Accretive growth is a fundamental mechanism in nature and technology. From coral
reefs and seashells to glaciers, 3D-printed objects, and biological tissues,
many systems evolve by progressively adding new material at their boundaries.
Understanding these processes poses major scientific challenges: the shapes of
the systems change over time in complex ways, and their evolution depends on
interactions between geometry, physical effects, and environmental factors.
This project aims to advance the mathematical theory of accretive growth. On the
one hand, it focuses on developing new methods from the calculus of variations,
partial differential equations, and front-propagation theory that are relevant
to growth problems. On the other hand, it targets three key applications: the
rupture of atherosclerotic plaques, strain buildup in 3D printing, and the
optimization of bioprinting strategies.