Exit_time

MATLAB codes to support two projects. These MATLAB codes require GMSH 4.7.1 to generate unstructured meshes for the finite volume and random walk calculations. The software can be downloaded at https://gmsh.info/

Simpson et al. (2021)

The first project is Simpson et al. (2021) Mean exit time for diffusion on irregular domains, New Journal of Physics, 23, 043030. https://doi.org/10.1088/1367-2630/abe60d

The MATLAB codes also include ellipse fitting tools from Szpak et al. (2015) https://link.springer.com/article/10.1007%2Fs10851-014-0536-x

• The main MATLAB scripts are

  • unperturbed_disc_main.m for the unperturbed disc problem;
  • unperturbed_ellipse_main.m for the unperturbed ellipse problem;
  • perturbed_disc_main.m for the perturbed disc problem;
  • perturbed_ellipse_main.m for the perturbed ellipse problem;
  • tasmania_analysis.m for the Tasmania case study;
  • taiwan_main.m for the Taiwan case study.

• Some notes for each figure:

  • To produce Figure 1, run unperturbed_disc_main.m Lines 1 through 64.
  • To produce Figure 2, run unperturbed_ellipse_main.m Lines 1 through 64.
  • To produce Figure 3, run perturbed_disc_main.m Lines 1 through 78,
  • To produce Figure 4, run perturbed_ellipse_main.m Lines 1 through 82.
  • To produce Figure 6, run tasmania_analysis.m Lines 1 through 214.
  • To produce Figure 7, run taiwan_analysis.m Lines 1 through 192.
  • To produce Figure 8, run perturbed_disc_main.m Lines 1 through 29, Line 37, Lines 80 through 136.
  • To produce Figure 9, run perturbed_ellipse_main.m Lines 1 through 42, Lines 84 through 123.

• About inpoly2: In perturbed_ellipse_walk_2.m, the inpoly2 function from Engwirda (2020) [https://github.com/dengwirda/inpoly] with a slight modification to prevent errors in the case of a single remaining walk. This modification is given in the documentation of perturbed_ellipse_walk_2.m.

Carr et al. (2022)

The second project is Carr et al. (2022) Mean exit time in irregularly-shaped annular and composite disc domains, Journal of Physics A: Mathematical and Theoretical, 55, 105002. https://doi.org/10.1088/1751-8121/ac4a1d

• The main MATLAB scripts are

  • perturbed_annulus_main.m for the perturbed annulus problem;
  • perturbed_compound_disc_main.m for the perturbed compound disc problem.

• Some notes for each figure:

  • To produce Figure 2, run perturbed_annulus_main.m with Case = 'P1' (uncomment Line 14 and comment Lines 11-13,15,16).
  • To produce Figure 3, run perturbed_annulus_main.m with Case = 'P2' (uncomment Line 15 and comment Lines 11-14,16).
  • To produce Figure 4, run perturbed_annulus_main.m with Case = 'P3' (uncomment Line 16 and comment Lines 11-15).
  • To produce Figure 5, run perturbed_compound_disc_main.m with Case = 'P1' (uncomment Line 13 and comment Lines 11,12,14).
  • To produce Figure 6, run perturbed_compound_disc_main.m with Case = 'P2' (uncomment Line 14 and comment Lines 11-13).