@article{mccormick_garcia_siewert_2018, title={Biographical Memoir and Publications of Paul F. Zweifel}, volume={47}, ISSN={["2332-4325"]}, DOI={10.1080/23324309.2018.1508474}, abstractNote={Abstract Paul Zweifel served as the founding editor of the Transport Theory and Statistical Physics journal from 1971 to 1981. An overview of his professional life gives a detailed list of his publications, broken down by his research interests, and also illustrates his leadership of the International Conference on Transport Theory meetings over the past 50 years. This paper provides supplementary material to the Paul Frederick Zweifel obituary published in Physics Today 70 (8):73 (2017); doi:10.1063/PT.3.3671.}, number={1-3}, journal={JOURNAL OF COMPUTATIONAL AND THEORETICAL TRANSPORT}, author={McCormick, Norman J. and Garcia, Roberto D. M. and Siewert, Charles E.}, year={2018}, month={Apr}, pages={187–208} }
 @article{garcia_siewert_thomas_2017, title={A Computationally Viable Version of the PN Method for Spheres}, volume={186}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2016.1273627}, abstractNote={Abstract The long-standing problem of implementing the method effectively for spherical geometry is revisited in this work. It is shown that a least-squares approach to the method resolves to a great extent the numerical instability reported for the first time by Aronson in 1984. In the proposed version of the method, a small loss of accuracy is still observed for intermediate orders of the approximation, but in high order (typically ), full accuracy is recovered, and the method can be used with confidence even for extremely high orders of the approximation. Numerical results of benchmark quality are tabulated for the quantities of interest for two basic transport problems in spherical geometry: the albedo problem for a sphere and the critical-sphere problem, both including cases that show the effects of scattering anisotropy described by the binomial law.}, number={2}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Garcia, R. D. M. and Siewert, C. E. and Thomas, J. R., Jr.}, year={2017}, month={May}, pages={103–119} }
 @article{mccormick_siewert_ganapol_prinja_2017, title={Paul Frederick Zweifel}, volume={70}, ISSN={["1945-0699"]}, DOI={10.1063/pt.3.3671}, abstractNote={Paul Frederick Zweifel died on 12 February 2017 in Blacksburg, Virginia. He was a prominent leader in the mathematical theory of nuclear reactors and the mathematical development of transport theory. Paul Frederick Zweifel PPT|High resolutionBorn in New York City on 21 June 1929, Paul later moved with his family to Spartanburg, South Carolina. At age 15 he was awarded a Pepsi-Cola scholarship to attend the college of his choice, Carnegie Institute of Technology (now Carnegie Mellon University). There he shared living quarters with John Nash Jr, the US mathematician who received the 1994 Nobel Memorial Prize in Economic Sciences. After graduating from Carnegie Tech in three years, he attended Duke University, where he received his PhD in physics in 1954 under the guidance of Eugene Greuling. The title of his dissertation was “Capture-positron branching ratios.” During his years of graduate study, he was a sports journalist at the Durham Sun newspaper, where he interviewed Willie Mays and other athletes.After completing his PhD, Paul worked at the General Electric Knolls Atomic Power Laboratory. For his contributions to the theory of the slowing down and thermalization of neutrons, which are important in the design and development of water-moderated nuclear reactors, he received an Ernest Orlando Lawrence Memorial Award from the Department of Energy in 1972.From 1958 to 1968, Paul was a professor of nuclear engineering at the University of Michigan. There he began working with physicist Kenneth Case, who made groundbreaking contributions to neutron transport theory at Los Alamos during the Manhattan Project. In 1967 they published their widely cited monograph Linear Transport Theory (Addison-Wesley) on the linear Boltzmann equation. That equation is used, for example, to analyze energy transport by neutrons in a nuclear reactor or photons in an absorbing and scattering medium. Paul and Case’s mathematical approach enables a more direct solution to many problems of the type analyzed by Boris Davison in Neutron Transport Theory (Clarendon Press, 1957) and Subrahmanyan Chandrasekhar in Radiative Transfer (Dover, 1960).During a sabbatical year at the Middle East Technical University in 1965, Paul and physicist Erdal İnönü organized a NATO Advanced Study Institute on transport theory in Ankara, Turkey.In 1968 Paul moved to Blacksburg, Virginia, where he became a professor of physics at Virginia Tech and was soon appointed as University Distinguished Professor. In 1969 he founded a series of conferences now known as the International Conferences on Transport Theory (ICTT). The biennial meetings continue to bring together experts in mathematical and applied transport theory in multifarious science and engineering disciplines from around the world. Because of his leadership and the force of his personality, the conferences, which are not affiliated with any professional society, have been held in the US 14 times, Italy 3 times, and once each in China, Brazil, Sweden, Russia, England, and Hungary; Paul hosted six of the conferences in Blacksburg.The journal Transport Theory and Statistical Physics (TTSP), with Paul as its founding editor from 1971 until 1983, has published the proceedings of nearly every ICTT meeting. The journal was retitled in 2014 as the Journal of Computational and Theoretical Transport in recognition of the growing popularity of numerical techniques in transport theory.Perhaps Paul’s most notable work in transport theory was pioneering the use of rigorous mathematics to bring order to the chaos of mathematical approaches for solving the linear transport equation. He developed existence and uniqueness theorems for the neutron transport equation and investigated the spectrum of the linear transport operator under general conditions.Paul retired from Virginia Tech in 1996. He was an opera lover, a musician, and a vocalist. He also was fluent in Italian; with his wife, Kathy, they provided supertitles for opera companies across the US, and they advertised their services with “Have Projector, Will Travel” business cards. He published articles on the mathematical theory of ancient and modern music. Paul loved to travel, and one of his most memorable trips, which he took with his family, was his 1983–84 sabbatical in Florence, Italy, where he also served as choir director of St James Episcopal Church. Throughout his life, Paul continued his passions for Gilbert and Sullivan musical theater, sports, and bridge.To those who study particle transport theory, Paul was a special figure. He was as comfortable with practical applications of the transport equation, particularly to nuclear reactors, as he was with the underlying mathematics. He had a flare for the unusual, and he often provided readers of TTSP with book reviews on esoteric subjects and entertained audiences with presentations on topics such as why Albert Einstein should have received five Nobel Prizes. Intellectually, Paul cast a large shadow on our community. Although sometimes contentious and seldom politically correct, with his witty sense of humor he could flatter with ridicule, critique with praise, and encourage with affection. He was an inspiration to us and a delightful colleague who will be greatly missed.© 2017 American Institute of Physics.}, number={8}, journal={PHYSICS TODAY}, author={McCormick, Norman J. and Siewert, Charles E. and Ganapol, Barry D. and Prinja, Anil K.}, year={2017}, month={Aug}, pages={73–73} }
