Relevant bibliographies by topics / Numerical Methods for Neutron Transport

Academic literature on the topic 'Numerical Methods for Neutron Transport'

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Published: 14 March 2023

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Journal articles on the topic "Numerical Methods for Neutron Transport"

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Zhao, Zhengang, and Yunying Zheng. "Numerical Approximation for Fractional Neutron Transport Equation." Journal of Mathematics 2021 (March 13, 2021): 1–14. http://dx.doi.org/10.1155/2021/6676640.

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Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.
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Aixiang, Huang, and Ma Yichen. "The application of modern numerical methods to the neutron transport equation." Transport Theory and Statistical Physics 26, no. 1-2 (January 1997): 65–83. http://dx.doi.org/10.1080/00411459708221775.

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Shafii, Mohamad Ali. "Solution methods of neutron transport equation in nuclear reactors." Jurnal ILMU DASAR 14, no. 2 (December 4, 2013): 59. http://dx.doi.org/10.19184/jid.v14i2.320.

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A few numerical methods that usually used to solve neutron transport equation in nuclear reactor are SN dan PN method, Monte Carlo, Collision Probability and Methods of Characteristics . First two methods have been developed using diffusion approach, and last three methods suitable are applicated for transport approximation. Those of three methods have important role in the desain of nuclear reactors. In addition to follow the development of advanced reactor designs, the three methods were chosen because they do not use diffusion approach these are more accurate methods, as well as less need considerable computer memory. Of all the existing methods, the CP method has several advantages among the others. Keywords : Neutron transport, SN, PN, CP, MOC, MC
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Yíldíz, C. "Calculation of the higher order eigenvalues for a homogeneous sphere using the FN method." Kerntechnik 66, no. 1-2 (January 1, 2001): 33–36. http://dx.doi.org/10.1515/kern-2001-0008.

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Abstract The transport of monoenergetic neutrons in spherical geometry with forward scattering and vacuum boundary conditions is considered. The scaled transport equation is solved using the Fn method by considering the pseudo-slab problem. Numerical results for the fundamental and higher order eigenvalues are presented for several significant figures. Some selected results are compared with those obtained using various methods in the literature. Finally, a few remarks about the behavior of the criticality eigenvalue of the neutron transport equation with forward scattering is given.
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Carta, M., S. Dulla, V. Peluso, P. Ravetto, and G. Bianchini. "Calculation of the Effective Delayed Neutron Fraction by Deterministic and Monte Carlo Methods." Science and Technology of Nuclear Installations 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/584256.

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The studies on Accelerator-Driven Systems (ADSs) have renewed the interest in the theoretical and computational evaluation of the main integral parameters characterizing subcritical systems (e.g., reactivity, effective delayed neutron fractionβeff, and mean prompt neutron generation time). In particular, some kinetic parameters, as the effective delayed neutron fraction, are evaluated in Monte Carlo codes by formulations which do not require the calculation of the adjoint flux. This paper is focused on a theoretical and computational analysis about how the differentβeffdefinitions are connected and which are the approximations inherent to the Monte Carlo definition with respect to the standard definition involving weighted integrals. By means of a refined transport computational analysis carried out in a coherent and consistent way, that is, using the same deterministic code and neutron data library for theβeffevaluation in different ways, the theoretical analysis is numerically confirmed. Both theoretical and numerical results confirm the effectiveness of the Monte Carloβeffevaluation, at least in cases where spectral differences between total and prompt fluxes are negligible with respect to the value of the functionals entering the classicalβeffformulation.
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Itoh, Naoki. "Transport Processes in Dense Stellar Plasmas." International Astronomical Union Colloquium 147 (1994): 394–419. http://dx.doi.org/10.1017/s0252921100026464.

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AbstractTransport processes in dense stellar plasmas which are relevant to the interiors of white dwarfs and neutron stars are reviewed. The emphasis is placed on the accuracy of the numerical results. In this review we report on the electrical conductivity and the thermal conductivity of dense matter. The methods of the calculations are different for the liquid metal phase and the crystalline lattice phase. We will broadly review the current status of the calculations of the transport properties of dense matter, and try to give the best instructions available at the present time to the readers.
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Burke, Paul E., Kyle E. Remley, and David P. Griesheimer. "GPU ACCELERATION OF DOPPLER BROADENING FOR NEUTRON TRANSPORT CALCULATIONS1." EPJ Web of Conferences 247 (2021): 04017. http://dx.doi.org/10.1051/epjconf/202124704017.

