Geometric shape optimization of membrane in the presence of a diffusion field

Abstract

In this work we study the geometric shape optimization of membrane in the presence of a diffusion field of molecules, such as proteins which have the ability to adsorb on, and to desorb from the membrane. The main idea of this study is to vary the position of the boundaries of a given initial shape of the membrane, without changing its topology which remains the same as the initial shape. We develop a model that includes, molecular diffusion along the membrane as well as the attachment and detachment of molecules to and from the membrane. The numerical simulations based on Level-Set method show that the coupling between the membrane and the molecules makes the membrane suffer from morphological instability.