 @article{garcia_siewert_2015, title={The linearized Boltzmann equation with Cercignani-Lampis boundary conditions: Heat transfer in a gas confined by two plane-parallel surfaces}, volume={86}, ISSN={["0306-4549"]}, DOI={10.1016/j.anucene.2015.01.013}, abstractNote={The analytical discrete-ordinates method is used to solve the problem of heat transfer for a single-species gas confined by two plane-parallel surfaces. The formulation of the problem is based on the linearized Boltzmann equation for rigid-sphere interactions between gas particles and the Cercignani–Lampis kernel for gas–surface interactions. Accurate numerical results are reported for the density, temperature, and heat-flow perturbations from a reference (equilibrium) state and are compared with similar results from five kinetic models. An interesting finding of this work is that there are combinations of the four numerical values of the accommodation coefficients used to define the Cercignani–Lampis boundary conditions that give rise to heat flows that are larger for the transition regime than for the free-molecular regime, an effect not observed when the standard (Maxwell) boundary conditions are used.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2015}, month={Dec}, pages={45–54} }
 @article{garcia_siewert_2014, title={On the dispersion function for complex values of the parameter c}, volume={69}, ISSN={["0306-4549"]}, DOI={10.1016/j.anucene.2014.02.015}, abstractNote={The dispersion function relevant to one-speed transport theory with isotropic scattering is analyzed for the case of complex values of c, and an explicit expression is given for the discrete eigenvalue ν0.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2014}, month={Jul}, pages={203–204} }
 @article{garcia_siewert_2011, title={A simplified implementation of the discrete-ordinates method for a class of problems in radiative transfer with polarization}, volume={112}, ISSN={["0022-4073"]}, DOI={10.1016/j.jqsrt.2011.08.010}, abstractNote={A simplified implementation of the analytical discrete ordinates (ADO) method in radiative transfer with polarization is presented in this work. The class of problems that can be solved with the simplified ADO approach consists of problems defined in plane-parallel geometry and driven by external illumination in the form of obliquely incident parallel rays. Numerical results of benchmark quality are tabulated for the albedo problem with polarization and Lambert reflection. The new results improve on a tabulation made available in a previous work by the authors that was based on the (less accurate) spherical harmonics method.}, number={18}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2011}, month={Dec}, pages={2801–2813} }
 @article{barichello_siewert_2011, title={Some evaluations of basic nodal-like schemes for a selection of classical problems in particle transport theory}, volume={38}, ISSN={["0306-4549"]}, DOI={10.1016/j.anucene.2011.05.005}, abstractNote={In order to provide some basic evaluations of elementary nodal techniques, as used in the general area of particle transport theory, critical and albedo problems for cylinders, spheres, and slabs are solved approximately in terms of averaged quantities and compared to exact results.}, number={9}, journal={ANNALS OF NUCLEAR ENERGY}, author={Barichello, L. B. and Siewert, C. E.}, year={2011}, month={Sep}, pages={2101–2104} }
 @article{garcia_siewert_2010, title={On the use of a nascent delta function in radiative-transfer calculations for multi-layer media subject to Fresnel boundary and interface conditions}, volume={111}, ISSN={["0022-4073"]}, DOI={10.1016/j.jqsrt.2009.06.004}, abstractNote={The “pre-processing” procedure and the “break-point” analysis developed in a previous work based on the ADO (analytical discrete ordinates) method are used, along with a nascent delta function to describe the polar-angle dependence of an incident beam, to solve the classical albedo problem for radiative transfer in a plane-parallel, multi-layer medium subject to Fresnel boundary and interface conditions. As a result of the use of a nascent delta function, rather than the Dirac distribution, to model the polar-angle dependence of the incident beam, the computational work is significantly simplified (since a particular solution is not required) in comparison to an approach where both the polar-angle and the azimuthal-angle dependence of the incident beam are formulated in terms of Dirac delta distributions. The numerical results from this approach are (when a sufficiently small “narrowness” parameter is used to define the nascent delta) found to be in complete agreement with already reported (high-quality) results for a set of challenging multi-layer problems.}, number={1}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2010}, month={Jan}, pages={128–133} }
 @article{garcia_siewert_2010, title={Viscous-slip, thermal-slip, and temperature-jump coefficients based on the linearized Boltzmann equation (and five kinetic models) with the Cercignani-Lampis boundary condition}, volume={29}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2010.01.005}, abstractNote={A polynomial expansion procedure and the ADO (analytical discrete-ordinates) method are used to compute the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient from the linearized Boltzmann equation (LBE) for rigid-sphere interactions and the Cercignani–Lampis (CL) boundary condition. These same quantities are also computed from five kinetic models, with the CL condition, and compared to the LBE result. Equivalent results for the LBE and the kinetic models, all based on the usual Maxwell boundary condition, are also reported.}, number={3}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2010}, pages={181–191} }
 @article{garcia_siewert_2009, title={The linearized Boltzmann equation with Cercignani-Lampis boundary conditions: Basic flow problems in a plane channel}, volume={28}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2008.12.001}, abstractNote={A polynomial expansion procedure and the ADO (analytical discrete-ordinates) method are used to solve a collection of basic flow problems based on the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary conditions with a free choice of the accommodation coefficients at each boundary. In particular, three classical problems defined by flow in a plane-parallel channel (Poiseuille, thermal-creep, and Couette flow) are solved (essentially) analytically and evaluated to a very high numerical standard. Some comparisons with known kinetic models are also reported.}, number={3}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2009}, pages={387–396} }
 @article{garcia_siewert_2008, title={Couette flow of a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation}, volume={27}, ISSN={["0997-7546"]}, DOI={10.1016/j.euromechflu.2008.01.004}, abstractNote={A concise and accurate solution to the problem of plane Couette flow for a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation and general (specular-diffuse) Maxwell boundary conditions for each of the two species of gas particles is developed. An analytical version of the discrete-ordinates method is used to establish the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species. Accurate numerical results are given for the case of a mixture of helium and argon confined between molybdenum and tantalum plates.}, number={6}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2008}, pages={823–836} }
 @article{garcia_siewert_yacout_2008, title={On the use of Fresnel boundary and interface conditions in radiative-transfer calculations for multilayered media}, volume={109}, ISSN={["0022-4073"]}, DOI={10.1016/j.jqsrt.2007.09.013}, abstractNote={The ADO (analytical discrete ordinates) method is used to establish a concise and accurate solution for a multi-layer radiative-transfer problem with Fresnel boundary and interface conditions. A finite plane-parallel medium composed of a number (K) of sub-strata with different material properties is considered to be illuminated by isotropically incident radiation. While a general result is obtained, emphasis in the numerical work is given to computing accurately the currents and the intensities that exit each of the two exterior surfaces. Monochromatic forms (with anisotropic scattering) of the radiative-transfer equation are used, and numerical results are given for several specific cases. The complications introduced by the Fresnel boundary and interface conditions are well resolved, so that the numerical results obtained are thought to define a very high standard.}, number={5}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Garcia, R. D. M. and Siewert, C. E. and Yacout, A. M.}, year={2008}, month={Mar}, pages={752–769} }