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In radiation transport calculations, the effects of material temperature on neutron/nucleus interactions must be taken into account through Doppler broadening adjustments to the microscopic cross section data. Historically, Monte Carlo transport simulations have accounted for this temperature dependence by interpolating among precalculated Doppler broadened cross sections at a variety of temperatures. More recently, there has been much interest in on-the-fly Doppler broadening methods, where reference data is broadened on-demand during particle transport to any temperature. Unfortunately, Doppler broadening operations are expensive on traditional central processing unit (CPU) architectures, making on-the-fly Doppler broadening unaffordable without approximations or complex data preprocessing. This work considers the use of graphics processing unit (GPU)s, which excel at parallel data processing, for on-the-fly Doppler broadening in continuous-energy Monte Carlo simulations. Two methods are considered for the broadening operations – a GPU implementation of the standard SIGMA1 algorithm and a novel vectorized algorithm that leverages the convolution properties of the broadening operation in an attempt to expose additional parallelism. Numerical results demonstrate that similar cross section lookup throughput is obtained for on-the-fly broadening on a GPU as cross section lookup throughput with precomputed data on a CPU, implying that offloading Doppler broadening operations to a GPU may enable on-the-fly temperature treatment of cross sections without a noticeable reduction in cross section processing performance in Monte Carlo transport codes.
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Bernal, Álvaro, Rafael Miró, Damián Ginestar, and Gumersindo Verdú. "Resolution of the Generalized Eigenvalue Problem in the Neutron Diffusion Equation Discretized by the Finite Volume Method." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/913043.

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Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.
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Mimoun, Jordan G., Carlos Torres-Verdín, and William E. Preeg. "Quantitative interpretation of pulsed neutron capture logs: Part 1 — Fast numerical simulation." GEOPHYSICS 76, no. 3 (May 2011): E81—E93. http://dx.doi.org/10.1190/1.3569600.

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Pulsed neutron capture (PNC) logs are commonly used for formation evaluation behind casing and to assess time-lapse variations of hydrocarbon pore volume. Because conventional interpretation methods for Σ logs assume homogeneous formations, errors may arise, especially in thinly bedded formations, when appraising petrophysical properties of hydrocarbon-bearing beds. There exist no quantitative interpretation methods to account for shoulder-bed effects on Σ logs acquired in sand-shale laminated reservoirs. Because of diffusion effects between dissimilar beds, Σ logs acquired in such formations do not obey mixing laws between the Σ responses of pure-sand and pure-shale end members of the sedimentary sequence. We have developed a new numerical method to simulate PNC rapidly and accurately logs. The method makes use of late-time, thermal-neutron flux sensitivity functions (FSFs) to describe the contribution of multilayer formations toward the measured capture cross section. It includes a correction procedure based on 1D neutron diffusion theory that adapts the transport-equation-derived, base-case FSF of a homogeneous formation to simulate the response of vertically heterogeneous formations. Benchmarking exercises indicate that our simulation method yields average differences smaller than two capture units within seconds of computer central processing unit time with respect to PNC logs simulated with rigorous Monte Carlo methods for a wide range of geometrical, petrophysical, and fluid properties.
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Varma, Vishnu, Bernhard Müller, and Martin Obergaulinger. "A comparison of 2D Magnetohydrodynamic supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes." Monthly Notices of the Royal Astronomical Society 508, no. 4 (October 19, 2021): 6033–48. http://dx.doi.org/10.1093/mnras/stab2983.

