Academic literature on the topic 'Neutron transport problem'
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Journal articles on the topic "Neutron transport problem"
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Jarmouni-Idrissi, K., and L. Thevenot. "HOMOGENIZATION OF A NONLINEAR NEUTRON TRANSPORT PROBLEM." Transport Theory and Statistical Physics 31, no. 2 (May 21, 2002): 93–123. http://dx.doi.org/10.1081/tt-120003969.
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Vosoughi, Naser, Akbar Salehi, Majid Shahriari, and Enzo Tonti. "Direct discrete method and its application to neutron transport problems." Nuclear Technology and Radiation Protection 18, no. 2 (2003): 12–23. http://dx.doi.org/10.2298/ntrp0302012v.
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The objective of this paper is to introduce a new direct method for neutronic calculations. This method, called direct discrete method, is simpler than the application of the neutron transport equation and more compatible with the physical meanings of the problem. The method, based on the physics of the problem, initially runs through meshing of the desired geometry. Next, the balance equation for each mesh interval is written. Considering the connection between the mesh intervals, the final discrete equation series are directly obtained without the need to pass through the set up of the neutron transport differential equation first. In this paper, one and multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without the associated clad and the coolant regions each with two different external boundary conditions. The validity of the results from this new method is tested against the results obtained by the MCNP-4B and the ANISN codes.
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TÜRECİ, R. Gökhan. "Machine Learning Applications to the One-speed Neutron Transport Problems." Cumhuriyet Science Journal 43, no. 4 (December 27, 2022): 726–38. http://dx.doi.org/10.17776/csj.1163514.
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Machine learning is a branch of artificial intelligence and computer science. The purpose of machine learning is to predict new data by using the existing data. In this study, two different machine learning methods which are Polynomial Regression (PR) and Artificial Neural Network (ANN) are applied to the neutron transport problems which are albedo problem, the Milne problem, and the criticality problem. ANN applications contain two different activation functions, Leaky Relu and Elu. The training data set is calculated by using the HN method. PR and ANN results are compared with the literature data. The study is only based on the existing data; therefore, the study could be thought only data mining on the one-speed neutron transport problems for isotropic scattering.
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Tsyfra, Ivan, and Tomasz Czyżycki. "Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/724238.
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We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.
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Sengupta, A. "Full range solution of half space neutron transport problem." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 46, no. 1 (January 1995): 40–60. http://dx.doi.org/10.1007/bf00952255.
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Kadem, Abdelouahab. "Analytical solutions for the neutron transport using the spectral methods." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–11. http://dx.doi.org/10.1155/ijmms/2006/16214.
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We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.
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Bourhrara, Lahbib, and Richard Sanchez. "Existence Result for the Kinetic Neutron Transport Problem in the Presence of Delayed Neutrons." Transport Theory and Statistical Physics 35, no. 3-4 (August 2006): 137–56. http://dx.doi.org/10.1080/00411450600901748.
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Ozturk, Hakan. "The influence of linear anisotropic scattering of one-speed neutrons on the critical size of a slab with reflective boundary conditions." Nuclear Technology and Radiation Protection 32, no. 3 (2017): 236–41. http://dx.doi.org/10.2298/ntrp1703236o.
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The criticality problem for one-speed neutrons in a slab is investigated using Chebyshev polynomials of first kind in the series expansion of the neutron angular flux in stationary neutron transport equation. The medium is assumed to let the neutrons to scatter anisotropically and to be surrounded by a reflector. The critical thicknesses for the neutrons in a uniform finite slab are computed for selected values of the reflection coefficient and the anisotropy parameter and they are given in the tables. The numerical results obtained from the present method are in good accordance with the results already existed in literature.
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Mancusi, Davide, and Andrea Zoia. "TOWARDS ZERO-VARIANCE SCHEMES FOR KINETIC MONTE-CARLO SIMULATIONS." EPJ Web of Conferences 247 (2021): 04010. http://dx.doi.org/10.1051/epjconf/202124704010.
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The solution of the time-dependent transport problem for neutrons and precursors in a nuclear reactor is hard to treat in a naive Monte-Carlo framework because of the largely different time scales associated to the prompt-fission chains and to the decay of precursors. The increasing computer power and the development of variance-reduction techniques specific for reactor kinetics have recently unlocked the possibility to calculate reference solutions to the time-dependent transport problem. However, the application of time-dependent Monte Carlo to large systems (i.e., a full reactor core) is still stifled by the enormous computational requirements. In this paper, we formulate the construction of an optimal Monte-Carlo strategy (in the sense that it results in a zero-variance estimator) for a specific observable in time-dependent transport, in analogy with the existing schemes for stationary problems. As far as we are aware, zero-variance Monte-Carlo schemes for neutron-precursor kinetics have never been proposed before. We verify our construction with numerical calculations for a benchmark transport problem.