 @article{garcia_siewert_2008, title={Particular solutions of the linearized Boltzmann equation for a binary mixture of rigid spheres}, volume={59}, ISSN={["1420-9039"]}, DOI={10.1007/s00033-007-6106-y}, number={2}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2008}, month={Mar}, pages={281–292} }
 @article{garcia_siewert_yacout_2008, title={Radiative transfer in a multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination by obliquely incident parallel rays}, volume={109}, ISSN={["0022-4073"]}, DOI={10.1016/j.jqsrt.2008.03.012}, abstractNote={The ADO (analytical discrete ordinates) method, a pre-processing procedure, and the break-point analysis developed for azimuthally symmetric problems in a previous work are generalized and used to solve a radiative-transfer problem defined by a finite, plane–parallel, multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination in the form of obliquely incident parallel rays. Illumination is modeled by Dirac distributions in each of the two angles (polar and azimuthal) that define the direction of propagation of the incident rays. Accurate numerical results are tabulated for two sets of test problems.}, number={12-13}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Garcia, R. D. M. and Siewert, C. E. and Yacout, A. M.}, year={2008}, pages={2151–2170} }
 @article{siewert_2007, title={A note on radiative transfer in a finite layer}, volume={40}, ISSN={["1751-8121"]}, DOI={10.1088/1751-8113/40/8/007}, abstractNote={An ADO (analytical discrete ordinates) solution is used to establish a concise and accurate result for a basic radiative transfer problem in a finite layer described by the grey equation of transfer with general anisotropic scattering. As a specific application, the solution is evaluated for the case of Fresnel boundary conditions to yield numerical results (of a high standard) for several specific cases.}, number={8}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Siewert, C. E.}, year={2007}, month={Feb}, pages={1785–1789} }
 @article{garcia_siewert_2007, title={Channel flow of a binary mixture of rigid spheres described by the linearized Boltzmann equation and driven by temperature, pressure, and concentration gradients}, volume={67}, ISSN={["0036-1399"]}, DOI={10.1137/060673606}, abstractNote={An analytical version of the discrete‐ordinates method (the ADO method) is used with recently established analytical expressions for the rigid‐sphere scattering kernels in a study devoted to the flow of a binary gas mixture in a plane channel. In particular, concise and accurate solutions to basic flow problems in a plane channel driven by temperature, pressure, and concentration gradients and described by the linearized Boltzmann equation are established for the case of Maxwell boundary conditions for each of the two species. The velocity, heat‐flow, and shear‐stress profiles, as well as the mass‐ and heat‐flow rates, are established for each species of particles, and numerical results are reported for two binary mixtures (Ne‐Ar and He‐Xe).}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2007}, pages={1041–1063} }
 @article{garcia_siewert_2007, title={Heat transfer between parallel plates: An approach based on the linearized Boltzmann equation for a binary mixture of rigid-sphere gases}, volume={19}, ISSN={["2329-7778"]}, DOI={10.1063/1.2511039}, abstractNote={An analytical version of the discrete-ordinates method is used to develop a concise and particularly accurate solution of the heat-transfer problem for a binary gas mixture confined between two parallel plates. The formulation of the problem allows general (specular-diffuse) Maxwell boundary conditions for each of the two types of particles and is based on a form of the linearized Boltzmann equation that incorporates recently established analytical expressions for the relevant rigid-sphere kernels. Numerical results are reported for the density, the temperature, and the heat-flow profiles relative to each species in Ne-Ar and He-Xe mixtures.}, number={2}, journal={PHYSICS OF FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2007}, month={Feb} }
 @article{garcia_siewert_2007, title={Some solutions (linear in the spatial variables) and generalized Chapman-Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres}, volume={58}, ISSN={["1420-9039"]}, DOI={10.1007/s00033-006-0074-5}, number={2}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2007}, month={Mar}, pages={262–288} }
 @article{garcia_siewert_2007, title={The temperature-jump problem based on the linearized Boltzmann equation for a binary mixture of rigid spheres}, volume={26}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2006.04.001}, abstractNote={An analytical version of the discrete-ordinates method (the ADO method) is used with recently reported analytical forms for the rigid-sphere scattering kernels to establish a concise and particularly accurate solution to the temperature-jump problem for a binary gas mixture described by the linearized Boltzmann equation. The solution yields, in addition to the temperature-jump coefficient for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the density, the temperature and the heat-flow profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations.}, number={1}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2007}, pages={132–153} }
 @article{garcia_siewert_2007, title={The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation}, volume={26}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2006.12.002}, abstractNote={An analytical version of the discrete-ordinates method (the ADO method) is used with recently established analytical expressions for the rigid-sphere scattering kernels to develop concise and particularly accurate solutions to the viscous-slip, the diffusion-slip, and the half-space thermal-creep problems for a binary gas mixture described by the linearized Boltzmann equation. In addition to a computation of the viscous-slip, the diffusion-slip, and the thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow, and shear-stress profiles are established for each species of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations.}, number={6}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2007}, pages={749–778} }
 @article{siewert_2006, title={A Legendre expansion and some exact solutions basic to the McCormack model for binary gas mixtures}, volume={25}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2005.04.005}, abstractNote={A Legendre expansion of the scattering kernel, a conservation condition and some exact solutions are reported for the McCormack kinetic model that is used to describe a binary mixture of rarefied gases.}, number={1}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Siewert, CE}, year={2006}, pages={130–136} }
 @article{garcia_siewert_2006, title={Some exact results basic to the linearized Boltzmann equations for a binary mixture of rigid spheres}, volume={57}, ISSN={["1420-9039"]}, DOI={10.1007/s00033-005-0027-4}, number={6}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Garcia, R. D. M. and Siewert, C. E.}, year={2006}, month={Nov}, pages={999–1010} }
 @article{garcia_siewert_2005, title={The McCormack model for gas mixtures: Plane Couette flow}, volume={17}, ISSN={["1070-6631"]}, DOI={10.1063/1.1845911}, abstractNote={An analytical version of the discrete-ordinates method is used to establish a concise and particularly accurate solution to the problem of plane Couette flow for a binary gas mixture described by the McCormack kinetic model. The solution yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species of gas particles. Highly accurate numerical results are reported for the case of a helium–argon mixture confined between molybdenum and tantalum plates. The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2GHz Pentium 4 machine to compute all quantities of interest with at least five figures of accuracy.}, number={3}, journal={PHYSICS OF FLUIDS}, author={Garcia, RDM and Siewert, CE}, year={2005}, month={Mar} }
 @article{siewert_2005, title={The McCormack model for gas mixtures: The temperature-jump problem}, volume={56}, ISSN={["0044-2275"]}, DOI={10.1007/s00033-004-3116-x}, number={2}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Siewert, CE}, year={2005}, month={Mar}, pages={273–292} }
