# Nonclassical Particle Transport

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.

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### Publications

[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

Kai Krycki, Richard Vasques

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

[J5] 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

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

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

Robert K. Palmer, Richard Vasques

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

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

[J13] 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(109078), 2020 Feb

Robert K. Palmer, Richard Vasques

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

The nonclassical simplified P2 and P3 equations with anisotropic scattering

Robert K. Palmer, Richard Vasques

To appear in Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Raleigh, NC, 2021 Oct

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

To appear in the Journal of Computational and Applied Mathematics, 2021