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Chen, Gen-Shun, and Anthony W. Leung. "Positive Solutions for Reactor Multigroup Neutron Transport Systems: Criticality Problem." SIAM Journal on Applied Mathematics 49, no. 3 (June 1989): 871–87. http://dx.doi.org/10.1137/0149051.
Full textDissertations / Theses on the topic "Neutron transport problem"
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Scipolo, Vittorio. "Scattered neutron tomography based on a neutron transport problem." Texas A&M University, 2004. http://hdl.handle.net/1969.1/2791.
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Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions. Classical tomography fails to reconstruct the optical properties of thick scattering objects because it does not adequately account for the scattering component of the neutron beam intensity exiting the sample.
We proposed a new method of computed tomography which employs an inverse problem analysis of both the transmitted and scattered images generated from a beam passing through an optically thick object.
This inverse problem makes use of a computationally efficient, two-dimensional forward problem based on neutron transport theory that effectively calculates the detector readings around the edges of an object. The forward problem solution uses a Step-Characteristic (SC) code with known uncollided source per cell, zero boundary flux condition and Sn discretization for the angular dependence. The calculation of the uncollided sources is performed by using an accurate discretization scheme given properties and position of the incoming beam and beam collimator. The detector predictions are obtained considering both the collided and uncollided components of the incoming radiation.
The inverse problem is referred as an optimization problem. The function to be minimized, called an objective function, is calculated as the normalized-squared error between predicted and measured data. The predicted data are calculated by assuming a uniform distribution for the optical properties of the object. The objective function depends directly on the optical properties of the object; therefore, by minimizing it, the correct property distribution can be found. The minimization of this multidimensional function is performed with the Polack Ribiere conjugate-gradient technique that makes use of the gradient of the function with respect to the cross sections of the internal cells of the domain.
The forward and inverse models have been successfully tested against numerical results obtained with MCNP (Monte Carlo Neutral Particles) showing excellent agreements.
The reconstructions of several objects were successful. In the case of a single intrusion, TNTs (Tomography Neutron Transport using Scattering) was always able to detect the intrusion. In the case of the double body object, TNTs was able to reconstruct partially the optical distribution. The most important defect, in terms of gradient, was correctly located and reconstructed. Difficulties were discovered in the location and reconstruction of the second defect.
Nevertheless, the results are exceptional considering they were obtained by lightening the object from only one side. The use of multiple beams around the object will significantly improve the capability of TNTs since it increases the number of constraints for the minimization problem.
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Scheben, Fynn. "Iterative methods for criticality computations in neutron transport theory." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.
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This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem contains valuable information about the status of the fission chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations. Because of the practical importance, efficient numerical methods to solve the criticality problem are needed, and these are the focus of this thesis. In the theory we consider the time-independent neutron transport equation in the monoenergetic homogeneous case with isotropic scattering and vacuum boundary conditions. This is an unsymmetric integro-differential equation in 5 independent variables, modelling transport, scattering, and fission, where the dependent variable is the neutron angular flux. We show that, before discretisation, the nonsymmetric eigenproblem for the angular flux is equivalent to a related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator(in space only). Furthermore, we prove the existence of a simple smallest positive real eigenvalue with a corresponding eigenfunction that is strictly positive in the interior of the reactor. We discuss approaches to discretise the problem and present discretisations that preserve the underlying symmetry in the finite dimensional form. The thesis then describes methods for computing the criticality in nuclear reactors, i.e. the smallest positive real eigenvalue, which are applicable for quite general geometries and physics. In engineering practice the criticality problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inneriterations. This leads to inexact iterative methods for criticality computations, for which there appears to be no rigorous convergence theory. The fact that, under appropriate assumptions, the integro-differential eigenvalue problem possesses an underlying symmetry (in a space of reduced dimension) allows us to perform a systematic convergence analysis for inexact inverse iteration and related methods. In particular, this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. The theory is illustrated with numerical examples on several test problems of physical relevance, using GMRES as the inner solver. We also illustrate the use of Monte Carlo methods for the solution of neutron transport source problems as well as for the criticality problem. Links between the steps in the Monte Carlo process and the underlying mathematics are emphasised and numerical examples are given. Finally, we introduce an iterative scheme (the so-called “method of perturbation”) that is based on computing the difference between the solution of the problem of interest and the known solution of a base problem. This situation is very common in the design stages for nuclear reactors when different materials are tested, or the material properties change due to the burn-up of fissile material. We explore the relation ofthe method of perturbation to some variants of inverse iteration, which allows us to give convergence results for the method of perturbation. The theory shows that the method is guaranteed to converge if the perturbations are not too large and the inner problems are solved with sufficiently small tolerances. This helps to explain the divergence of the method of perturbation in some situations which we give numerical examples of. We also identify situations, and present examples, in which the method of perturbation achieves the same convergence rate as standard shifted inverse iteration. Throughout the thesis further numerical results are provided to support the theory.