 @article{garcia_siewert_2005, title={The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas}, volume={57}, ISSN={["0044-2275"]}, DOI={10.1007/s00033-005-0007-8}, number={1}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Garcia, RDM and Siewert, CE}, year={2005}, month={Nov}, pages={94–122} }
 @article{siewert_valougerogis_2004, title={Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions}, volume={23}, ISSN={["0997-7546"]}, DOI={10.1016/j.euromechflu.2003.12.002}, abstractNote={An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the viscous-slip and the half-space thermal-creep problems for a binary gas mixture. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. In addition to a computation of the viscous-slip and thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles are established for both types of particles. Numerical results are reported for three binary mixtures (Ne–Ar, He–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and the solution of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than 0.1 seconds on a 1.2 GHz Pentium-based PC to solve both problems.}, number={5}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Siewert, CE and Valougerogis, D}, year={2004}, pages={709–726} }
 @article{barichello_rodrigues_siewert_2004, title={On computing the Chapman-Enskog and Burnett functions}, volume={86}, ISSN={["1879-1352"]}, DOI={10.1016/j.jqsrt.2003.10.001}, abstractNote={An expansion and projection technique based on Legendre polynomials is used to solve, in an efficient and accurate way, the Chapman-Enskog equations for viscosity and heat transfer and to compute the Burnett functions required, for example, for Poiseuille-flow problems based on rigid-sphere collisions and the linearized Boltzmann equation.}, number={1}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Rodrigues, P and Siewert, CE}, year={2004}, month={Jun}, pages={109–114} }
 @article{siewert_2004, title={On computing the thermal-slip coefficient from Kramers' problem}, volume={16}, ISSN={["1089-7666"]}, DOI={10.1063/1.1728157}, abstractNote={Classical techniques are used to derive a variant of an Onsager relation (used typically for Poiseuille flow and thermal-creep flow) that yields a convenient relationship between the heat flow of Kramers’ problem and the thermal-slip coefficient. The analysis is based on the linearized Boltzmann equation for rigid-sphere interactions, and wall interactions are described by a general law that includes, for example, the Maxwell model (a mixture of specular and diffuse reflection) and the Cercignani–Lampis model.}, number={6}, journal={PHYSICS OF FLUIDS}, author={Siewert, CE}, year={2004}, month={Jun}, pages={2132–2135} }
 @article{garcia_siewert_2004, title={The McCormack model for gas mixtures: Heat transfer in a plane channel}, volume={16}, ISSN={["1070-6631"]}, DOI={10.1063/1.1773711}, abstractNote={An analytical version of the discrete-ordinates method (the ADO method) is used to establish a concise and particularly accurate solution to the heat-transfer problem in a plane channel for a binary gas mixture described by the McCormack kinetic model. The solution yields for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the density and temperature profiles for both types of particles, as well as the overall heat flow associated with each of the two species of gas particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe). The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium 4 machine to compute all quantities of interest.}, number={9}, journal={PHYSICS OF FLUIDS}, author={Garcia, RDM and Siewert, CE}, year={2004}, month={Sep}, pages={3393–3402} }
 @article{siewert_valougeorgis_2004, title={The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients}, volume={23}, ISSN={["1873-7390"]}, DOI={10.1016/j.euromechflu.2004.03.003}, abstractNote={An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problems of Poiseuille flow, thermal-creep flow and diffusion flow for a binary gas mixture confined between parallel walls. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. The analysis yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and a solver of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium IV machine to solve all three problems.}, number={4}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Siewert, CE and Valougeorgis, D}, year={2004}, pages={645–664} }
 @article{siewert_2004, title={The temperature-jump problem based on the CES model of the linearized Boltzmann equation}, volume={55}, ISSN={["1420-9039"]}, DOI={10.1007/s00033-003-1140-x}, number={1}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Siewert, CE}, year={2004}, month={Jan}, pages={92–104} }
 @article{siewert_2003, title={Heat transfer and evaporation/condensation problems based on the linearized Boltzmann equation}, volume={22}, ISSN={["1873-7390"]}, DOI={10.1016/S0997-7546(03)00053-0}, abstractNote={A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve four basic problems, all based on the linearized Boltzmann equation for rigid-sphere interactions, that describe heat transfer and/or evaporation–condensation between two parallel surfaces or for the case of a semi-infinite half space. Relevant to the case of two surfaces, the basic problem of heat transfer driven by a temperature difference at two confining walls described by a general Maxwell gas–surface interaction law (a mixture of specular and diffuse reflection) is solved for the case where different accommodation coefficients can be used for each of the two bounding surfaces. In addition, the classical problem of “reverse temperature gradient” in the theory of evaporation and condensation is also solved for the case of two parallel liquid–vapor interfaces kept at different temperatures. In regard to half-space applications, an evaporation/condensation problem based on a presumed known interface condition and a heat-conduction problem (with no net flow) driven by energy flow from a bounding surface with know properties are each solved with what is considered a high degree of accuracy.}, number={4}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Siewert, CE}, year={2003}, pages={391–408} }
 @article{barichello_siewert_2003, title={Some comments on modeling the linearized Boltzmann equation}, volume={77}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(02)00074-2}, abstractNote={Some exact solutions of the homogeneous and the inhomogeneous linearized Boltzmann equation (LBE) for rigid-sphere collisions are used to define two model equations in the general area of rarefied-gas dynamics. These equations are obtained from a systematic development of two synthetic scattering kernels that yield model equations that have as exact solutions certain known exact solutions of the homogeneous and of the inhomogeneous LBE. The first model established is defined in terms of the collisional invariants and the Chapman–Enskog integral equations for viscosity and for heat conduction. An extended model is defined also in terms of the collisional invariants and the Chapman–Enskog functions for viscosity and heat conduction, but the first and second Burnett functions are also included in the model. The variable collision frequency or generalized BGK model is also obtained as a special case. In addition, the exact mean-free paths defined, for rigid-sphere collisions and the LBE, in terms of viscosity or heat conduction are employed to define approximations of these quantities that are consistent with the use of the variable collision frequency model.}, number={1}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Siewert, CE}, year={2003}, month={Feb}, pages={43–59} }
 @article{siewert_2003, title={The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems}, volume={54}, ISSN={["0044-2275"]}, DOI={10.1007/s000330300005}, number={2}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Siewert, CE}, year={2003}, month={Mar}, pages={273–303} }
