Research Software Theory, validation, and figures

Stepping-Stone Volume Constants

Heriberto Espino-Montelongo and Héctor Maravillo

2026

Summary

Python tools for evaluating normalized stepping-stone diversion-region volume constants, validating the numerical results by Monte Carlo simulation, and reproducing the project figures.

$$ a_{d,\mathrm{SS}}(\alpha)=2\kappa_{d-1}\int_{2^{-1/\alpha}}^1 y_\alpha(u)^{d-1}x_\alpha^{\prime}(u)\,du $$

Context

The theoretical one-dimensional representation is checked independently through acceptance Monte Carlo sampling in a bounding cylinder.

Main contributions

  • Implements the one-dimensional representation for normalized stepping-stone diversion-region volume constants.
  • Validates numerical values independently through acceptance Monte Carlo sampling.
  • Provides reproducible experiment entry points, numerical tests, retained validation results, and figure-generation scripts.
  • Includes an interactive three-dimensional visualization of the normalized diversion neighborhood.