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Carreño, Sánchez Amanda María. "Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation." Doctoral thesis, Universitat Politècnica de València, 2020. http://hdl.handle.net/10251/144771.
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[ES] Uno de los objetivos más importantes en el análisis de la seguridad en el campo de la ingeniería nuclear es el cálculo, rápido y preciso, de la evolución de la potencia dentro del núcleo del reactor. La distribución de los neutrones se puede describir a través de la ecuación de transporte de Boltzmann. La solución de esta ecuación no puede obtenerse de manera sencilla para reactores realistas, y es por ello que se tienen que considerar aproximaciones numéricas.
En primer lugar, esta tesis se centra en obtener la solución para varios problemas estáticos asociados con la ecuación de difusión neutrónica: los modos lambda, los modos gamma y los modos alpha. Para la discretización espacial se ha utilizado un método de elementos finitos de alto orden. Diversas características de cada problema espectral se analizan y se comparan en diferentes reactores.
Después, se investigan varios métodos de cálculo para problemas de autovalores y estrategias para calcular los problemas algebraicos obtenidos a partir de la discretización espacial. La mayoría de los trabajos destinados a la resolución de la ecuación de difusión neutrónica están diseñados para la aproximación de dos grupos de energía, sin considerar dispersión de neutrones del grupo térmico al grupo rápido. La principal ventaja de la metodología que se propone es que no depende de la geometría del reactor, del tipo de problema de autovalores ni del número de grupos de energía del problema.
Tras esto, se obtiene la solución de las ecuaciones estacionarias de armónicos esféricos. La implementación de estas ecuaciones tiene dos principales diferencias respecto a la ecuación de difusión neutrónica. Primero, la discretización espacial se realiza a nivel de pin. Por tanto, se estudian diferentes tipos de mallas. Segundo, el número de grupos de energía es, generalmente, mayor que dos. De este modo, se desarrollan estrategias a bloques para optimizar el cálculo de los problemas algebraicos asociados.
Finalmente, se implementa un método modal actualizado para integrar la ecuación de difusión neutrónica dependiente del tiempo. Se presentan y comparan los métodos modales basados en desarrollos en función de los diferentes modos espaciales para varios tipos de transitorios. Además, también se desarrolla un control de paso de tiempo adaptativo, que evita la actualización de los modos de una manera fija y adapta el paso de tiempo en función de varias estimaciones del error.[CAT] Un dels objectius més importants per a l'anàlisi de la seguretat en el camp de l'enginyeria nuclear és el càlcul, ràpid i precís, de l'evolució de la potència dins del nucli d'un reactor. La distribució dels neutrons pot modelar-se mitjançant l'equació del transport de Boltzmann. La solució d'aquesta equació per a un reactor realístic no pot obtenir's de manera senzilla. És per això que han de considerar-se aproximacions numèriques. En primer lloc, la tesi se centra en l'obtenció de la solució per a diversos problemes estàtics associats amb l'equació de difusió neutrònica: els modes lambda, els modes gamma i els modes alpha. Per a la discretització espacial s'ha utilitzat un mètode d'elements finits d'alt ordre. Algunes de les característiques dels problemes espectrals s'analitzaran i es compararan per a diferents reactors. Tanmateix, diversos solucionadors de problemes d'autovalors i estratègies es desenvolupen per a calcular els problemes obtinguts de la discretització espacial. La majoria dels treballs per a resoldre l'equació de difusió neutrònica estan dissenyats per a l'aproximació de dos grups d'energia i sense considerar dispersió de neutrons del grup tèrmic al grup ràpid. El principal avantatge de la metodologia exposada és que no depèn de la geometria del reactor, del tipus de problema d'autovalors ni del nombre de grups d'energia del problema. Seguidament, s'obté la solució de les equacions estacionàries d'harmònics esfèrics. La implementació d'aquestes equacions té dues principals diferències respecte a l'equació de difusió. Primer, la discretització espacial es realitza a nivell de pin a partir de l'estudi de diferents malles. Segon, el nombre de grups d'energia és, generalment, major que dos. D'aquesta forma, es desenvolupen estratègies a blocs per a optimitzar el càlcul dels problemes algebraics associats. Finalment, s'implementa un mètode modal amb actualitzacions dels modes per a integrar l'equació de difusió neutrònica dependent del temps. Es presenten i es comparen els mètodes modals basats en l'expansió dels diferents modes espacials per a diversos tipus de transitoris. A més a més, un control de pas de temps adaptatiu es desenvolupa, evitant l'actualització dels modes d'una manera fixa i adaptant el pas de temps en funció de vàries estimacions de l'error.
