clearya1/jax-pv

jax-pv: Point Vortices in JAX

Authors: Andrew Cleary, Jacob Page

jax-pv is a fully differentable point vortex solver, for both unbounded and rotating disc-bounded domains, implemented in JAX.

For full details about the possibilities of using jax-pv, read our paper Exploring the free energy landscape of a rotating superfluid.

Getting Started

There are currently 3 demo scripts in this repository, each of which outlines how to use jax-pv to answer a different research question:

• Search for relative equilibria in an unbounded domain
• Search for energy-minimising pathways between relative equilibria
• Search for homoclinic connections between relative equilibira

Organization

As well as the above demo scripts, jax-pv contains the following:

• data: folder containing the relative equilibria we computed for various numbers of vortices.
• arnoldi.py : Code to implement the arnoldi iteration in the Newton-GMRES-hookstep.
• dneb.py : Code to implement the (Doubly) Nudged Elastic Band method.
• hungarian.py : Code to implement the hungarian algorithm.
• loss_functions.py : A script with useful loss functions to find relative equilibria and connections.
• newton.py : Code to implement the Newton-GMRES-hookstep method to find relative equilibria.
• stability.py : Code to compute the linear stability of relative equilibria.
• utils.py : Generic, useful functions for manipulating systems of point vortices.
• velocity_transforms.py : Code to convert from Cartesian to angular velocities.
• VorticesMotion.py : Contains the Vortices class, the fully differentiable point vortex solver in the unbounded domain.
• VorticesMotionDisc.py : Contains the VorticesDisc class, the fully differentiable point vortex solver in the rotating, disc-bounded domain.

Citation

If you use jax-pv, please cite: