transport-noninteger-wavenumber

Code repository accompanying the publication entitled "Transport mechanisms associated with non-integer wavenumbers in a discontinuous nontwist map".

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

Requirements

To generate the all the data, you will need a Fortran compiler, either gfortran or ifx. All figures are made with Python, using the matplotlib library. To install all required Python packages, please run

pip install -r requirements.txt

Generating the data

All the data will be stored in a directory called Data/, so please remember to create it.

Figures 1 and 2

The data of Figs. 1 and 2 are generated within the Plots.ipynb Jupyter notebook under the Fig. 1 and Fig. 2 cells.

Figure 3

To generate the transmissivity data from Fig. 3, compile the transmissivity_vs_m.f90 program as

gfortran params_dp.f90 functions.f90 transmissivity_vs_m.f90 -fopenmp

or

ifx params_dp.f90 functions.f90 transmissivity_vs_m.f90 -fopenmp

This program takes on seven parameters: num_ic, m_ini, m_end, dm, y0, esc_y, and N. Run the program as

./a.out num_ic m_ini m_end dm y0 esc_y N

with num_ic = 10000, m_ini = -10, m_end = 10, dm = 0.01, and N = 1000000. The y0 and esc_y parameters have different values. For the blue curve, use y0 = -1 and esc_y = 1 and for the red curve, use y0 = 1 and esc_y = -1.

Figures 4, 5, and 6

To generate the elliptic and hyperbolic points of both the upper and lower period-11 stability islands, run

python exe_elliptic_points.py
python exe_hyperbolic_points.py

These scripts will compile the elliptic_points.f90 and hyperbolic_points.f90 programs and execute them with the appropriate parameter values. After that, run

python exe_manifolds.py

This script will compile the manifolds.f90 program and execute it to generate the stable and unstable manifolds of both upper and lower hyperbolic points. The exe_*.py scripts use gfrotran by default. You can use ifx instead by running

python exe_elliptic_points.py ifx
python exe_hyperbolic_points.py ifx
python exe_manifolds.py ifx

Figure 7

To generate the transmissivity data from Fig. 7(a), compile the transmissivity_vs_N.f90 program as

gfortran params_dp.f90 functions.f90 transmissivity_vs_N.f90 -fopenmp

or

ifx params_dp.f90 functions.f90 transmissivity_vs_N.f90 -fopenmp

This program takes on five parameters: num_ic, m, y0, esc_y, and N. Run the program as

./a.out num_ic m y0 esc_y N

with num_ic = 10000, m = -1, and N = 10000000000. The y0 and esc_y parameters have different values. For the blue curve, use y0 = -1 and esc_y = 1 and for the red curve, use y0 = 1 and esc_y = -1.

To generate the rotation number data from Fig. 7(b), compile the rotation_number.f90 program as

gfortran params_dp.f90 functions.f90 rotation_number.f90 -fopenmp

or

ifx params_dp.f90 functions.f90 rotation_number.f90 -fopenmp

and simply execute it as

./a.out

Plotting the figures

After executing all the programs, simply run all cells in the Jupyter notebook Plots.ipynb to generate all the figures shown in the paper. The figures will be stored in a directory called Figures/ which is created automatically by the Jupyter notebook.

Citation

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

M. Rolim Sales et al., Transport mechanisms associated with non-integer wavenumbers in a discontinuous nontwist map, Chaos, Solitons and Fractals 200 (2025) 116966

bibtex @article{RolimSales2025, title = {Transport mechanisms associated with non-integer wavenumbers in a discontinuous nontwist map}, journal = {Chaos, Solitons \& Fractals}, volume = {200}, pages = {116966}, year = {2025}, issn = {0960-0779}, doi = {https://doi.org/10.1016/j.chaos.2025.116966}, url = {https://www.sciencedirect.com/science/article/pii/S0960077925009798}, author = {Matheus {Rolim Sales} and Michele Mugnaine and Ana L. R. {de Moraes} and Edson Denis Leonel and Chris G. Antonopoulos and Iberê Luiz Caldas and José Danilo Szezech}, }

Contact

For questions or feedback, feel free to email me.