[EN] One of the most important targets in nuclear safety analyses is the fast and accurate computation of the power evolution inside of the reactor core. The distribution of neutrons can be described by the neutron transport Boltzmann equation. The solution of this equation for realistic nuclear reactors is not straightforward, and therefore, numerical approximations must be considered. First, the thesis is focused on the attainment of the solution for several steady-state problems associated with neutron diffusion problem: the $\lambda$-modes, the $\gamma$-modes and the $\alpha$-modes problems. A high order finite element method is used for the spatial discretization. Several characteristics of each type of spectral problem are compared and analyzed on different reactors. Thereafter, several eigenvalue solvers and strategies are investigated to compute efficiently the algebraic eigenvalue problems obtained from the discretization. Most works devoted to solve the neutron diffusion equation are made for the approximation of two energy groups and without considering up-scattering. The main property of the proposed methodologies is that they depend on neither the reactor geometry, the type of eigenvalue problem nor the number of energy groups. After that, the solution of the steady-state simplified spherical harmonics equations is obtained. The implementation of these equations has two main differences with respect to the neutron diffusion. First, the spatial discretization is made at level of pin. Thus, different meshes are studied. Second, the number of energy groups is commonly bigger than two. Therefore, block strategies are developed to optimize the computation of the algebraic eigenvalue problems associated. Finally, an updated modal method is implemented to integrate the time-dependent neutron diffusion equation. Modal methods based on the expansion of the different spatial modes are presented and compared in several types of transients. Moreover, an adaptive time-step control is developed that avoids setting the time-step with a fixed value and it is adapted according to several error estimations.
Carreño Sánchez, AM. (2020). Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/144771
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Willert, Jeffrey Alan. "Hybrid Deterministic/Monte Carlo Methods for Solving the Neutron Transport Equation and k-Eigenvalue Problem." Thesis, North Carolina State University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3575891.
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The goal of this thesis is to build hybrid deterministic/Monte Carlo algorithms for solving the neutron transport equation and associated k-eigenvalue problem. We begin by introducing and deriving the transport equation before discussing a series of deterministic methods for solving the transport equation. To begin we consider moment-based acceleration techniques for both the one and two-dimensional fixed source problems. Once this machinery has been developed, we will apply similar techniques for computing the dominant eigenvalue of the neutron transport equation. We'll motivate the development of hybrid methods by describing the deficiencies of deterministic methods before describing Monte Carlo methods and their advantages. We conclude the thesis with a chapter describing the detailed implementation of hybrid methods for both the fixed-source and k-eigenvalue problem in both one and two space dimensions. We'll use a series of test problems to demonstrate the effectiveness of these algorithms before hinting at some possible areas of future work.
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Picoloto, Camila Becker. "Formulações espectronodais em cálculos neutrônicos multidimensionais." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/118888.
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In this work, an analytical approach is used along with nodal schemes for the solution of xed source two-dimensional neutron transport problems, in Cartesian geometry, de ned in heterogeneous medium, with anisotropic scattering. The methodology is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric angular quadrature set. One-dimensional equations for the averaged angular uxes are obtained by transverse integration of the original problem. Such equations are solved by the ADO method. Explicit expressions in spatial variables are derived for averaged uxes in each region in which the domain is subdivided. The solution in each region is coupled with that of its neighbouring regions to provide the solution in the whole domain, without resorting to using iterative methods. As usual in nodal schemes, auxiliary equations are needed. Here two di erent treatments were given to this issue: one based on relations between the unknown ows in the contours of the regions and the average angular uxes, and another in which these ows are approximated by polynomials of order zero being in this case, incorporated into the source term. Numerical results were compared with available literature showing the solution preserve the computational e ciency which has been a good feature of the ADO method when applied to different problems.Neste trabalho, uma abordagem analítica é utilizada juntamente com esquemas nodais na resolução de problemas bidimensionais de transporte de nêutrons de fonte fixa, em geometria cartesiana, definidos em meio heterogêneo, com espalhamento anisotrópico. A metodologia proposta é desenvolvida a partir da versão em ordenadas discretas da equação de transporte bidimensional, juntamente com o esquema de quadratura simétrica de nível. As equações em ordenadas discretas são integradas transversalmente, originando equações unidimensionais para os fluxos angulares médios. Tais equações unidimensionais são resolvidas pelo método ADO (Analytical Discrete Ordinates). Expressões explícitas nas variáveis espaciais são derivadas para os fluxos angulares médios em cada região em que o domínio foi subdividido. A solução em cada região é acoplada às regiões vizinhas, para fornecer a solução no domínio todo, sem a utilização de métodos iterativos. Como usual em esquemas nodais, equações auxiliares são necessárias, recebendo neste estudo dois tratamentos distintos: um em que os fluxos desconhecidos nos contornos das regiões assumem relações de proporcionalidade, com os fluxos angulares médios; e, outro, em que esses fluxos são aproximados por polinômios de ordem zero sendo, nesse caso, incorporados ao termo fonte. Resultados numéricos obtidos e comparados com disponíveis na literatura mostram a viabilidade da formulação, mantendo a eficiência computacional já verificada no tratamento de outros problemas, com o uso do método ADO.
