Optimal Worm Shapes in a Caustic Environment

We study the optimal shapes flatworms take when they are placed in a caustic solution by introducing an energy model that takes a variational approach to optimal shapes. The context is the e↵ect a caustic solution has on the worm exterior. Through variational calculus, we derive Euler-Lagrange equations and then a descent flow PDE for sending an initial worm shape to its minimum energy state. Numerically, we handle this PDE using finite di↵erence methods and front tracking. Using simulations in di↵erent settings, we present further study of solutions under various conditions. The results using such a geometric and variational approach show promise in describing succinctly the ways that flatworms respond to caustic solutions in their environment.