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ABSTRACT Code comparisons are a valuable tool for the verification of supernova simulation codes and the quantification of model uncertainties. Here, we present a first comparison of axisymmetric magnetohydrodynamic (MHD) supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes, which use distinct methods for treating the MHD induction equation and the neutrino transport. We run two sets of simulations of a rapidly rotating 35M⊙ gamma-ray burst progenitor model with different choices for the initial field strength, namely $10^{12}\, \mathrm{G}$ for the maximum poloidal and toroidal field in the strong-field case and $10^{10}\, \mathrm{G}$ in the weak-field case. We also investigate the influence of the Riemann solver and the resolution in CoCoNuT-FMT. The dynamics is qualitatively similar for both codes and robust with respect to these numerical details, with a rapid magnetorotational explosion in the strong-field case and a delayed neutrino-driven explosion in the weak-field case. Despite relatively similar shock trajectories, we find sizeable differences in many other global metrics of the dynamics, like the explosion energy and the magnetic energy of the proto-neutron star. Further differences emerge upon closer inspection, for example, the disc-like surface structure of the proto-neutron star proves high sensitivity to numerical details. The electron fraction distribution in the ejecta as a crucial determinant for the nucleosynthesis is qualitatively robust, but the extent of neutron- or proton-rich tails is sensitive to numerical details. Due to the complexity of the dynamics, the ultimate cause of model differences can rarely be uniquely identified, but our comparison helps gauge uncertainties inherent in current MHD supernova simulations.
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Dissertations / Theses on the topic "Numerical Methods for Neutron Transport"

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ALCARO, FABIO. "Quasi-static Methods in Neutron Transport." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2501653.

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The present work represents a little but valuable contribution to the advancement of the research in the field of the neutron kinetics of innovative nuclear reactors. As modern computer frames are becoming more and more performing and because the treatment of innovative nuclear reactor systems requires high accuracy results, the neutron transport theory is currently being adopted for full-core calculations. Embracing such tendency, in the present work the quasi-static approach has been adopted and implemented for the design of computational codes capable of performing reliable transient calculations. The underlying idea has been the development of the kinetic module on top of the transport solver, in such a way that the former can be flexibly plugged into the codes ystem, independently from the transport solver itself. In particular, two computer codes have been developed: the first has been designed coupling the stand-alone DRAGON transport solver to an "ad hoc" reactor kinetic module; the second code has been developed within the ERANOS code system. A Java object-oriented platform developed by CEA-Cadarache constitutes the framework where a kinetic package has been designed, adopting the code's API (Application Programming Interface) for the full integration in the code system. The well known Improved Quasi-static Method (IQM) and the innovative Predictor-Corrector Quasi-static Method (PCQM) have been implemented in both computer codes. In the present work a deep analysis of the two types of quasi-static schemes has been carried out as well as the description and validation of the aforementioned computer codes.
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BARBARINO, ANDREA. "Numerical Methods for Neutron Transport Calculations of Nuclear Reactors." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2561774.

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The objective of this thesis, which in clearly inspired by an industrial framework, is to try and narrow the gap between theoretical neutron modelling and application in the context of nuclear reactor design. This thesis is divided into three main chapters, preceded by a general overview. This structure reflects the three main topics which were chosen for this research project. The first topic develops the Spectral Element Method (SEM) approach and its use in conjunction with transport approximations. As it is documented in the specialized numerical analysis handbooks and in previous works by the author, the method has an excellent convergence rate which outperforms most classical schemes, but it has also some important drawbacks which sometimes seem to discourage its use for linear transport problems applied to nontrivial benchmarks. In order to elaborate the methodology of the specific problems encountered in reactor physics, three aspects are addressed looking for improvements. The first topic analyzed is related to the convergence order, whose value is less straightforward to define a priori by means of functional analysis than other numerical schemes. The adjective “spectral” refers in fact to the maximum order claimed, exponential with respect to the average size of the mesh. A comprehensive set of convergence tests is carried out applying SEM to a few transport models and with the aid of manufactured solutions, thus isolating the numerical effects from the deviations which are due only to modelling approximations. The hypothesis of grid conformity is also relaxed, replacing the classical Galerkin variational formulation with the Discontinuous Galerkin theory, characterized by a more flexible treatment of the mesh interfaces; this scheme allows local grid refinement and opens the way, in perspective, to mesh adaption. Finally, a simple and sufficiently flexible technique to deform the boundaries of each mesh is introduced and applied, in order to adapt the grid to curved geometries. In this way, the advantages of SEM can be applied to a vast class of common problems like lattice calculations. Moreover, thanks to a change of the basis functions used in SEM, it is possible to obtain elements with three sides (straight or deformed), that are a typical war horse of the Finite Element approach. The second topic is essentially devoted to the most “industrial” part of the thesis, developed entirely during the stay of the author in the AREVA NP headquarters in Paris. In AREVA, and in all other nuclear engineering enterprises, neutron diffusion is still the preferred neutronic model for full-core studies. Better approximations are reserved for library preparation, fuel studies and code validation, none of these being typically too much time or budget-constrained. Today needs start to require a certain level of improvement also in full-core analyses, trying to fitly model localized dis-homogeneities and reduce the penalizing engineering margins which are taken as provisions. On the other hand, a change in the model does not mean only an effort to write a new code, but has huge follow-ups due to the validation processes required by the authorities. Second-order transport may support the foreseen methodology update because it can be implemented re-using diffusion routines as the computational engine. The AN method, a second-order approximation of the transport equation, has been introduced in some studies, and its effect is discussed. Moreover, some effort has been reserved to the introduction of linear anisotropy in the model. The last topic deals with ray effects; they are a known issue of the discrete ordinate approach (SN methods) which is responsible for a reduction in the accuracy of the solution, especially in penetration problems with low scattering, like several shielding calculations performed for operator safety concerns. Ray effects are here characterized from a formal point of view in both static and time dependent situations. Then, quantitative indicators are defined to help with the interpretation of the SN results. Based on these studies, some mitigation measures are proposed and their efficacy is discussed.
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Marquez, Damian Jose Ignacio. "Multilevel acceleration of neutron transport calculations." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19731.