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Mosher, Scott William. "A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5070.
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A Variational Transport Theory Method for
Two-Dimensional Reactor Core Calculations
Scott W. Mosher
110 Pages
Directed by Dr. Farzad Rahnema
It seems very likely that the next generation of reactor analysis methods will be based largely on neutron transport theory, at both the assembly and core levels. Signifi-cant progress has been made in recent years toward the goal of developing a transport method that is applicable to large, heterogeneous coarse-meshes. Unfortunately, the ma-jor obstacle hindering a more widespread application of transport theory to large-scale calculations is still the computational cost.
In this dissertation, a variational heterogeneous coarse-mesh transport method has been extended from one to two-dimensional Cartesian geometry in a practical fashion. A generalization of the angular flux expansion within a coarse-mesh was developed. This allows a far more efficient class of response functions (or basis functions) to be employed within the framework of the original variational principle. New finite element equations were derived that can be used to compute the expansion coefficients for an individual coarse-mesh given the incident fluxes on the boundary. In addition, the non-variational method previously used to converge the expansion coefficients was developed in a new and more thorough manner by considering the implications of the fission source treat-ment imposed by the response expansion.
The new coarse-mesh method was implemented for both one and two-dimensional (2-D) problems in the finite-difference, multigroup, discrete ordinates approximation. An efficient set of response functions was generated using orthogonal boundary conditions constructed from the discrete Legendre polynomials. Several one and two-dimensional heterogeneous light water reactor benchmark problems were studied. Relatively low-order response expansions were used to generate highly accurate results using both the variational and non-variational methods. The expansion order was found to have a far more significant impact on the accuracy of the results than the type of method. The varia-tional techniques provide better accuracy, but at substantially higher computational costs. The non-variational method is extremely robust and was shown to achieve accurate re-sults in the 2-D problems, as long as the expansion order was not very low.
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Pounders, Justin Michael. "A coarse-mesh transport method for time-dependent reactor problems." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/39586.
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A new solution technique is derived for the time-dependent transport equation.
This approach extends the steady-state coarse-mesh transport method that is based on
global-local decompositions of large (i.e. full-core) neutron transport problems. The new
method is based on polynomial expansions of the space, angle and time variables in a
response-based formulation of the transport equation. The local problem (coarse mesh)
solutions, which are entirely decoupled from each other, are characterized by space-,
angle- and time-dependent response functions. These response functions are, in turn, used
to couple an arbitrary sequence of local problems to form the solution of a much larger
global problem. In the current work, the local problem (response function) computations
are performed using the Monte Carlo method, while the global (coupling) problem is
solved deterministically. The spatial coupling is performed by orthogonal polynomial
expansions of the partial currents on the local problem surfaces, and similarly, the timedependent
response of the system (i.e. the time-varying flux) is computed by convolving
the time-dependent surface partial currents and time-dependent volumetric sources
against pre-computed time-dependent response kernels.
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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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Mosher, Scott William. "Implementation of an adaptive importance sampling technique in MCNP for monoenergetic slab problems." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/17100.
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Militão, Damiano da Silva. "Um modelo para a reconstrução angular e espacial analítica do problema de transporte unidimensional de partículas neutras usando um método espectro-nodal." Universidade do Estado do Rio de Janeiro, 2007. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=416.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorNesta dissertação propomos a utilização do método espectro-nodal SGF, cf. spectral Greens function, para transporte SN de partículas neutras, para determinarmos os fluxos angulares nas interfaces das regiões homogêneas do domínio espacial heterogêneo, com espalhamento linearmente anisotrópico usando preferencialmente altas ordens de quadraturas angulares. As reconstruções espaciais analíticas dos fluxos angulares são feitas no interior das regiões homogêneas, determinando as constantes arbitrárias da solução analítica local das equações SN no interior dos nodos espaciais da grade de dicretização. A seguir, utilizando essas constantes, determinamos as expressões do fluxo escalar e da corrente de nêutrons, que são substituídas na equação de transporte unidimensional em geometria retangular Cartesiana no termo de fonte por espalhamento linearmente anisotrópico. Resolvemos analiticamente a equação de transporte com os termos do fluxo escalar e corrente de nêutrons assim aproximados para estimarmos o perfil do fluxo angular de nêutrons no domínio. Esta reconstrução analítica aproximada da solução da equação de transporte de partículas neutras em geometria unidimensional Cartesiana constitui um problema inverso, na medida em que a partir da solução nodal de malha grossa fazemos primeiramente uma reconstrução analítica espacial do fluxo angular nas direções das ordenadas discretas, para em seguida procedermos à reconstrução analítica aproximada do fluxo no domínio angular.
We describe the application of the spectral Greens function SN nodal method for one-speed neutral particle transport calculations to determine the angular fluxes at the homogeneized regions within heterogeneous domains, for linearly anisotropic scattering, using preferably high-order angular quadratures. The reconstruction scheme in the space variable of the angular flux is carried out within the homogenized regions using uniform spatial grid. We determine the arbitrary constants of the analytical SN general solution inside each spatial node. Then, we determine the SN expression for the scalar flux and total current that we substitute into the analytical slab-geometry transport equation, precisely into its linearly anisotropic scattering source term. Further, we solve analytically the slab-geometry transport equation, so approximated, to obtain the flux profile within the space and angular domains. This approximate analytical reconstruction scheme of the solution of the neutral particle transport equation in slab geometry is an inverse problem, in the sense that we use accurate coarse-mesh SN numerical solution, to recover the SN analytical solution in the space variable, and then reconstruct the solution approximately in the angular domain.
Books on the topic "Neutron transport problem"
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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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Kyncl, Jan. On the problem of criticality for neutron transport equation. Řež, Czech Republic: Nuclear Research Institite Řež plc, 2003.
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Modak, R. S. Transport synthetic acceleration scheme for multi-dimensional neutron transport problems. Mumbai: Bhabha Atomic Research Centre, 2005.
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Monte Carlo Principles and Neutron Transport Problems. Dover Publications, 2008.
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Keller, Herbert. Approximate Solutions of Steady-State Neutron Transport Problems for Slabs. Creative Media Partners, LLC, 2015.
Find full textBook chapters on the topic "Neutron transport problem"
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Pignedoli, Antonio. "On the Rigorous Analysis of the Problem of the Neutron Transport in a Slab Geometry And on Some Other Results." In Some Aspects of Diffusion Theory, 519–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11051-1_8.
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Prillinger, G., and M. Mattes. "The Importance of Anisotropic Scattering in High Energy Neutron Transport Problems." In Reactor Dosimetry, 287–93. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5378-9_28.
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Mori, T., K. Okumura, and Y. Nagaya. "Status of JAERI’s Monte Carlo Code MVP for Neutron and Photon Transport Problems." In Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, 625–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-18211-2_100.
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Pignedoli, Antonio. "Transformational Methods Applied To Some One-Dimensional Problems Concerning The Equations of The Neutron Transport Theory." In Some Aspects of Diffusion Theory, 503–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11051-1_7.
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Mokhtar-Kharroubi, M. "Stochastic formulations of neutron transport: Nonlinear problems." In Series on Advances in Mathematics for Applied Sciences, 215–44. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789812819833_0010.
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Jordinson, Chris. "3He transport and the solar neutrino problem." In Stellar Astrophysical Fluid Dynamics, 193–204. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9780511536335.014.
Full textConference papers on the topic "Neutron transport problem"
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Hao, Jianli, Wenzhen Chen, Shaoming Wang, and De Zhang. "Study of the Space-Time Neutron Multiplication Formula." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29279.
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The process of neutron multiplication is a discrete-time process, but the neutron transport theory takes neutron multiplication as a continuous neutron source, which ignores the discrete-time process of neutron multiplication, which would take in errors, so it is necessary for describing the process of neutron multiplication as a discrete-time process. “The neutron doubling formula including delayed neutrons” has been established which describes the process of neutron multiplication as a discrete-time process, but it has nothing to do with space. “The neutron doubling formula including delayed neutrons” could not be used to describe the variety of distributing of neutron density in transient process; it also could not be used to deal with the problem of three-dimensional space. In order to solve the problems mentioned above, the space-time neutron multiplication formula is established. Based on the theory of neutron multiplication, the concept of space is introduced to the neutron multiplication formula and the space-time neutron multiplication formula is established by taking into account of neutron transport. The formula can describe the inherent physical process of neutron multiplication in fission chain reaction system. The test of space-time neutron multiplication formula is done, which proves the formula is right. Given the initial neutron density as well as the multiplication factor, the formula can strictly describe the variety of neutron density (neutron flux density) with time. It could be used for setting a standard for estimating error for the measurement of neutron flux density as well as numerical calculation; the space-time neutron multiplication has larger applicability compared with the “neutron doubling formula including delayed neutrons”.
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Wu, Zeyun, and Marvin L. Adams. "Advances in Inverse Transport Methods." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29881.
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We present advances in inverse transport methods and demonstrate their application to neutron tomography problems that have significant scattering. The problem we consider is inference of the material distribution in an object by detection and analysis of the radiation exiting from it. Our approach combines both deterministic and stochastic optimization methods to find a material distribution that minimizes the difference between computed and measured detector responses. The main advances are dimension-reduction schemes that we have designed to take advantage of known and postulated constraints. One key constraint is that the cross sections for a given region in the object must be the cross sections for a real material. We illustrate our approach using a neutron tomography model problem on which we impose reasonable constraints, similar to those that in practice would come from prior information or engineering judgment. This problem shows that our method is capable of generating results that are much better than those of deterministic minimization methods and dramatically more efficient than those of typical stochastic methods.
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Vosoughi, Naser, Majid Shahriari, and Ali Akbar Salehi. "Direct Discrete Method for Neutronic Calculations." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22014.
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The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution.
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Gairola, A., Hitesh Bindra, Gaurav Agarwal, and Suneet Singh. "Lattice Boltzmann Method for Solving Time-Dependent Radiation Transport and Reactor Criticality Problems." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60058.
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The recently developed lattice Boltzmann equation (LBE) framework [1] for radiation transport is extended to solve time-dependent nonequilibrium neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling the radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE equations are obtained for corresponding radiative or neutron transport in constant source and reactor criticality search problems. Furthermore, a two-dimensional D2Q8 & D2Q16 LBEs are proposed for solving the time-dependent neutron transport equation in a heterogenous media (e.g., a checkerboard lattice with pure scattering and absorbing cells). The results obtained with LBE are in good agreement with the existing discrete ordinate method results for the benchmark 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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Koreshi, Zafar Ullah. "Stationarity Issues in Monte Carlo Simulation for Neutron Transport." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-15016.
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Monte Carlo (MC) simulation, especially suitable for large and complex nuclear systems, can become computationally expensive due to the large number of neutrons which must be simulated for statistically accurate and precise estimates. It is generally understood that a sample estimate will converge to the population mean when a ‘large’ sample size is taken. The term ‘large’ is usually based on a guess and hence MC simulation is understood to be both an art and a science. Considerable work has been done to analyze convergence of MC results and develop posterior diagnostic tools. This paper addresses the convergence of MC simulation for two problems viz (i) a fixed-source non-multiplying system, and (ii) a critical system represented by Godiva. A traditional approach is used in the first part of the work while a ‘new’ approach essentially following Signals and Systems techniques from Digital Signal Processing gives ‘orginality’ to the analysis as it provides insight into the convergence of didactic problems in neutron transport simulation. The methods used are (i) comparison of MC flux with exact transport and diffusion solutions and relative entropy, with the Kullback-Leibler (KL) divergence, to quantify the convergence of estimates for flux as a function of sample size in Monte Carlo simulations, (ii) the effect of ‘skip cycles’ on the keff estimate, and (iii) a system identification approach based on the ARX (Auto Regressive Exogenous Source) method to determine the correlation between generations. The latter can be incorporated in Monte Carlo codes leading to a priori rather than to a posteriori diagnostic tools for establishment of convergence. The main findings of this work for simple one-group problems are that a Kullback Leibler ε∼10−3 can be specified a priori for the convergence criteria of a fixed source problem while a system-identification approach for a simple Godiva simulation would need a large number of data points to build an accurate ARX model and hence would be more difficult to include as an a priori tool; so it would essentially serve a purpose similar to the FOM which gives a quality metric only after the simulation is completed.
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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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Yang, Wankui, Baoxin Yuan, Songbao Zhang, Haibing Guo, Yaoguang Liu, and Li Deng. "A Neutron Transport Calculation Method for Deep Penetration and its Preliminary Verification." In 2018 26th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icone26-81709.
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Deep penetration problems exist widely in reactor applications, such as SPRR300 (Swimming Pool Research Reactor 300), a light water moderated, enriched uranium fueled research reactor in China. Deterministic transport theory is intrinsically suitable for deep penetration. But there exist some problems when it’s applied in SPRR-300research reactors. First, the reactor core is complicated for geometry description in deterministic theory codes. Monte Carlo method has advantages in complex geometry modeling. And it uses continuous energy cross sections which are independent with specific reactor types and research objections. But usually it’s difficult to converge well enough to deal with deep penetration problems, even though there are a number of variance reduction techniques. Based on the advantages and disadvantages of Monte Carlo and Deterministic method, we proposed a coupled neutron transport calculation method for deep penetration. It combines advantages of these two methods. Firstly, we use Monte Carlo code to finish fine modeling and do the whole reactor core calculation. Domestically developed Monte Carlo code JMCT is used to do the neutron transport calculation. Then homogenized group constants in each mesh are calculated from JMCT output by a self-developed script. Afterwards, we do the whole reactor calculation with deterministic theory code TORT. It directly uses group constants generated by Monte Carlo code. Finally, we can get the deep penetration calculation results from TORT output. Verification is carried out by comparing the group constants of benchmark problem, and by comparing keff calculated by this method with continuous energy Monte Carlo method. Benchmark calculation is conducted with OECD/NEA slab benchmark problem. The comparison shows that group constants generated by this study are in good agreement with results from published references. Then above group constants are applied to 3-dimensional discrete ordinates deterministic theory transport code TORT. But keff calculated by TORT is a little lower than that calculated by Monte Carlo code JMCT. To minimize other influence factors, different Sn/Pn order, and different mesh size in TORT has been tried. Unfortunately the keff difference between these two methods remains. Even though the keff results in this benchmark are less than keff calculated by continuous energy MC method, Benchmark results show that all the group constants generated by this method are in good agreement with existing references. So it can be expected that after further verification and validation, this coupled method can be effectively applied to the deep penetration problem in such kind of research reactors.
