This research project was developed jointly with Natalie Ho and our supervisor Michael Kinach.
qball.py is made as part of a research project which would allow further study of Q-ball dynamics in more complex scenarios.
I highly recommend reading through the Q-ball scattering section of Relativistic Scattering of Solitons in Nonlinear Field Theory as this is the basis of the script in this project.
Q-balls are described by Scalar Fields and hence have a set of ODEs which can model them.
The system of Q-Balls' parameters are input into params.csv, these parameters are used to solve the Boundary-Eigenvalue problem for the ODE using the Shooting Method.
Using the eigenvalue and plot generated from this, an exponential decay tail is added to create the profile of a static Q-ball. The Q-ball profile is then interpolated on the (x,y) grid using Lagrange interpolation.
To take relativistic effects into account, the Scalar Fields are then Lorentz Transformed in the direction the Q-ball is travelling depending on the velocity and direction given in the input file.
The effects of individual Q-balls are imposed creating a system at t=0 consisting of 4 Scalar Fields.
A key aspect of the script was to provide readability which is the reason for verbose code in certain areas.
The initial system data generated can then be passed onto a separate existing code which computes the time evolution and generates the simulation you see below.
tri_v0.5.mp4
The Python script can now allow further study on new and different types of collisions such as the 3 Q-ball collision.
This was presented at the UBC Multidisciplinary Undergraduate Research Conference 2021 under the title The Complex Dynamical Behaviour of Q-balls in Collisions