I recently learnt how to make animations, and have been enjoying using this power to animate lots of things related to my work. This page shows all of them in one place, potentially devoid of context. Some of them are also released on wikimedia commons, and I'll link to them where they are. Most of them are also on my youtube channel in the animations playlist. You can download them from my Google Drive folder.
I'm releasing these all under the Creative Commons Attribution-Share Alike 4.0 International license (as is standard for wikimedia commons), which means you're free to share or adapt this work, provided appropriate attribution is given, and any adaptations are released under the same or comparable licence as the original.
Below is a table of contents of all the animations.
Zel'dovich and Schrödinger toy model animations
These animations principally relate to Gough & Uhlemann 2022, where we study a simple model of dark matter, building a wave (Schrödinger) analogue to the classical (Zel'dovich) approximation. I wrote a twitter thread about the paper which hopefully is a good starting point.
Generation of a phase space sheet from sinusoidal initial conditions under free evolution. The trajectories of individual particles are shown, and then projected down to spacetime, which shows the single- and multi-stream regions separated by a caustic.
The density of a collection of collisionless particles moving under the Zel'dovich approximation. At a=1, the density diverges as fluid streams flow through each other.
Comparison between the density of a simple 1D toy model under the Zel'dovich approximation and the same toy model under the free Schrödinger equation. Multi-streaming and infinite density divergences are replaced with rapid oscillations in the wavefunction.
Generation of a thread weaving representing particle trajectories through spacetime under the Zel'dovich approximation. As particles pass through each other a multi-stream region forms, separated from the single stream region by a cusped caustic line.
Optics inspired animations
Coffee cup caustic
Parallel light rays reflecting off a circular surface create a bright caustic region in the shape of a cardioid. This is shown here as the number of light rays increases.
A rainbow is a classic example of the simplest catastrophe, the fold caustic. This animation shows how the output angle of a light ray depends on its incident angle, s. Near a critical value of s, many different incident light rays are mapped to the same output angle (~42° for water/air interface) making that region appear brighter. I'm working on a more sophisticated version of this animation to make the link between to projection mappings and catastrophe theory clearer.