 @article{siewert_2003, title={The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem}, volume={77}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(02)00172-3}, abstractNote={Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coefficient are obtained (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.}, number={4}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2003}, month={Apr}, pages={417–432} }
 @article{siewert_2003, title={Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani-Lampis boundary condition}, volume={15}, ISSN={["1070-6631"]}, DOI={10.1063/1.1567284}, abstractNote={A polynomial expansion procedure and an analytical discrete-ordinates method are used to evaluate the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient as defined by a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary condition.}, number={6}, journal={PHYSICS OF FLUIDS}, author={Siewert, CE}, year={2003}, month={Jun}, pages={1696–1701} }
 @article{barichello_rodrigues_siewert_2002, title={An analytical discrete-ordinates solution for dual-mode heat transfer in a cylinder}, volume={73}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00181-9}, abstractNote={Abstract A modern analytical version of the discrete-ordinates method is used along with Hermite cubic splines and Newton's method to solve a class of coupled nonlinear radiation–conduction heat-transfer problems in a solid cylinder. Computational details of the solution are discussed, and the algorithm is implemented to establish high-quality results for various data sets which include some difficult cases.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Rodrigues, P and Siewert, CE}, year={2002}, month={Jun}, pages={583–602} }
 @article{siewert_valougeorgis_2002, title={An analytical discrete-ordinates solution of the S-model kinetic equations for flow in a cylindrical tube}, volume={72}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00189-3}, abstractNote={An integro-differential form of the linearized S-model kinetic equations for describing flow in a cylindrical tube is projected in such a way as to yield a pair of coupled transport equations that defines the desired velocity and heat-flow profiles. This system is then solved symbolically to yield a pair of coupled integral equations for the physical quantities required. At this point some transformations are carried out to yield a restatement of the original problem in terms of a “pseudo-problem” defined by plane-geometry variables. An analytical version of the discrete-ordinates method is then used to solve the pseudo-problem, and so, after both MATLAB and FORTRAN versions of the developed algorithm are implemented, results thought to be highly accurate are obtained for the case of diffuse reflection from the walls of a cylindrical tube. In addition to the velocity and heat-flow profiles, for the cases of Poiseuille flow and thermal-creep flow, the velocity slips, the heat-flow profiles evaluated at the wall, the particle-flow rates and the heat-flow rates for these two problems are reported for selected values of the tube radius.}, number={4}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE and Valougeorgis, D}, year={2002}, month={Feb}, pages={531–550} }
 @article{barichello_camargo_rodrigues_siewert_2002, title={An integral equation basic to the BGK model for flow in a cylindrical tube}, volume={53}, ISSN={["0044-2275"]}, DOI={10.1007/s00033-002-8182-3}, number={5}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Barichello, LB and Camargo, M and Rodrigues, P and Siewert, CE}, year={2002}, month={Sep}, pages={769–781} }
 @article{siewert_2002, title={Generalized boundary conditions for the S-model kinetic equations basic to flow in a plane channel}, volume={72}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00057-7}, abstractNote={An analytical version of the discrete-ordinates method is used to solve the classical problems of Poiseuille flow and thermal-creep flow in a plane channel. The kinetic theory for the rarefied-gas flow is based on the S model (a generalization of the BGK model), and in addition to the use of the diffuse–specular reflection model (based on a single accommodation coefficient) for describing particle scattering from the channel walls, the Cercignani–Lampis model defined in terms of normal and tangential accommodation coefficients is implemented. The established solution is tested numerically, and results for the velocity and heat-flow profiles, the particle-flow rate and the heat-flow rate thought to be correct to many significant figures are reported for various values of the channel width.}, number={1}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2002}, month={Jan}, pages={75–88} }
 @article{siewert_2002, title={Inverse solutions to radiative-transfer problems based on the binomial or the Henyey-Greenstein scattering law}, volume={72}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00161-3}, abstractNote={Analytical techniques are used to solve two inverse radiative-transfer problems, for a finite plane-parallel medium, that are (i) based on the binomial scattering law and (ii) based on the Henyey–Greenstein scattering law. In addition, previously reported analytical results (valid for isotropic scattering) that yield an analytical inverse solution for the unknown optical thickness of the medium are extended to the case of anisotropic scattering. The algorithms for the inversions are verified numerically, and some effects of noise on the simulated experimental data are observed.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2002}, month={Mar}, pages={827–835} }
 @article{siewert_2002, title={Inverse solutions to radiative-transfer problems with partially transparent boundaries and diffuse reflection}, volume={72}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00122-4}, abstractNote={Analytical techniques are used to solve a class of inverse radiative-transfer problems relevant to finite and semi-infinite plane-parallel media. While the assumption of isotropic scattering is made, diffuse reflection is allowed at the surface, for the semi-infinite case, and at both surfaces for the case of a finite layer. For the general case based on a semi-infinite medium, a cubic algebraic equation is used to define the basic result, but for the specific case of a semi-infinite medium illuminated by a constant incident distribution of radiation, very simple exact expressions are developed for the albedo for single scattering ϖ and the coefficient for diffuse reflection ρ. Analytical results are also developed (again in terms of a cubic algebraic equation) for the case of a finite layer with equal reflection coefficients relevant to the two surfaces. For the general case of a finite layer with unequal reflection coefficients, two specific formulations are given. The first algorithm is based on a system of three quadratic algebraic equations for the two reflection coefficients ρ1 and ρ2 and the single-scattering albedo ϖ. Secondly, an elimination between these three algebraic equations is carried out to yield two coupled algebraic equations for ρ1 and ρ2 plus an explicit expression for ϖ in terms of ρ1 and ρ2. In addition, an exact expression for τ0, the optical thickness of the finite layer, is developed in terms of ϖ, ρ1 and ρ2. As is typical with the considered class of inverse problems in radiative transfer, all surface quantities are either specified or considered available from experimental measurements. All basic results are tested numerically.}, number={4}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2002}, month={Feb}, pages={299–313} }
 @article{siewert_sharipov_2002, title={Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients}, volume={14}, ISSN={["1070-6631"]}, DOI={10.1063/1.1514973}, abstractNote={Various model equations are used to define the viscous-slip and the thermal-slip coefficients in rarefied gas dynamics. More specifically, the BGK model, the S model, the variable collision model and the CES model are used to establish the slip coefficients basic to Kramers’ problem and the half-space problem of thermal creep. While the most general results are developed from use of the Maxwell boundary condition, results for the BGK model and the S model as defined by the Cercignani–Lampis boundary condition are also reported. An analytical discrete-ordinates method is used to establish the reported numerical results, and when available results from a numerical solution of the linearized Boltzmann equation are used as reference values. In addition to the numerical work based on model equations, the important issue of how to define meaningful ways (appropriate mean-free paths) to compare the results for the various models is discussed.}, number={12}, journal={PHYSICS OF FLUIDS}, author={Siewert, CE and Sharipov, F}, year={2002}, month={Dec}, pages={4123–4129} }
