We ❤️ PDEs
Here are some examples of a PDE solutions on a domain based on a heart-shaped curve.
Excitability
Models like FitzHugh–Nagumo are the basis for a lot of work in cardiac electrophysiology and related areas. So let’s solve these PDEs in a heart!
- Load this FitzHugh–Nagumo simulation and enjoy. You can click and select 3D to get a 3D view of the beating heart.
- Try this growing simulation for a crude implementation of these equations on a growing domain.
Chemotaxis
The next example is based on the Keller–Segel model for chemotaxis.
- Load this Keller–Segel simulation and enjoy!
- Try this growing simulation for a crude implementation of these equations on a growing domain.
Warm hearted
By plotting vector fields on top of the solutions to PDEs, as exemplified in the heat equation, we can visualise how heat flows from a source as it traces out a heart in this interactive simulation.