Exact and approximate solutions of the fractional radiative transport equation

• Applicant: Dr. André Liemert
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 576424554

The classical radiative transport equation (RTE) is successfully applied since more than 100 years in different fields of science such as astrophysics, neutron transport theory, climate research, heat transfer, biomedical optics and computer graphics. It provides in many situations of high practical importance e.g.~the determination of the light propagation in random scattering media, a valid approximation of Maxwell's equations. However, although the classical RTE being widely used, a serious limitation of this integro-differential equation is the fact that it is not applicable for describing non-classical or generalized transport processes e.g.~when the path lengths between two interaction points are no longer distributed according to the standard Lambert-Beer law. Indeed, anomalous transport phenomena such as Lévy flights, which are typically characterized by a power-law jump length distribution, often occur in physical, chemical or biological systems such as light transport in superdiffusive media. In this project, it is intended to develop for the first time analytical approaches useable for solving the multidimensional fractional RTE in the steady-state and time domain. The derived analytical solutions will offer several decisive advantages compared with numerical solution approaches (stochastic and deterministic) in view of accuracy, computation time, implementation and the insights into the underlying physical effects. Moreover, all obtained analytical solutions will be compared and verified with Monte Carlo simulations. A further important task within this project will be the derivation of the corresponding (generalized) diffusion theory, especially with regard to the appropriate boundary conditions.

• DFG Programme: Research Grants