Dataset related to the publication "Anomalous radiative transfer in heterogeneous media"

This repository contains Monte Carlo results for anomalous light transport in a spherical geometry with homogeneous (Hom), heterogeneous layered (Lay), and homogeneous layered (VHom) configurations.

Part of these data is described in the publication:

F. Tommasi et al. "Anomalous radiative transfer in heterogeneous media" Advanced Theory and Simulations (2024) https://doi.org/10.1002/adts.202400182

Data is organized in two types of csv files:

• filename.csv containing information on the average path length and total path length distribution
• filename_Fluence.csv containing information on the fluence rate and radiance at each spherical layer boundary

Filenames contain information on the simulation parameters used:

The header of each output file contains general information on the simulation settings as detailed below:

• The number of layers
• The radius of each layer
• The refractive index of each layer and of the external region
• The critical angle for entering and exiting the sphere
• Reduced scattering coefficient of each layer
• Scattering function
• Type of illumination source
• Absorption coefficient of the sphere

Simulations for different scattering strengths are classified based on the optical thickness Taud of the sphere, corresponding to the product between the sphere diameter (10 mm) and the reduced scattering coefficient. Since we have results only for isotropic scattering, Taud is also the product of diameter and scattering coefficient.
For a layered sphere, Taud is given by the sum of the products between the scattering coefficient and radial thickness of each layer.
The symbol Taua is also used to denote the product between the sphere and the absorption coefficient. Since we have considered only non-absorbing media, this value is always zero.
Each simulation is carried out for different values of the reduced scattering coefficient in the layers, keeping their reciprocal ratios fixed, resulting in the following values of Taud: 1E-3, 2E-3, 5E-3, 1E-2, 2E-2, 5E-2, 1E-1, 2E-1, 5E-1, 1, 2, 5, 10, 20, 50, 100, which, in the case of the homogeneous sphere, correspond to reduced scattering coefficients comprised between 1E-4 and 10.
The standard error (SE) is also provided, based on the results of 100 independent simulations with 1E5 trajectories each, for a total of 1E7 total trajectories considered.

Structure of the pathlength files (filename.csv)

List of content for the calculated quantities shown:

• Ksc_Max: maximum number of scattering events in the medium
• de_max(mm): maximum pathlength followed by photons
• Number of Photons lost (always zero, all trajectories are collected)
• Total CW Exiting Radiation and Standard Error (SE)
• Mean Pathlength for Total Exiting Radiation and SE
• Solutions of the RTE for the non-absorbing sphere with Lambertian illumination given in terms of the mean pathlength in the sphere and partial pathlength in each layer
• Partial Mean Pathlengths for in each layer for the non-absorbing case
• Standard Error on Partial Mean Pathlengths in each layer
• Discrepancy and SE for the Pathlengths for the non-absorbing case
• Relative SE is shown for the Partial Mean Pathlengths in the non-absorbing case 
• Total Spread Function (mm-1) versus the pathlength of emerging photons l (mm) for each Taud value

Structure of the fluence files (filename_Fluence.csv)

List of content for the calculated quantities shown:

• Mean pathlength and partial pathlength
• CW fluence at each layer boundary
• SE: standard error for the CW fluence
• Discrepancy and SE of the CW fluence with respect to the expected value from the invariance properties. This is reported for each layer interface
• Relative Error of the CW fluence
• CW FLUX_P at each layer boundary
• Distribution of CW radiance at each layer boundary for all Taud values. The distribution expected from the invariance property is also listed in the columns adjacent to the Monte Carlo results. Radiance data is reported as a function of the angle at each layer boundary

Additional empty fields in the files refer to output quantities that can be optionally calculated during the simulations. These options were not selected for this study.

For convenience, we list below which files were used to prepare each Figure (some files are used multiple times for different Figures):

Figure 2

Hom/ISO_Hom_mism_k0_3_1e7_DS.csv
Hom/ISO_Hom_mism_k0_3_1e7_noDS.csv
Hom/ISO_Hom_mism_k0_7_1e7_DS.csv
Hom/ISO_Hom_mism_k0_7_1e7_noDS.csv
Lay/ISO_4Lay_mus_const_k0_3_1e7_DS.csv
Lay/ISO_4Lay_mus_const_k0_3_1e7_noDS.csv
Lay/ISO_4Lay_mus_const_k0_7_1e7_DS.csv
Lay/ISO_4Lay_mus_const_k0_7_1e7_noDS.csv
Lay/ISO_4Lay_mus_step_k0_3_1e7_DS.csv
Lay/ISO_4Lay_mus_step_k0_3_1e7_noDS.csv
Lay/ISO_4Lay_mus_step_k0_7_1e7_DS.csv
Lay/ISO_4Lay_mus_step_k0_7_1e7_noDS.csv

Figure 3

Lay/ISO_10lay_mism_k0_3_1e7_DS_Fluence.csv
Lay/ISO_10lay_mism_k0_3_1e7_noDS_Fluence.csv
Lay/ISO_10lay_mism_k0_7_1e7_DS_Fluence.csv
Lay/ISO_10lay_mism_k0_7_1e7_noDS_Fluence.csv

Figure 4

Hom/ISO_Hom_no_mism_k0_3_1e7_DS.csv
Hom/ISO_Hom_no_mism_k0_3_1e7_noDS.csv
Hom/ISO_Hom_no_mism_k0_7_1e7_DS.csv
Hom/ISO_Hom_no_mism_k0_7_1e7_noDS.csv
Hom/ISO_Hom_mism_k0_3_1e7_DS.csv
Hom/ISO_Hom_mism_k0_3_1e7_noDS.csv
Hom/ISO_Hom_mism_k0_7_1e7_DS.csv
Hom/ISO_Hom_mism_k0_7_1e7_noDS.csv

Figure 5

Hom/ISO_Hom_mism_k0_7_1e7_DS.csv
VHom/ISO_Vhom_lay2_mism_k0_7_1e7_DS.csv
VHom/ISO_Vhom_lay4_mism_k0_7_1e7_DS.csv
VHom/ISO_Vhom_lay8_mism_k0_7_1e7_DS.csv
VHom/ISO_Vhom_lay16_mism_k0_7_1e7_DS.csv