tunable-billiard-escape

Code repository accompanying the publication entitled "An investigation of escape and scaling properties of a billiard system".

This project contains the code to generate and plot the data from all figures.

Requirements

The required packages are listed in requirements.txt. To install them please execute pip install -r requirements.txt.

Figure 1

To generate Figure 1, run all cells within the heading named Fig. 1 in the Plots.ipynb Jupyter notebook.

Figure 2

To generate Figure 2, run all cells within the heading named Fig. 2 in the Plots.ipynb Jupyter notebook.

Figure 3

To generate Figure 3, run all cells within the heading named Fig. 3 in the Plots.ipynb Jupyter notebook.

Figure 4

To generate Figure 4, run all cells within the heading named Fig. 4 in the Plots.ipynb Jupyter notebook.

Figures 5, 6, and 7

To generate the data used in these Figures, run python survival_probability.py. It will generate the survival probability for xi = 0.45 with different hole sizes.

Figure 5

To generate Figure 5, run all cells within the heading named Fig. 5 in the Plots.ipynb Jupyter notebook.

Figure 6

To generate Figure 6, run all cells within the heading named Fig. 6 in the Plots.ipynb Jupyter notebook.

Figure 7

To generate Figure 7, run all cells within the heading named Fig. 7 in the Plots.ipynb Jupyter notebook. Make sure to run the cells within the heading named Fig. 6 before running these cells.

Figure 8

To generate the data in Figure 8(a), run python survival_probability_vs_pos.py. It generates the survival probability for a fixed hole size with different hole positions. To generate Figure 8, run all cells within the heading named Fig. 8 in the Plots.ipynb Jupyter notebook.

Figure 9

To generate the data of Figure 9, run python escape_basin_vs_h.py. It generates the escape basin for a fixed value of the control parameter with different hole sizes. To generate Figure 9, run all cells within the heading named Fig. 9 in the Plots.ipynb Jupyter notebook.

Figure 10 and 11

To generate the data of Figure 10 and 11, run python escape_basin_vs_h_vs_xi.py. It generates the escape basin for different values of the control parameter and different hole sizes. Then, run python basin_entropy_from_data.py. It calculates the basin entropy and the basin boundary entropy given the escape basin data.

Figure 10

To generate Figure 10, run all cells within the heading named Fig. 10 in the Plots.ipynb Jupyter notebook.

Figure 11

To generate Figure 10, run all cells within the heading named Fig. 11 in the Plots.ipynb Jupyter notebook.

Supplementary video

To generate the data used in the Supplementary Video, run python escape_basin_vs_h_vs_xi.py. It generates the escape basin for different values of the control parameter and different hole sizes. Then, run python basin_entropy_from_data.py. It calculates the basin entropy and the basin boundary entropy given the escape basin data. To generate the Figures used in the Video, run python plot_supplementary.py. It plots the escape basins for changing parameter control with 6 different hole sizes.

Citation

If you use this repository or parts of it in your work, please consider citing our research paper:

M. Rolim Sales et al., An investigation of escape and scaling properties of a billiard system, Chaos 34, 113122 (2024).

bibtex @article{RolimSales2024, author = {Rolim Sales, Matheus and Borin, Daniel and da Costa, Diogo Ricardo and Szezech Jr., José Danilo, and Leonel, Edson Denis}, title = {An investigation of escape and scaling properties of a billiard system}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {34}, number = {11}, pages = {113122}, year = {2024}, month = {11}, doi = {10.1063/5.0222215}, url = {https://doi.org/10.1063/5.0222215}, }

Contact

rolim.sales.m[at]gmail.com