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Thesis (M.S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Stacey, Weston M.; Committee Co-Chair: de Oliveira, Cassiano R.E.; Committee Member: Hertel, Nolan; Committee Member: van Rooijen, Wilfred F.G.
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Blackburn, Megan Satterfield. "Numerical benchmarking of a coarse-mesh transport (COMET) method for medical physics applications." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29763.

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Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Farzad Rahnema; Committee Co-Chair: Eric Elder; Committee Member: C.-K. Chris Wang; Committee Member: Rebecca Howell; Committee Member: Sang Cho. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Byambaakhuu, Tseelmaa. "Development of Advanced Numerical Methods for Solving Neutron Transport Problems: DG-DSA and the Shishkin Mesh for Problems with Sharp Layers." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618855174338701.

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Blake, Jack. "Domain decomposition methods for nuclear reactor modelling with diffusion acceleration." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.698988.

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In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a nuclear fission reaction. Applications of this equation include modelling behaviour within nuclear reactors and the design of shielding around x-ray facilities in hospitals. Improvements in existing modelling techniques are an important way to address environmental and safety concerns of nuclear reactors, and also the safety of people working with or near radiation. The neutron transport equation typically has seven independent variables, however to facilitate rigorous mathematical analysis we consider the monoenergetic, steady-state equation without fission, and with isotropic interactions and isotropic source. Due to its high dimension, the equation is usually solved iteratively and we begin by considering a fundamental iterative method known as source iteration. We prove that the method converges assuming piecewise smooth material data, a result that is not present in the literature. We also improve upon known bounds on the rate of convergence assuming constant material data. We conclude by numerically verifying this new theory. We move on to consider the use of a specific, well-known diffusion equation to approximate the solution to the neutron transport equation. We provide a thorough presentation of its derivation (along with suitable boundary conditions) using an asymptotic expansion and matching procedure, a method originally presented by Habetler and Matkowsky in 1975. Next we state the method of diffusion synthetic acceleration (DSA) for which the diffusion approximation is instrumental. From there we move on to explore a new method of seeing the link between the diffusion and transport equations through the use of a block operator argument. Finally we consider domain decomposition algorithms for solving the neutron transport equation. Such methods have great potential for parallelisation and for the local application of different solution methods. A motivation for this work was to build an algorithm applying DSA only to regions of the domain where it is required. We give two very different domain decomposed source iteration algorithms, and we prove the convergence of both of these algorithms. This work provides a rigorous mathematical foundation for further development and exploration in this area. We conclude with numerical results to illustrate the new convergence theory, but also solve a physically-motivated problem using hybrid source iteration/ DSA algorithms and see significant reductions in the required computation time.
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ABRATE, NICOLO'. "Methods for safety and stability analysis of nuclear systems." Doctoral thesis, Politecnico di Torino, 2022. http://hdl.handle.net/11583/2971611.

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Di, Chicco Augusto. "Optimization of a calculation scheme through the parametric study of effective nuclear cross sections and application to the estimate of neutronic parameters of the ASTRID fast nuclear reactor." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.

