Transport Theory

Transport Theory

 

The Transport Theory is the study of laws that describe the migration of radiation and particles within a medium of interest, defined by the Boltzmann equation. In particular, Radiative Transfer is the theory of how radiation and matter interact based on the particle description of light and represents the theoretical underpinning of remote sensing. The Rarefied Gas Dynamics describes the behavior of particles, widely studied in fluid dynamics, relates to molecular-kinetic processes which occur in gases.

 

 

Chandrasekhar's Basic Problem in Radiative Transfer Solved via Theory of Functional Connections

 

Mario De Florio, Enrico Schiassi, Roberto Furfaro, Barry D. Ganapol, Domiziano Mostacci

 

In this work, we present a novel approach to solving the Chandrasekhar’s problem in Radiative Transfer using the recently developed Theory of Functional Connections. The method is designed to efficiently and accurately solve the Linear Boundary Value Problem arising from the integrodifferential Boltzmann equation for Radiative Transfer. The proposed algorithm follows under the category of numerical methods for the solution of Transport Equations. The accuracy of this new method is tested by benchmarks comparison for Mie and Haze L scattering laws.

 

The problem is reduced to the following linear system of algebraic equations:                                                                                      where:

 

 

 

Our Publications

  • De Florio, M., Schiassi, E., Furfaro, R., Ganapol, B.D., Mostacci, D. (2020). Solutions of Chandrasekhar’s Basic Problem in Radiative Transfer via Theory of Functional Connections. Journal of Quantitative Spectroscopy & Radiative Transfer. DOI: https://doi.org/10.1016/j.jqsrt.2020.107384
  • Picca, P., & Furfaro, R. (2019). A quasi-static approach for the solution of steady-state linear transport problems. Annals of Nuclear Energy, 133, 805-815. DOI: https://doi.org/10.1016/j.anucene.2019.07.015
  • Picca, P., & Furfaro, R. (2018). Reactivity determination using the hybrid transport point kinetics and the area method. Annals of Nuclear Energy, 114, 191-197. DOI: https://doi.org/10.1016/j.anucene.2017.12.019
  • Picca, P., & Furfaro, R. (2017). Application of the Transport-Driven Diffusion Approach for Criticality Calculations. Journal of Computational and Theoretical Transport, 46(4), 258-282. DOI: 10.1080/23324309.2017.1352515
  • Picca, P., & Furfaro, R. (2017). Application of Extreme Learning Machines to inverse neutron kinetics. Annals of Nuclear Energy, 100, 1-8. DOI: 10.1016/j.anucene.2016.08.031
  • Schiassi, E., Furfaro, R., & Mostacci, D. (2016). Bayesian inversion of coupled radiative and heat transfer models for asteroid regoliths and lakes. Radiation Effects and Defects in Solids, 171(9-10), 736-745. DOI: http://dx.doi.org/10.1080/10420150.2016.1253091
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2016). Application of non-linear extrapolations for the convergence acceleration of source iteration. Journal of Computational and Theoretical Transport, 45(5), 351-367. DOI: 10.1080/23324309.2016.1167742
  • Picca, P., & Furfaro, R. (2015). Closed-form solution of the first-order Transport-Driven Diffusion approximation. Annals of Nuclear Energy, 76, 431-438. DOI: 10.1016/j.anucene.2014.10.016
  • Picca, P., & Furfaro, R. (2014). A hybrid method for the solution of linear Boltzmann equation. Annals of Nuclear Energy, 72, 214-236. DOI: 10.1016/j.anucene.2014.05.014
  • Furfaro, R., Previti, A., Picca, P., Kargel, J. S., & Bishop, M. P. (2014). Radiative transfer modeling in the cryosphere. In Global Land Ice Measurements from Space (pp. 53-73). Springer, Berlin, Heidelberg. DOI: 10.1007/978-3-540-79818-7_3
  • Picca, P., & Furfaro, R. (2014). Hybrid-transport point kinetics for initially-critical multiplying systems. Progress in Nuclear Energy, 76, 232-243. DOI: 10.1016/j.pnucene.2014.05.013
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2013). A highly accurate technique for the solution of the non-linear point kinetics equations. Annals of Nuclear Energy, 58, 43-53. DOI: 10.1016/j.anucene.2013.03.004
  • Picca, P., & Furfaro, R. (2013). Analytical discrete ordinate method for radiative transfer in dense vegetation canopies. Journal of Quantitative Spectroscopy and Radiative Transfer, 118, 60-69. DOI: 10.1016/j.jqsrt.2012.12.007
  • Picca, P., & Furfaro, R. (2012). Neutron inverse kinetics via Gaussian Processes. Annals of Nuclear Energy, 47, 146-154. DOI: 10.1016/j.anucene.2012.03.023
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2012). On radiative transfer in dense vegetation canopies. Transport Theory and Statistical Physics, 41(3-4), 223-244. DOI: 10.1080/00411450.2012.671218
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2012). An efficient multiproblem strategy for accurate solutions of linear particle transport problems in spherical geometry. Nuclear science and engineering, 170(2), 103-124. DOI: 10.13182/NSE11-05
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2012). Derivation of a physically based hybrid technique for the solution of source-driven time-dependent linear Boltzmann equations. Transport Theory and Statistical Physics, 41(1-2), 23-39. DOI: 10.1080/00411450.2012.671219
  • Picca, P., Furfaro, R., & Ganapol, B. D. (2011). A Hybrid Transport Point-Kinetic method for simulating source transients in subcritical systems. Annals of Nuclear Energy, 38(12), 2680-2688. DOI: 10.1016/j.anucene.2011.08.005
  • Previti, A., Furfaro, R., Picca, P., Ganapol, B. D., & Mostacci, D. (2011). Solving radiative transfer problems in highly heterogeneous media via domain decomposition and convergence acceleration techniques. Applied Radiation and Isotopes, 69(8), 1146-1150. DOI: 10.1016/j.apradiso.2010.11.016
  • Picca, P., Furfaro, R., Kargel, J., & Ganapol, B. D. (2008, April). Forward and inverse models for photon transport in soil-ice mixtures and their application to the problem of retrieving optical properties of planetary surfaces. In Space Exploration Technologies (Vol. 6960, p. 69600O). International Society for Optics and Photonics. DOI: 10.1117/12.777479