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:

ISO
isotropic scattering

K0_X
value of the k coefficient of the Generalized Pareto Distribution used in the Monte Carlo simulation (X = 0.3 or 0.7)

1e7
number of total trajectories considered

DS, noDS
simulation performed used the proposed set of rules for anomalous transport in bounded media (DS) or with the standard set of rules (noDS).

Hom
homogeneous sphere configuration

NLay
number of layers used in the layered configurations

mism, no_mism
configuration with (mism) or without (no_mism) refractive index mismatch with the environment or between layers

Vhom_layN
layered homogeneous sphere configuration with N layers

mus_const, mus_step
simulations performed using a constant scattering coefficient (mus_const) or different values across different layers (mus_step)

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.csvHom/ISO_Hom_mism_k0_3_1e7_noDS.csvHom/ISO_Hom_mism_k0_7_1e7_DS.csvHom/ISO_Hom_mism_k0_7_1e7_noDS.csvLay/ISO_4Lay_mus_const_k0_3_1e7_DS.csvLay/ISO_4Lay_mus_const_k0_3_1e7_noDS.csvLay/ISO_4Lay_mus_const_k0_7_1e7_DS.csvLay/ISO_4Lay_mus_const_k0_7_1e7_noDS.csvLay/ISO_4Lay_mus_step_k0_3_1e7_DS.csvLay/ISO_4Lay_mus_step_k0_3_1e7_noDS.csvLay/ISO_4Lay_mus_step_k0_7_1e7_DS.csvLay/ISO_4Lay_mus_step_k0_7_1e7_noDS.csv

Figure 3

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

Figure 4

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

Figure 5

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