Order and Chaos in a 2D potential

Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)

Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000, Strasbourg, France

Requirements

The project requires python (tested with version 3.13.1), with the venv module and pip, a bash interpreter (/usr/bin/env bash by default), and at least 450 kiB of available space.

Installation

Place all the content of the archive in a directory. You can use:

git clone https://github.com/Yael-II/MSc2-Project-Chaos

Then, in this directory, to create the virtual environment, run:

python3 -m venv ./venv

Then, to install the requirements, run:

source activate.sh && pip install -r requirements.txt && deactivate

Finally, you will have to authorize execution of the shell scripts with

chmod u+x *.sh

Usage

1. To compute the Poincaré sections, run:

./poincare_sections.sh

and then, enter P to plot only the "Parallel" output. Alternatively, to run the linear algorithm (without parallel array computing; much more slower), use:

./poincare_sections_linear.sh

The result of the simulations are saved in the Output directory, with the prefix poincare_section_parallel_ or poincare_section_linear_ followed by 1/E (e.g. 12 for E = 1/12). The ASCII file contains all the Poincare section points (y on the first line, v on the second line) separated by blank spaces. 2. To compute the area above and below the critical squared phase--space distance, use:

./area.sh

3. To run the tests, use:
   • To test the potentials:

   ./test_potentials.sh
   

   • to test the evolution of a particle in a HH potential:

   ./test_evolution.sh
   ./test_evolution_chaotic.sh
   

   • To test the generation of particles in this potential with a given energy:

   ./test_initial_E.sh
   

   • To test the different integrators we tried:

   ./test_integrators
   

   • To get the running time of both Poincaré sections computations (parallel vs. linear algorithms):

   ./time_poincare_sections.sh