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Anomalous Radiative Transfer in Heterogeneous Media.

Federico Tommasi1, Lorenzo Pattelli2,3, Stefano Cavalieri1

  • 1Dipartimento di Fisica e Astronomia dell'Università degli Studi di Firenze, via Giovanni Sansone 1, 50019, Sesto Fiorentino, Italy.

Advanced Theory and Simulations
|August 22, 2025
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Summary
This summary is machine-generated.

This study introduces new rules for Monte Carlo (MC) simulations in anomalous diffusion, applicable to complex geometries. These rules ensure compatibility with pathlength invariance and radiometric concepts, advancing anomalous transport modeling.

Keywords:
Anomalous transportGeneralized Radiative Transfer EquationHeterogeneous mediaMonte Carlo simulationsRandom walks trajectories

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Area of Science:

  • Physics
  • Computational Science

Background:

  • Monte Carlo (MC) simulations are crucial for understanding transport phenomena.
  • Established MC methods exist for classical transport but lack general approaches for anomalous transport.

Purpose of the Study:

  • To develop a universally applicable set of rules for MC simulations in anomalous diffusion media.
  • To ensure these rules are compatible with finite-size geometries and heterogeneous inclusions.

Main Methods:

  • Identification of a novel set of rules for MC simulations in anomalous diffusion.
  • Validation of these rules for pathlength invariance and radiometric concepts like fluence.

Main Results:

  • The proposed rules are applicable to anomalous transport phenomena beyond radiative transfer.
  • Demonstrated compatibility with finite-size geometries and heterogeneous inclusions.
  • Revealed the possibility of resetting the 'memory' of non-exponential step-length distributions at interfaces.

Conclusions:

  • The developed MC simulation rules provide a robust framework for anomalous transport.
  • These findings have significant implications for physical interpretation and experimental verification of anomalous transport phenomena.