 @article{siewert_2002, title={On computing the Chapman-Enskog functions for viscosity and heat transfer and the Burnett functions}, volume={74}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00289-8}, abstractNote={Hermite cubic splines and collocation are used to solve, in an efficient and accurate way, the Chapman–Enskog equations for viscosity and heat transfer and to compute the Burnett functions required for Poiseuille-flow problems based on rigid-sphere collisions and the linearized Boltzmann equation.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2002}, month={Sep}, pages={789–796} }
 @article{siewert_2002, title={Poiseuille, thermal creep and Couette flow: results based on the CES model of the linearized Boltzmann equation}, volume={21}, ISSN={["0997-7546"]}, DOI={10.1016/S0997-7546(02)01202-5}, abstractNote={A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model.}, number={5}, journal={EUROPEAN JOURNAL OF MECHANICS B-FLUIDS}, author={Siewert, CE}, year={2002}, pages={579–597} }
 @article{barichello_bartz_camargo_siewert_2002, title={The temperature-jump problem for a variable collision frequency model}, volume={14}, ISSN={["1070-6631"]}, DOI={10.1063/1.1416192}, abstractNote={An analytical version of the discrete-ordinates method is used here in the field of rarefied-gas dynamics to solve a version of the temperature-jump problem that is based on a linearized, variable collision frequency model of the Boltzmann equation. In addition to a complete development of the discrete-ordinates method for the application considered, the computational algorithm is implemented to yield accurate numerical results for three specific cases: the classical BGK model, the Williams model (the collision frequency is proportional to the magnitude of the velocity), and the rigid-sphere model.}, number={1}, journal={PHYSICS OF FLUIDS}, author={Barichello, LB and Bartz, ACR and Camargo, M and Siewert, CE}, year={2002}, month={Jan}, pages={382–391} }
 @article{siewert_2002, title={Two half-space problems based on a synthetic-kernel model of the linearized Boltzmann equation}, volume={75}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(01)00290-4}, abstractNote={Abstract An analytical discrete-ordinates method is used to solve two basic half-space problems based on a new synthetic-kernel model of the linearized Boltzmann equation. In particular, Kramers’ problem and the half-space problem of thermal creep, both basic to the general area of rarefied-gas dynamics, are defined by model equations that are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented to yield numerical results for the slip coefficients and the velocity and heat-flow profiles that compare well with solutions derived from much more computationally intensive techniques.}, number={1}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2002}, month={Aug}, pages={21–38} }
 @article{siewert_2001, title={Kramers' problem for a variable collision frequency model}, volume={12}, ISSN={["0956-7925"]}, DOI={10.1017/s0956792501004491}, abstractNote={The often-studied problem known as Kramers' problem, in the general area of rarefied-gas 
dynamics, is investigated in terms of a linearized, variable collision frequency model of 
the Boltzmann equation. A convenient change of variables is used to reduce the general 
case considered to a canonical form that is well suited for analysis by analytical and/or 
numerical methods. While the general formulation developed is valid for an unspecified 
collision frequency, a recently developed version of the discrete-ordinates method is used 
to compute the viscous-slip coefficient and the velocity defect in the Knudsen layer for 
three specific cases: the classical BGK model, the Williams model (the collision frequency is 
proportional to the magnitude of the velocity) and the rigid-sphere model.}, journal={EUROPEAN JOURNAL OF APPLIED MATHEMATICS}, author={Siewert, CE}, year={2001}, month={Apr}, pages={179–191} }
 @article{siewert_2001, title={The critical problem with high-order anisotropic scattering}, volume={28}, ISSN={["0306-4549"]}, DOI={10.1016/S0306-4549(00)00090-6}, abstractNote={A synthetic scattering kernel is used with one-speed transport theory to evaluate the effect of high-order anisotropic scattering on the critical half thickness for a multiplying, unreflected, plane-parallel medium.}, number={8}, journal={ANNALS OF NUCLEAR ENERGY}, author={Siewert, CE}, year={2001}, month={May}, pages={825–829} }
 @article{siewert_valougeorgis_2001, title={The temperature-jump problem for a mixture of two gases}, volume={70}, ISSN={["1879-1352"]}, DOI={10.1016/S0022-4073(00)00142-4}, abstractNote={An analytical variation of the discrete-ordinates method is used to establish a concise and accurate solution to the temperature-jump problem for a binary gas mixture. The analysis is based on Boltzmann equations of the BGK type subject to Maxwell's boundary conditions with arbitrary accommodation coefficients. The results include the complete temperature and density fields for specified mass, density and collision frequency ratios. The numerical results are of benchmark quality, and the required computational time is only a few seconds on a typical PC.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE and Valougeorgis, D}, year={2001}, month={Aug}, pages={307–319} }
 @article{barichello_camargo_rodrigues_siewert_2001, title={Unified solutions to classical flow problems based on the BGK model}, volume={52}, ISSN={["0044-2275"]}, DOI={10.1007/pl00001559}, number={3}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Barichello, LB and Camargo, M and Rodrigues, P and Siewert, CE}, year={2001}, month={May}, pages={517–534} }
 @article{siewert_2000, title={A concise and accurate solution to Chandrasekhar's basic problem in radiative transfer}, volume={64}, ISSN={["0022-4073"]}, DOI={10.1016/s0022-4073(98)00144-7}, abstractNote={A recently developed version of the discrete-ordinates method is used along with elementary numerical linear-algebra techniques to establish an efficient and especially accurate solution to what can be called Chandrasekhar’s basic problem in radiative transfer, namely the problem of computing the radiation intensity in a finite plane-parallel layer illuminated by an incident beam of radiation and in which scattering can be described by a (rather) general scattering law.}, number={2}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2000}, month={Jan}, pages={109–130} }
 @article{siewert_2000, title={A discrete-ordinates solution for multigroup transport theory with upscattering}, volume={64}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(99)00098-9}, abstractNote={Abstract A recently developed version of the discrete-ordinates method is used along with elementary numerical linear-algebra techniques to establish an efficient and especially accurate solution to a class of multigroup transport problems for which upscattering is an important aspect of the model. The problems considered are defined for finite plane-parallel media, and anisotropic scattering from any group to any group is included in the formulation. Computational details of the solution are discussed, and accurate numerical results for two previously defined test problems are established.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2000}, month={Feb}, pages={255–273} }
 @article{siewert_2000, title={A discrete-ordinates solution for radiative-transfer models that include polarization effects}, volume={64}, ISSN={["1879-1352"]}, DOI={10.1016/S0022-4073(99)00006-0}, abstractNote={A recently developed version of the discrete-ordinates method is used along with elementary numerical linear-algebra techniques to establish an accurate solution for all components in a Fourier representation of the Stokes vector basic to the scattering of polarized light. Computational aspects of the solution are discussed, and numerical results for each of the four Stokes parameters are given for a test case based on an atmosphere of randomly orientated oblate spheroids.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={2000}, month={Feb}, pages={227–254} }
