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

<p>This repository contains Monte Carlo results for anomalous light transport in a spherical geometry with homogeneous (<code>Hom</code>), heterogeneous layered (<code>Lay</code>), and homogeneous layered (<code>VHom</code>) configurations.</p> <p>Part of these data is described in the publication:</p> <p>F. Tommasi et al. "Anomalous radiative transfer in heterogeneous media" <em>Advanced Theory and Simulations</em> (2024) <a href="https://doi.org/10.1002/adts.202400182">https://doi.org/10.1002/adts.202400182</a></p> <p><br>Data is organized in two types of csv files:</p> <ul> <li><code>filename.csv</code> containing information on the average path length and total path length distribution</li> <li><code>filename_Fluence.csv</code> containing information on the fluence rate and radiance at each spherical layer boundary</li> </ul> <p>Filenames contain information on the simulation parameters used:</p> <table> <tbody> <tr> <td><code>ISO</code></td> <td>isotropic scattering</td> </tr> <tr> <td><code>K0_X</code></td> <td>value of the k coefficient of the Generalized Pareto Distribution used in the Monte Carlo simulation (<code>X</code> = 0.3 or 0.7)</td> </tr> <tr> <td><code>1e7</code></td> <td>number of total trajectories considered</td> </tr> <tr> <td><code>DS</code>, <code>noDS</code></td> <td>simulation performed used the proposed set of rules for anomalous transport in bounded media (<code>DS</code>) or with the standard set of rules (<code>noDS</code>).</td> </tr> <tr> <td><code>Hom</code></td> <td>homogeneous sphere configuration</td> </tr> <tr> <td><code>NLay</code></td> <td>number of layers used in the layered configurations</td> </tr> <tr> <td><code>mism, no_mism</code></td> <td>configuration with (<code>mism</code>) or without (<code>no_mism</code>) refractive index mismatch with the environment or between layers</td> </tr> <tr> <td><code>Vhom_layN</code></td> <td>layered homogeneous sphere configuration with N layers</td> </tr> <tr> <td><code>mus_const</code>, <code>mus_step</code></td> <td>simulations performed using a constant scattering coefficient (<code>mus_const</code>) or different values across different layers (<code>mus_step</code>)</td> </tr> </tbody> </table> <p>&nbsp;</p> <p>The header of each output file contains general information on the simulation settings as detailed below:</p> <ul> <li>The number of layers</li> <li>The radius of each layer</li> <li>The refractive index of each layer and of the external region</li> <li>The critical angle for entering and exiting the sphere</li> <li>Reduced scattering coefficient of each layer</li> <li>Scattering function</li> <li>Type of illumination source</li> <li>Absorption coefficient of the sphere</li> </ul> <p>Simulations for different scattering strengths are classified based on the optical thickness <code>Taud</code> 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, <code>Taud</code> is also the product of diameter and scattering coefficient.<br>For a layered sphere, <code>Taud</code> is given by the sum of the products between the scattering coefficient and radial thickness of each layer.<br>The symbol <code>Taua</code> 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.<br>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.<br>The standard error (<code>SE</code>) is also provided, based on the results of 100 independent simulations with 1E5 trajectories each, for a total of 1E7 total trajectories considered.