Math Biology Seminar: Laurent Charette

Pattern formation is quite recurrent in the natural world such as in the stripes or dots in some animals' coat. The morphogen hypothesis introduced by Turing in 1952 has been used and studied extensively to explain such patterns on several different domain shapes. In this talk we use the spherical cap domain. This is motivated by the shape of the the tip of a conifer embryo, where branching patterns emerge as the tip flattens. Previous results have been achieved to characterize the different patterns obtained on the cap for different radius and curvature values for a constant domain in time. Here we work with a non-autonomous domain with slowly decreasing curvature. We start with previously obtained results from center manifold reduction and finite elements methods. After that we continue by broadly introducing the closest point method for solving PDEs, explain how we use the method on a flattening spherical cap and end with some very preliminary results.