 @article{barichello_garcia_siewert_2000, title={Particular solutions for the discrete-ordinates method}, volume={64}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(98)00146-0}, abstractNote={A full-range orthogonality relation is developed and used to construct the infinite-medium Green’s function for a general form of the discrete-ordinates approximation to the transport equation in plane geometry. The Green’s function is then used to define a particular solution that is required in the solution of inhomogeneous versions of the discrete-ordinates equations.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Garcia, RDM and Siewert, CE}, year={2000}, month={Feb}, pages={219–226} }
 @article{siewert_2000, title={Poiseuille and thermal-creep flow in a cylindrical tube}, volume={160}, ISSN={["0021-9991"]}, DOI={10.1006/jcph.2000.6464}, abstractNote={A version of the discrete-ordinates method is used to solve, for the case of flow in a cylindrical tube, the classical Poiseuille and thermal-creep problems based on the Bhatnagar, Gross, and Krook model in the theory of rarefied-gas dynamics. In addition to the development of a discrete-ordinates solution that is valid for a wide range of the Knudsen number, the solution is evaluated numerically for selected cases to yield results, thought to be correct to many significant figures, for the slip velocities, the macroscopic velocity profiles, and the flow rates.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Siewert, CE}, year={2000}, month={May}, pages={470–480} }
 @article{barichello_siewert_2000, title={The searchlight problem for radiative transfer in a finite slab}, volume={157}, ISSN={["0021-9991"]}, DOI={10.1006/jcph.1999.6396}, abstractNote={A version of the discrete-ordinates method recently developed for radiative-transfer calculations is used along with numerical linear-algebra techniques and two-dimensional Fourier-transform procedures to establish the radiation flux and the z component of the radiation current at all locations in a finite plane-parallel layer irradiated by a beam incident only at one point on one surface. In addition to a general formulation basic to a beam that is incident at an oblique angle, for which the flux and current depend on three spatial variables, the Fourier transforms of the flux and current are inverted numerically for the two-dimensional case relevant to a normally incident beam. The reported numerical procedures, while computationally intensive, are thought to yield, for the considered test case, the radiation flux and the normal component of the radiation current with five figures of accuracy.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Barichello, LB and Siewert, CE}, year={2000}, month={Jan}, pages={707–726} }
 @article{barichello_siewert_2000, title={The temperature-jump problem in rarefied-gas dynamics}, volume={11}, ISSN={["0956-7925"]}, DOI={10.1017/S0956792599004180}, abstractNote={An analytical version of the discrete-ordinates method is used here to solve the classical 
temperature-jump problem based on the BGK model in rarefied-gas dynamics. In addition to 
a complete development of the discrete-ordinates method for the application considered, the 
computational algorithm is implemented to yield very accurate results for the temperature 
jump and the complete temperature and density distributions in the gas. The algorithm is 
easy to use, and the developed code runs typically in less than a second on a 400 MHz 
Pentium-based PC.}, journal={EUROPEAN JOURNAL OF APPLIED MATHEMATICS}, author={Barichello, LB and Siewert, CE}, year={2000}, month={Aug}, pages={353–364} }
 @article{garcia_siewert_2000, title={The transport of neutral hydrogen atoms in a hydrogen plasma}, volume={136}, ISSN={["0029-5639"]}, DOI={10.13182/NSE00-A2150}, abstractNote={Abstract An analytical version of the discrete ordinates method is used to solve a class of boundary-value problems based on a linear Boltzmann equation relevant to the transport of neutral hydrogen atoms in a hydrogen plasma. In addition to a complete development of the discrete ordinates method for the considered application, the computational algorithm is implemented to yield very accurate results for a number of half-space and finite-slab problems. The developed code is also used to correct some entries in a previously reported tabulation of results. The established algorithm is considered especially easy to use, and the code runs (typically) in <1 s on a 400-MHz Pentium-based personal computer.}, number={1}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Garcia, RDM and Siewert, CE}, year={2000}, month={Sep}, pages={140–149} }
 @article{siewert_1999, title={A concise and accurate solution for a polarization model in radiative transfer}, volume={62}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(98)00097-1}, abstractNote={The discrete-ordinates method is used to develop a solution to a basic polarization problem in radiative transfer. In particular, a solution for the coupled I and Q components of the Stokes vector is developed for a polarization model based on a mixture of Rayleigh and isotropic scattering. The solution is evaluated for the case of a finite plane-parallel layer that has a polarized beam incident on one surface and which has Lambertian reflection on the other surface.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE}, year={1999}, month={Aug}, pages={677–684} }
 @article{barichello_siewert_1999, title={A discrete-ordinates solution for Poiseuille flow in a plane channel}, volume={50}, ISSN={["0044-2275"]}, DOI={10.1007/s000000050189}, number={6}, journal={ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK}, author={Barichello, LB and Siewert, CE}, year={1999}, month={Nov}, pages={972–981} }
 @article{barichello_siewert_1999, title={A discrete-ordinates solution for a non-grey model with complete frequency redistribution}, volume={62}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(98)00096-X}, abstractNote={The discrete-ordinates method is used to develop a solution to a class of non-grey problems in the theory of radiative transfer. The model considered allows for scattering with complete frequency redistribution (completely non-coherent scattering) and continuum absorption. In addition to a general formulation for semi-infinite and finite plane-parallel media, specific computations, for both the Doppler and the Lorentz profiles of the line-scattering coefficient, are discussed in regard to a half-space application concerning a linearly varying Planck function and also in regard to a basic problem from which, except for the conservative case, the classical X and Y functions can be extracted.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Siewert, CE}, year={1999}, month={Aug}, pages={665–675} }
 @article{barichello_siewert_1999, title={A discrete-ordinates solution for a polarization model with complete frequency redistribution}, volume={513}, ISSN={["0004-637X"]}, DOI={10.1086/306834}, abstractNote={The discrete-ordinates method is used to develop a solution to a class of polarization problems in the theory of radiative transfer. The I and Q components of the Stokes vector are used to describe the polarized radiation field, and the model considered allows a mixture of Rayleigh and isotropic scattering with complete frequency redistribution (completely noncoherent scattering) and continuum absorption. In addition to a general formulation for a finite plane-parallel medium, specific computations for both the Doppler and the Lorentz profiles of the line-scattering coefficient are reported for a general problem with internal emission and radiation incident on one surface of the layer.}, number={1}, journal={ASTROPHYSICAL JOURNAL}, author={Barichello, LB and Siewert, CE}, year={1999}, month={Mar}, pages={370–382} }
