Nonclassical Particle Transport



In classical particle transport, the probability that a particle interacts with the background medium is proportional to the path length traveled by that particle, and the proportionality constant depends on the density of the medium and on the particle’s energy. This typically leads to an exponential attenuation law, i.e. the particle flux decreases as an exponential function of the path length (Beer-Lambert law).
However, certain real systems exhibit correlations where particles can clump together, or they exhibit spatial fluctuations that are not resolved by the model. These correlations between the particles lead to a nonexponential free-path distribution, where exponential decay fails to hold. The classical techniques in use are not capable of preserving the true nonexponential attenuation law that arises in these heterogeneous systems, leading to unreliable estimates of the particle flux. This project addresses the challenges of modeling systems with this type of nonexponential particle attenuation.

Applications include atmospheric sciences, nuclear engineering, health physics, medical imaging, and computer graphics.


Part of this research is done in collaboration with the Rio de Janeiro State University, funded by the Brazilian Government through a CAPES-Print grant.

Publications


[P32] The nonclassical simplified P2 and P3 equations with anisotropic scattering


Robert K. Palmer, Richard Vasques

Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Virtual Meeting (Raleigh, NC), 2021 Oct, pp. 368-378


[P33] A review of the deterministic solution of nonclassical transport problems


Leonardo R. C. Moraes, Ricardo C. Barros, Richard Vasques

Proceedings of International Nuclear Atlantic Conference - INAC 2021, Virtual Meeting, Brazil, 2021 Nov


[J18] An improved spectral approach for solving the nonclassical neutral particle transport equation


Leonardo R.C. Moraes, Japan K. Patel, Ricardo C. Barros, Richard Vasques

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 490(-), 2022, p. 108282


[J17] On the application of the analytical discrete ordinates method to the solution of nonclassical transport problems in slab geometry


Leonardo R. C. Moraes, Liliane B. Barichello, Ricardo C. Barros, Richard Vasques

Journal of Computational Physics, vol. 455(-), 2022, p. 110982


[P7] Anisotropic diffusion in model 2-D pebble-bed reactor cores


Richard Vasques, Edward W. Larsen

Proceedings of International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics, Saratoga Springs, NY, 2009 May


[J3] A generalized linear Boltzmann equation for non-classical particle transport


Edward W. Larsen, Richard Vasques

Journal of Quantitative Spectroscopy & Radiative Transfer, vol. 112(4), 2011, pp. 619-631


[P9] Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system


Richard Vasques

Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering, Sun Valley, ID, 2013 May


[P11] Numerical schemes for a non-classical linear Boltzmann equation for transport through spatially correlated media


Kai Krycki, Richard Vasques

Proceedings of NumHyp: Numerical approximations of hyperbolic systems with source terms and applications, Aachen, Germany, 2013 Sep


[J6] Non-classical particle transport with angular-dependent path-length distributions. I: Theory


Richard Vasques, Edward W. Larsen

Annals of Nuclear Energy, vol. 70(-), 2014, pp. 292-300


[J5] Non-classical particle transport with angular-dependent path-length distributions. II: Application to pebble bed reactor cores


Richard Vasques, Edward W. Larsen

Annals of Nuclear Energy, vol. 70(-), 2014, pp. 301-311


[P17] On the accuracy of the non-classical transport equation in 1- D random periodic media


Richard Vasques, Kai Krycki

Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method, Nashville, TN, 2015 Apr


[P18] Boundary conditions for the 1-D non-classical transport equation


Richard Vasques, Kai Krycki

Proceedings of 24th ICTT: International Conference on Transport Theory, Taormina, Italy, 2015 Sep


[J8] The nonclassical Boltzmann equation and diffusion-based approximations to the Boltzmann equation


Martin Frank, Kai Krycki, Edward W. Larsen, Richard Vasques

Siam Journal on Applied Mathematics, vol. 75(3), 2015, pp. 1329-1345


[P20] Nonclassical particle transport in the 1-D diffusive limit


Richard Vasques, Rachel N. Slaybaugh, Kai Krycki

Transactions of the American Nuclear Society, vol. 114(1), 2016, pp. 361-364


[J9] The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation


Richard Vasques

Applied Mathematics Letters, vol. 53(-), 2016, pp. 63-68


[P21] Simplified PN equations for nonclassical transport with isotropic scattering


Richard Vasques, Rachel N. Slaybaugh

Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, South Korea, 2017 Apr


[P22] A generalized volume rendering approach for computer graphics


Magnus Wrenninge, Richard Vasques, Rachel N. Slaybaugh

Proceedings of 25th ICTT: International Conference on Transport Theory, Monterey, CA, 2017 Oct


[P23] Exact transport representations of the classical and nonclassical simplified PN equations


Ilker Makine, Richard Vasques, Rachel N. Slaybaugh

Proceedings of 25th ICTT: International Conference on Transport Theory, Monterey, CA, 2017 Oct


[J11] Nonclassical particle transport in one-dimensional random periodic media


Richard Vasques, Kai Krycki, Rachel N. Slaybaugh

Nuclear Science and Engineering, vol. 185(1), 2017, pp. 78-106


[J12] Exact transport representations of the classical and nonclassical simplified PN equations


Ilker Makine, Richard Vasques, Rachel N. Slaybaugh

Journal of Computational and Theoretical Transport, vol. 47(4-6), 2018, pp. 326-349


[P26] Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering


Robert K. Palmer, Richard Vasques

Proceedings of 26th ICTT: International Conference on Transport Theory, Paris, France, 2019 Sep


[P27] A nonclassical Monte Carlo algorithm for transport problems in diffusive binary stochastic media


Richard Vasques, Patrick S. Brantley, Robert K. Palmer

Proceedings of 26th ICTT: International Conference on Transport Theory, Paris, France, 2019 Sep


[P28] P1 synthetic acceleration for nonclassical spectral SN equations in slab geometry


Japan K. Patel, Leonardo R. C. Moraes, Richard Vasques, Ricardo C. Barros

Proceedings of 26th ICTT: International Conference on Transport Theory, Paris, France, 2019 Sep


[J14] A spectral approach for solving the nonclassical transport equation


Richard Vasques, Leonardo R. C. Moraes, Ricardo Carvalho de Barros, Rachel N. Slaybaugh

Journal of Computational Physics, vol. 402(-), 2020, p. 109078


[J13] Asymptotic derivation of the simplified PN equations for nonclassical transport with anisotropic scattering


Robert K. Palmer, Richard Vasques

Journal of Computational and Theoretical Transport, vol. 49(7), 2020, pp. 331-348


[J16] Transport synthetic acceleration for the solution of the one-speed nonclassical spectral SN equations in slab geometry


Japan K. Patel, Leonardo R. C. Moraes, Richard Vasques, Ricardo C. Barros

Journal of Computational and Applied Mathematics, vol. 401(-), 2022 , p. 113768


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