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This thesis presents the project for the optimization of the APOLLO3® neutronic calculation scheme applied to the 4th generation fast neutron reactor ASTRID. APOLLO3® is the new multipurpose neutronic platform developed by the CEA. It incorporates many of the previous generation codes used in the French reactor core design supply chain. Like all deterministic codes, APOLLO3® solves the neutron transport equation with a discretization of the variables of interest: multi-group method for the energy, discrete ordinates and spherical harmonics for the angular variable, collision probabilities and characteristics methods for the spatial variable. The resolution of the transport equation handles useful quantities such as the neutron flux and multiplication factor, fission rates and cross sections to understand the physical behaviour of the reactor core. Currently it is not possible to use deterministic codes to simulate an entire reactor with a heterogeneous 3D geometry and a fine energy description, so to simplify the study of complete neutron field at core level, the calculation scheme is divided into two phases: lattice and core calculation. The main purpose of this work is to find an optimal degree of approximations of the calculation scheme for the evaluation of a desired physical effect and of the user constraints. In order to reach this optimum, several studies have been carried out with different levels of approximations. The results have been benchmarked with the ones obtained using the stochastic code TRIPOLI4®, used as a reference and to ensure a good accuracy. Furthermore, several sensitivity studies have been carried out to understand how the different approximations affect the macroscopic cross sections evaluation, because these dependences are not yet fully understood.
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Sheehan, B. P. "Multigrid methods for isotropic neutron transport." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256437.

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Muddle, John Christopher. "Advanced numerical methods for neutron star interfaces." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/375551/.

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Books on the topic "Numerical Methods for Neutron Transport"

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Lewis, E. E. Computational methods of neutron transport. La Grange Park, Ill., USA: American Nuclear Society, 1993.

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Ivanovich, Lebedev Vi͡a︡cheslav, ed. Numerical methods in the theory of neutron transport. 2nd ed. Chur, Switzerland: Harwood, 1986.

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Computational methods for two-phase flow and particle transport. Singapore: World Scientific Publishing Co., 2013.

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László, Koblinger, ed. Monte Carlo particle transport methods: Neutron and photon calculations. Boca Raton: CRC Press, 1991.

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1941-, Greenberg W., and Polewczak J. 1952-, eds. Modern mathematical methods in transport theory. Basel: Birkhäuser Verlag, 1991.

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A, Silebi C., ed. Computational transport phenomena: Numerical methods for the solution of transport problems. Cambridge, U.K: Cambridge University Press, 1997.

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Gupta, Anurag. Krylov sub-space methods for K-eigenvalue problem in 3-D multigroup neutron transport. Mumbai: Bhabha Atomic Research Centre, 2004.

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Frank, Graziani, ed. Computational methods in transport: Verification and validation. Berlin: Springer, 2008.

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Center, Langley Research, ed. Development of deterministic transport methods for low energy neutrons for shielding in space. Tucson, Ariz: Engineering Experiment Station, College of Engineering and Mines, University of Arizona, 1993.

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Ackroyd, Ron T. Finite element methods for particle transport: Applications to reactor and radiation physics. Taunton, Somerset, England: Research Studies Press, 1997.

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Book chapters on the topic "Numerical Methods for Neutron Transport"

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Marguet, Serge. "Computational Neutron Transport Methods." In The Physics of Nuclear Reactors, 593–727. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59560-3_9.

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Lewis, E. E. "Second-Order Neutron Transport Methods." In Nuclear Computational Science, 85–115. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3411-3_2.

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Poirier, D. R., and G. H. Geiger. "Numerical Methods and Models." In Transport Phenomena in Materials Processing, 571–610. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48090-9_16.

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Zohuri, Bahman. "Numerical Methods in Modeling Neutron Diffusion." In Neutronic Analysis For Nuclear Reactor Systems, 255–88. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42964-9_5.

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Zohuri, Bahman. "Numerical Methods in Modeling Neutron Diffusion." In Neutronic Analysis For Nuclear Reactor Systems, 253–83. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04906-5_5.

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Durran, Dale R. "Beyond One-Dimensional Transport." In Numerical Methods for Fluid Dynamics, 147–201. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6412-0_4.