 @article{siewert_1999, title={A discrete-ordinates solution for heat transfer in a plane channel}, volume={152}, ISSN={["0021-9991"]}, DOI={10.1006/jcph.1999.6244}, abstractNote={A recently established version of the discrete-ordinates method is used to develop a solution to a class of problems in the theory of rarefied-gas dynamics where temperature and density effects are coupled. In particular, accurate solutions for the temperature perturbation, the density perturbation, and the heat flux are developed and evaluated for the flow, described by the Bhatnagar, Gross, and Krook model, of a rarefied gas between two parallel plates at which arbitrary and unequal accommodation is allowed. Numerical results are obtained for various choices of the accommodation coefficients and a wide range of the inverse Knudsen number.}, number={1}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Siewert, CE}, year={1999}, month={Jun}, pages={251–263} }
 @article{siewert_wright_1999, title={Efficient eigenvalue calculations in radiative transfer}, volume={62}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(98)00099-5}, abstractNote={An efficient method is used to compute the eigenvalues required in a discrete-ordinates solution to a special class of radiative-transfer problems. The basis for this computation is an algorithm for finding eigenvalues of a matrix that consists of the sum of a diagonal matrix and a rank-one matrix, a form that can arise in a discrete-ordinates solution of some basic transport problems. To illustrate the efficiency of the approach, a radiative-transfer problem relevant to a non-gray model with scattering that allows complete frequency redistribution is discussed.}, number={6}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE and Wright, SJ}, year={1999}, month={Aug}, pages={685–688} }
 @misc{siewert_1999, title={Some comments concerning the discrete eigenvalue}, volume={131}, number={3}, journal={Nuclear Science and Engineering}, author={Siewert, C. E.}, year={1999}, pages={439} }
 @article{barichello_siewert_1998, title={A computation of the X and Y functions for a non-grey model with complete frequency redistribution}, volume={60}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(98)00004-1}, abstractNote={The FN method is used to compute the classical X and Y functions for use in the solution of a class of non-grey radiative-transfer problems defined for finite layers. The model considered allows for scattering with complete frequency redistribution (completely noncoherent scattering) and continuum absorption. Some test problems based on Doppler and Lorentz profiles of the line-scattering coefficient are discussed, and numerical results (thought to be correct to five significant figures) are given for selected cases.}, number={4}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Siewert, CE}, year={1998}, month={Oct}, pages={649–656} }
 @article{barichello_garcia_siewert_1998, title={A spherical-harmonics solution for radiative-transfer problems with reflecting boundaries and internal sources}, volume={60}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(97)00176-3}, abstractNote={The spherical-harmonics method, including some recent improvements, is used to establish the complete solution for a general problem concerning radiative transfer in a plane-parallel medium. An L-th order Legendre expansion of the phase function is allowed, internal sources and reflecting boundaries are included in the model, and since a non-normally incident beam is impinging on one surface, all components in a Fourier decomposition of the intensity are required in the solution. Numerical results for two test problems are reported.}, number={2}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Garcia, RDM and Siewert, CE}, year={1998}, month={Aug}, pages={247–260} }
 @article{barichello_siewert_1998, title={On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer}, volume={130}, ISSN={["0029-5639"]}, DOI={10.13182/NSE98-A1991}, abstractNote={In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quad- rature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre func- tions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given.}, number={1}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Barichello, LB and Siewert, CE}, year={1998}, month={Sep}, pages={79–84} }
 @article{garcia_siewert_1998, title={The F-N method for multigroup transport theory with upscattering}, volume={130}, ISSN={["0029-5639"]}, DOI={10.13182/NSE98-A2000}, abstractNote={An integral transform technique and the F N method are used to develop solutions to a class of multigroup radiation-transport problems. The multigroup model considered allows an anisotropic scat- tering law and transfer from any group to any group. Computational aspects of the developed solution are discussed, and especially accurate numerical results are reported for two test cases.}, number={2}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Garcia, RDM and Siewert, CE}, year={1998}, month={Oct}, pages={194–212} }
 @article{barichello_siewert_1998, title={The F-N method for spectral-line formation by completely noncoherent scattering}, volume={60}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(97)00171-4}, abstractNote={The FN method is used to develop a solution to a class of nongrey problems in the theory of radiative transfer. The model considered allows for scattering with complete frequency redistribution (completely noncoherent scattering) and continuum absorption. In addition to a general formulation, a specific solution is developed for an inhomogeneous source term (Planck function) that varies linearly with optical depth in a semi-infinite medium. Test problems based on Doppler and Lorentz profiles of the line-scattering coefficient are considered, and numerical results (thought to be correct to five significant figures) are given for the frequency-dependent intensity exiting the medium and for the source function within the medium. For comparison purposes, a previously reported solution that is expressed in terms of Chandrasekhar's H function is evaluated numerically.}, number={2}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Siewert, CE}, year={1998}, month={Aug}, pages={261–276} }
 @article{garcia_siewert_1998, title={The F-N method in atmospheric radiative transfer}, volume={36}, ISSN={["0020-7225"]}, DOI={10.1016/S0020-7225(98)00051-2}, abstractNote={The FN method for solving atmospheric radiative-transfer problems is reviewed. In particular, a new choice of basis functions and collocation points that was found to perform very well for a class of problems characterized by highly anisotropic scattering (a standing challenge to the method) is reported, along with some improved computational techniques.}, number={12-14}, journal={INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE}, author={Garcia, RDM and Siewert, CE}, year={1998}, pages={1623–1649} }
 @article{barichello_garcia_siewert_1997, title={On inverse boundary-condition problems in radiative transfer}, volume={57}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(96)00095-7}, abstractNote={Abstract Some elementary computations are reported to suggest that a certain type of inverse boundary-condition problem in radiative transfer can, in some cases, be solved quite simply.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Barichello, LB and Garcia, RDM and Siewert, CE}, year={1997}, month={Mar}, pages={405–410} }
 @inproceedings{barichello_garcia_siewert_1997, title={Radiative transfer with asymmetric ground reflection}, number={1997}, booktitle={Proceedings of the 2nd Italian-Latinamerican Conference on Applied and Industrial Mathematics - ITLA 97, Roma, 1997}, author={Barichello, L. B. and Garcia, R. D. M. and Siewert, C. E.}, year={1997}, pages={13} }
 @article{siewert_mccormick_1997, title={Some identities for Chandrasekhar polynomials}, volume={57}, ISSN={["0022-4073"]}, DOI={10.1016/S0022-4073(96)00122-7}, abstractNote={Basic techniques of linear algebra are used to derive some identities involving the Chandrasekhar polynomials that play a vital role in the spherical-harmonics (PN) solution to basic radiative-transfer problems.}, number={3}, journal={JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER}, author={Siewert, CE and McCormick, NJ}, year={1997}, month={Mar}, pages={399–404} }