</p> <h3>Structure of the pathlength files (<code>filename.csv</code>)</h3> <p>List of content for the calculated quantities shown:</p> <ul> <li><code>Ksc_Max</code>: maximum number of scattering events in the medium</li> <li><code>de_max(mm)</code>: maximum pathlength followed by photons</li> <li>Number of Photons lost (always zero, all trajectories are collected)</li> <li>Total CW Exiting Radiation and Standard Error (SE)</li> <li>Mean Pathlength for Total Exiting Radiation and SE</li> <li>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</li> <li>Partial Mean Pathlengths for in each layer for the non-absorbing case</li> <li>Standard Error on Partial Mean Pathlengths in each layer</li> <li>Discrepancy and SE for the Pathlengths for the non-absorbing case</li> <li>Relative SE is shown for the Partial Mean Pathlengths in the non-absorbing case&nbsp;</li> <li>Total Spread Function (mm-1) versus the pathlength of emerging photons l (mm) for each Taud value</li> </ul> <h3>Structure of the fluence files (<code>filename_Fluence.csv</code>)</h3> <p>List of content for the calculated quantities shown:</p> <ul> <li>Mean pathlength and partial pathlength</li> <li>CW fluence at each layer boundary</li> <li><code>SE</code>: standard error for the CW fluence</li> <li>Discrepancy and SE of the CW fluence with respect to the expected value from the invariance properties. This is reported for each layer interface</li> <li>Relative Error of the CW fluence</li> <li><code>CW FLUX_P</code> at each layer boundary</li> <li>Distribution of CW radiance at each layer boundary for all <code>Taud</code> 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</li> </ul> <p>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.</p> <p>For convenience, we list below which files were used to prepare each Figure (some files are used multiple times for different Figures):</p> <h3>Figure 2</h3> <p><code>Hom/ISO_Hom_mism_k0_3_1e7_DS.csv</code><br><code>Hom/ISO_Hom_mism_k0_3_1e7_noDS.csv</code><br><code>Hom/ISO_Hom_mism_k0_7_1e7_DS.csv</code><br><code>Hom/ISO_Hom_mism_k0_7_1e7_noDS.csv</code><br><code>Lay/ISO_4Lay_mus_const_k0_3_1e7_DS.csv</code><br><code>Lay/ISO_4Lay_mus_const_k0_3_1e7_noDS.csv</code><br><code>Lay/ISO_4Lay_mus_const_k0_7_1e7_DS.csv</code><br><code>Lay/ISO_4Lay_mus_const_k0_7_1e7_noDS.csv</code><br><code>Lay/ISO_4Lay_mus_step_k0_3_1e7_DS.csv</code><br><code>Lay/ISO_4Lay_mus_step_k0_3_1e7_noDS.csv</code><br><code>Lay/ISO_4Lay_mus_step_k0_7_1e7_DS.csv</code><br><code>Lay/ISO_4Lay_mus_step_k0_7_1e7_noDS.csv</code></p> <h3>Figure 3</h3> <p><code>Lay/ISO_10lay_mism_k0_3_1e7_DS_Fluence.csv</code><br><code>Lay/ISO_10lay_mism_k0_3_1e7_noDS_Fluence.csv</code><br><code>Lay/ISO_10lay_mism_k0_7_1e7_DS_Fluence.csv</code><br><code>Lay/ISO_10lay_mism_k0_7_1e7_noDS_Fluence.csv</code></p> <h3>Figure 4</h3> <p><code>Hom/ISO_Hom_no_mism_k0_3_1e7_DS.csv</code><br><code>Hom/ISO_Hom_no_mism_k0_3_1e7_noDS.csv</code><br><code>Hom/ISO_Hom_no_mism_k0_7_1e7_DS.csv</code><br><code>Hom/ISO_Hom_no_mism_k0_7_1e7_noDS.csv</code><br><code>Hom/ISO_Hom_mism_k0_3_1e7_DS.csv</code><br><code>Hom/ISO_Hom_mism_k0_3_1e7_noDS.csv</code><br><code>Hom/ISO_Hom_mism_k0_7_1e7_DS.csv</code><br><code>Hom/ISO_Hom_mism_k0_7_1e7_noDS.csv</code></p> <h3>Figure 5</h3> <p><code>Hom/ISO_Hom_mism_k0_7_1e7_DS.csv</code><br><code>VHom/ISO_Vhom_lay2_mism_k0_7_1e7_DS.csv</code><br><code>VHom/ISO_Vhom_lay4_mism_k0_7_1e7_DS.csv</code><br><code>VHom/ISO_Vhom_lay8_mism_k0_7_1e7_DS.csv</code><br><code>VHom/ISO_Vhom_lay16_mism_k0_7_1e7_DS.csv</code></p>