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Kersch, Alfred, and William J. Morokoff. "Numerical Methods for Rarefied Gas Dynamics." In Transport Simulation in Microelectronics, 77–99. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9080-9_3.

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Dautray, Robert, and Jacques-Louis Lions. "Transport." In Mathematical Analysis and Numerical Methods for Science and Technology, 209–416. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-58004-8_3.

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Poirier, E. J., and D. R. Poirier. "Numerical Methods and Models." In Solutions Manual To accompany Transport Phenomena in Materials Processing, 305–13. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-65130-9_16.

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Yeh, Gourt-Tsyh. "Numerical Methods for Advection-Dominant Transport." In Computational Subsurface Hydrology, 93–198. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4371-8_3.

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Conference papers on the topic "Numerical Methods for Neutron Transport"

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Wu, Hongchun, Guoming Liu, Liangzhi Cao, and Qichang Chen. "Determinant Methods for Solving Neutron Transport Equation in Unstructured Geometry." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29442.

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The spherical harmonics (Pn) finite element method, the Sn finite element method, the triangle transmission probability method and the discrete triangle nodal method were all introduced to solve the neutron transport equation for unstructured fuel assembly respectively. The computing codes of each method were encoded and numerical results were discussed and compared. It was demonstrated that these four methods can solve neutron transport equations with unstructured-meshes very effectively and correctly, they can be used to solve unstructured fuel assembly problem.
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Zhang, J. "A coupled thermo-mechanical and neutron diffusion numerical model for irradiated concrete." In AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-4.

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Abstract: Neutron irradiation plays an important role in nuclear-induced degradation for concrete shielding materials, specifically in determining the radiation induced volume expansion (RIVE) phenomenon driving its failure. When analyzing at the structural level the effects of nuclear radiation on concrete, a non-uniformed distribution of neutron radiation must be considered. This can be done via particle transport calculations preventive to the thermo-mechanic study, or by solving numerically the coupled set of governing equations of the problem. In this work the second approach is pursued in the theoretical framework of the Finite Element Method (FEM). The proposed formulation not only considers an accurate neutron transport model based on the two-group theory, but also it includes the effects induced by thermal neutrons to the temperature field. The formulation lends itself to include RIVE and the other relevant radiation induced effects on the mechanical field. The governing equations are presented and discussed, and some results obtained by using the general 3D numerical formulation proposed herein are compared to results from literature obtained via analytical methods addressing simplified 1D problems.
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Panta Pazos, Rube´n, and Marco Tu´llio de Vilhena. "Variational Approach in Transport Theory." In 12th International Conference on Nuclear Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/icone12-49233.

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In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method.
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Ganapol, Barry D. "A 1D Monoenergetic Neutron Transport Benchmark in an Infinite Medium." In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30156.

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Analytical or semi-analytical benchmarks for the neutron transport equation are relatively infrequent. Some may argue they are no longer necessary because of the enormous computing power and computational technology that is now available. While to some extent true, they can still provide valuable code verification and also serve to teach theoretical and numerical transport methods not taught by executing MATLAB, MAPLE or MATHEMATICA programs or Monte Carlo simulations. The focus of this presentation is on a new analytical solution technique for the solution of the 1D, monoenergetic Green’s function for neutron transport. In this formulation, we consider the analytical solution to a three–term recurrence for flux moments resulting in a semi–analytical benchmark. We then apply the benchmark to assess the accuracy of the PN approximation leading to a rather unexpected result.
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Koreshi, Zafar Ullah, and Sadaf Siddiq. "Monte Carlo Simulation Compared With Classic Deterministic Solutions for Neutron Transport and Diffusion." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29971.

