
vendredi 23 mai 2014, 11h00 - 12h00
This talk will concern the growth-induced morphogenesis, particularly of the low-dimensional structures such as fillaments, laminae and their assemblies, arising routinely in biological systems and their artificial mimics. The physical basis for morphogenesis can be presented in terms of a simple principle: differential growth in a body leads to residual strains that generically result in changes of the body’s shape. Eventually, the growth patterns are expected to be regulated by these strains, so that this principle might well be the basis for the physical self-organization of the tissues.
We will be mainly concerned with the analysis of elastic films exhibiting residual stress at free equilibria, i.e. in the absence of any boundary conditions and external forces. There, it is conjectured that the growth process results in the formation of non-Euclidean, Riemannian metrics and it can be studied through a variational model, pertaining to the non-Euclidean version of the nonlinear elasticity.
In the lecture, we will discuss some analytical findings in this description, as well as open problems deriving from the comparison with experimental results.