SupplementaryData

Reference notebooks, scripts, and precomputed data accompanying the scattering cross-section study for five models of two-phase media in two and three dimensions.

Layout

• Debye.ipynb, Equilibrium.ipynb, Polydisperse.ipynb, SHU.ipynb, g2-invariant.ipynb: Reproducible workflows to load precomputed spectral data/structure factors, compute attenuation functions with scripts/computeF.py, and derive scattering mean free paths (strong-contrast and Mie estimates).

• data/: Precomputed inputs/outputs (spectral densities, structure factors, attenuation functions, scattering results). Most .txt files are ignored by git except SHU/PolyHU inputs.

• scripts/: Reusable code:

  • shared.py: Plot style, geometry helpers, Bruggeman mixing.
  • computeF.py: Attenuation function calculator (type='chik' or type='sk'). Use the --help command for details. Cite the following references:
  1. Torquato S, Kim J. Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime. Phys. Rev. X. 2021;11(2):021002. doi: 10.1103/Phys‐RevX.11.021002 -- 2D, 3D cases.
  2. Kim J, Torquato S. Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media beyond the Quasistatic Regime. Optica. 2023;10:965–972. doi:10.1364/optica.489797 -- 1D case
  3. Kim J, Torquato S. Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites beyond the Long‐Wavelength Regime. Opt. Mater. Express. 2024;14(1):194. doi:10.1364/OME.507918 -- 2D cases

  • Microstructure helpers: Approx_2DHSF.py, Analytic_3DHSF.py, Analytic_Debye.py, g2_invariant.py.

  • Scattering utilities: Formulas.py (strong-contrast series), MieCylinder.py, MieSphere.py.

Typical run (notebooks)

1. Set d, volume fraction, and the appropriate input parameters. For SHU/polyHU, there are some precomputed input in data/.
2. Load/plot spectral density or structure factor.
3. Evaluate attenuation function via computeF.py with matching type.
4. Compute scattering mean free paths (strong-contrast approximation and/or Mie estimate).

Notes

• No analytic evaluation is done for SHU/PolyHU; those notebooks only read the provided data/ inputs.
• Ensure scripts/ is on sys.path when running notebooks locally.***

Environment

• Conda environment name: sca
• Install with: bash env-setup.sh
• Required Python packages: python>=3.11, numpy, scipy, matplotlib

Scripts

• env-setup.sh: creates the sca conda environment with the above dependencies.