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The Monte Carlo (MC) simulation method, known to handle complex problems which may be formidable for deterministic methods, will always require validation with classic problems that have evolved historically from deterministic methods [1–5] based on Chandrasekhar’s method in radiative transfer, Fourier transforms, Green’s functions, Weiner-Hopf method etc which are restricted to simple geometries, such as infinite or semiinfinite media, and simple scattering laws too for practical application. This work compares deterministic results with MC simulation results for neutron flux in a slab. We consider mono-energetic transport problem in an infinite medium and in a 1-D finite slab with isotropic scattering. The transport theory solutions used in infinite geometry are the Green’s function solution and the spherical harmonics (P1, P3) solutions, while for the 1-D finite slab, we refer to a transport benchmark for which an exact solution is available. For diffusion theory, we consider the Green’s function infinite geometry solution, and the exact and eigen-function numerical solution for finite geometry (1-D slab). The objective of this work is to illustrate the results from all the methods considered especially near the source and boundaries, and as a function of the scattering probability. The results are plotted for six elements that include a strong absorber, such as gadolinium, and a strong “scaterrer” such as aluminium. The present work is didactic and focuses on problems which are simple enough, yet important, to illustrate the conceptual difference and computational complexity of the deterministic and stochastic approaches.
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Sun, Qizheng, Tengfei Zhang, Xiaojing Liu, Xiang Chai, and Jinbiao Xiong. "A Discrete-Ordinates Variational Nodal Method for Solving Multi-Dimensional Neutron Transport Equation With Unstructured Mesh." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-91525.

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Abstract The variational nodal method (VNM) is an advanced nodal method in the field of reactor physics. The VNM solves neutron transport equations directly without transverse leakage interpolations used in other nodal methods. Moreover, the VNM can tackle arbitrary expansion orders. Given its benefits, VNM performs well in a variety of applications. However, with the advancement of nuclear science and technology, the ability to handle complex unstructured problems becomes indispensable. In order to increase the geometric compatibility of the VNM, an unstructured-mesh variational nodal method (VNM) for solving multi-dimensional neutron transport equations is presented in this paper. The neutron transport equation is transformed into a variational formulation, in which an even-parity Lagrange multipliers enforce neutron conservation in each node, to obtain the weak-form solution. The entire problem domain is spatially meshed into several unstructured nodes. And the neutron flux, source, and current are spatially approximated by a set of complete orthogonal polynomials. The conception of the unique node is adopted to reduce the memory and improve efficiency. Orthogonal polynomials are established in a standard node for spatial discretization, and each unstructured node is related to the standard node by the coordinate mapping matrix, respectively. The discrete-ordinates (SN) method is employed to deal with angle variables so that the original equation is decoupled into several equations with different discretization directions. Then, the variational formulation is completely discretized, and the response equations are derived. Finally, different types of benchmarks are employed to validate and evaluate the proposed method. Numerical results demonstrate that unstructured-mesh VNM exhibits significant geometric compatibility and comparable accuracy.
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Jevremovic, Tatjana, Mathieu Hursin, Nader Satvat, John Hopkins, Shanjie Xiao, and Godfree Gert. "Performance, Accuracy and Efficiency Evaluation of a Three-Dimensional Whole-Core Neutron Transport Code AGENT." In 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/icone14-89561.

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The AGENT (Arbitrary GEometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) the theory of R-functions used to generate real three-dimensional whole-cores of square, hexagonal or triangular cross sections, (2) the planar method of characteristics used to solve isotropic neutron transport in non-homogenized 2D) reactor slices, and (3) the one-dimensional diffusion theory used to couple the planar and axial neutron tracks through the transverse leakage and angular mesh-wise flux values. The R-function-geometrical module allows a sequential building of the layers of geometry and automatic submeshing based on the network of domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through a set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: Coarse Mesh Rebalancing (CMR) and Coarse Mesh Finite Difference (CMFD). The stand-alone originally developed graphical user interface of the AGENT code design environment allows the user to view and verify input data by displaying the geometry and material distribution. The user can also view the output data such as three-dimensional maps of the energy-dependent mesh-wise scalar flux, reaction rate and power peaking factor. The AGENT code is in a process of an extensive and rigorous testing for various reactor types through the evaluation of its performance (ability to model any reactor geometry type), accuracy (in comparison with Monte Carlo results and other deterministic solutions or experimental data) and efficiency (computational speed that is directly determined by the mathematical and numerical solution to the iterative approach of the flux convergence). This paper outlines main aspects of the theories unified into the AGENT code formalism and demonstrates the code performance, accuracy and efficiency using few representative examples. The AGENT code is a main part of the so called virtual reactor system developed for numerical simulations of research reactors. Few illustrative examples of the web interface are briefly outlined.
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Panta Pazos, Ruben, Marco Tullio de Vilhena, and Eliete Biasotto Hauser. "Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22611.

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In the last decade Vilhena and coworkers10 reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional SN equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTSN method9, which consists in the application of the Laplace transform to the set of nodal SN equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of SN up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal SN equations for N up to 16 and we begin the convergence of the SN nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation6.
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Liu, Guoming, and Hongchun Wu. "Transmission Probability Method Based on Triangular-Z Mesh for Solving Neutron Transport Equation in Three-Dimensional Geometry." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48607.

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This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The neutron source within the mesh is assumed to be spatially uniform and isotropic. On the mesh surface, the constant and the simplified P1 approximation are invoked for the anisotropic angular neutron flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry. The numerical results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (PN) method.
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Liang, Liang, Hongchun Wu, Liangzhi Cao, and Youqi Zheng. "Development of a Two-Dimensional Modularity Characteristics Code for Neutron Transport Calculation." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-15725.

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The method of characteristics (MOC) has been widely used in lattice code for its high precision and easy complement. However, the long characteristics method needs large quantity of PC memory when dealing with large scale problems. The modularity MOC method could significantly reduce the PC memory when calculating the problem which contains lots of repeatedly geometries, like the fuel assembly in the reactor. In this method, only typical geometric cells are selected to trace the rays, and then the geometry information of these cells is stored. So, the modularity MOC method is feasible to perform well in the calculation with large scale. When tracing the rays, the technique of mesh ray generating and the corresponding azimuthal quadrature set are both applied. The techniques make sure that each ray has the reflected ray in the boundary so it is convenient to describe the boundary condition. The optimal polar angle and the Guass quadrature set are selected as the polar quadrature set. Furthermore, the coarse mesh finite difference (CMFD) is employed to accelerate the calculation. A pin cell is chosen as the coarse mesh. The CMFD solution provides the MOC with much faster converged fission and scattering source distributions. The LOTUS code is developed and the numerical results show that the code is precise for engineering application and the CMFD acceleration is effective.
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Reports on the topic "Numerical Methods for Neutron Transport"

1

Brown, P. N. Novel Parallel Numerical Methods for Radiation& Neutron Transport. Office of Scientific and Technical Information (OSTI), March 2001. http://dx.doi.org/10.2172/15005562.

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Nicholas Tsoulfanidis and Elmer Lewis. Neutron Transport Methods for Accelerator-Driven Systems. Office of Scientific and Technical Information (OSTI), February 2005. http://dx.doi.org/10.2172/836901.

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Cai, Wei. Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada572398.

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Cai, Wei. Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems. Fort Belvoir, VA: Defense Technical Information Center, October 2014. http://dx.doi.org/10.21236/ada617374.

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Taylor, G., C. Dong, and S. Sun. NUMERICAL MODELING OF CONTAMINANT TRANSPORT IN FRACTURED POROUS MEDIA USING MIXED FINITE ELEMENT AND FINITE VOLUME METHODS. Office of Scientific and Technical Information (OSTI), March 2010. http://dx.doi.org/10.2172/974328.

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Chang, B. Analytical Tests for Ray Effect Errors in Discrete Ordinate Methods for Solving the Neutron Transport Equation. Office of Scientific and Technical Information (OSTI), March 2004. http://dx.doi.org/10.2172/15014046.

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Wharry, Janelle, and Won Sik Yang. Steady-State Thermal-Hydraulic Analysis and Bowing Reactivity Evaluation Methods Based on Neutron and Gamma Transport Calculations. Office of Scientific and Technical Information (OSTI), December 2018. http://dx.doi.org/10.2172/1493700.

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Wang, Dean, Thomas Downar, Yunlin Xu, Yulong Xing, and Emily Shemon. Development of a Novel Accelerator for Neutron Transport Solution Using the Galerkin Spectral Element Methods (Final Report). Office of Scientific and Technical Information (OSTI), April 2019. http://dx.doi.org/10.2172/1511575.

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9

Gill, Daniel Fury. Behavior of the Diamond Difference and Low-Order Nodal Numerical Transport Methods in the Thick Diffusion Limit for Slab Geometry. Office of Scientific and Technical Information (OSTI), May 2007. http://dx.doi.org/10.2172/903208.

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10

Sagar, B., and A. Runchal. PORFLO-3: A mathematical model for fluid flow, heat, and mass transport in variably saturated geologic media; Theory and numerical methods, Version 1.0. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/137710.

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