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Carreño, Amanda, Antoni Vidal Ferrándiz, Damián Ginestar Peiró, and Gumersindo Verdú. "Block strategies to compute the lambda modes associated with the neutron diffusion equation." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.13470.
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Given a configuration of a nuclear reactor core, the neutronic distribution of the power can beapproximated by means of the multigroup neutron diffusion equation. This is an approximationof the neutron transport equation that assumes that the neutron current is proportional to thegradient of the scalar neutron ux with a diffusion coeffcient [1]. This approximation is known asthe Fick's first law. To define the steady-state problem, the criticality of the system must be forced.In this work, the -modes problem is used. That yields a generalized eigenvalue problem whoseeigenvector associated with the dominant eigenvalue represents the distribution of the neutron uxin steady-state.The spatial discretization of the equation is made by a continuous Galerkin high order finite elementmethod is applied [2] to obtain an algebraic eigenvalue problem. Usually, the matrices obtainedfrom the discretization are huge and sparse. Moreover, they have a block structure given by the different number of energy groups. In this work, block strategies are developed to optimize thecomputation of the associated eigenvalue problems.First, different block eigenvalue solvers are studied. On the other hand, the convergence of theseiterative methods mainly depends on the initial guess and the preconditioner used. In this sense,different multilevel techniques to accelerate the rate of convergence are proposed. Finally, the sizeof the problems can be suffciently large to be unfeasible to be solved in personal computers. Thus,a matrix-free methodology that avoids the allocation of the matrices in memory is applied [3].Three-dimensional benchmarks are used to show the effciency of the methodology proposed.REFERENCES[1] Stacey, W. M. Nuclear reactor physics (Vol. 2). Weinheim: wiley-vch, 2018[2] Vidal-Ferrandiz, A., Fayez, R., Ginestar, D., and Verdú, G. Solution of the Lambda modesproblem of a nuclear power reactor using an h-p finite element method. Annals of NuclearEnergy, 72, pp. 338{349, 2018[3] Carreño Sánchez, A. M. Integration methods for the time dependent neutron diffusion equationand other approximations of the neutron transport equation. Doctoral dissertation, 2020.
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Xiao, Wei, Tengfei Zhang, Xiaojing Liu, Donghao He, and Qingquan Pan. "Application of Stiffness Confinement Method on Pin Resolved Variational Nodal Method and Its Implementation to C5G7-TD Benchmark Problem." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-92399.
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Abstract This paper presents an implementation of the stiffness confinement method in the framework of the variational nodal method (VNM) to solve time-dependent pin resolved neutron transport equations. With frequency-transform, the time-dependent neutron transport equation is decoupled from the precursor equation and transformed into a transient eigenvalue problem (TEVP) which can be solved with the in-house VNM code VITAS-FE. The verification tests were performed using the C5G7-TD benchmark problems. The result agrees well with solutions of the MPACT. The study indicates that the VNM and SCM can be applied to solve the high-fidelity pin-resolved transient problem accurately.
Reports on the topic "Neutron transport problem"
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William Charlton. Scattered Neutron Tomography Based on A Neutron Transport Inverse Problem. Office of Scientific and Technical Information (OSTI), July 2007. http://dx.doi.org/10.2172/915225.
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Ondis, L. A. ,. II, L. J. Tyburski, and B. S. Moskowitz. RCPO1 - A Monte Carlo program for solving neutron and photon transport problems in three dimensional geometry with detailed energy description and depletion capability. Office of Scientific and Technical Information (OSTI), March 2000. http://dx.doi.org/10.2172/755403.
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Chen, Yona, Jeffrey Buyer, and Yitzhak Hadar. Microbial Activity in the Rhizosphere in Relation to the Iron Nutrition of Plants. United States Department of Agriculture, October 1993. http://dx.doi.org/10.32747/1993.7613020.bard.
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Iron is the fourth most abundant element in the soil, but since it forms insoluble hydroxides at neutral and basic pH, it often falls short of meeting the basic requirements of plants and microorganisms. Most aerobic and facultative aerobic microorganisms possess a high-affinity Fe transport system in which siderophores are excreted and the consequent Fe complex is taken up via a cognate specific receptor and a transport pathway. The role of the siderophore in Fe uptake by plants and microorganisms was the focus of this study. In this research Rhizopus arrhizus was found to produce a novel siderophore named Rhizoferrin when grown under Fe deficiency. This compound was purified and its chemical structure was elucidated. Fe-Rhizoferrin was found to alleviate Fe deficiency when applied to several plants grown in nutrient solutions. It was concluded that Fe-Rhizoferrin is the most efficient Fe source for plants when compared with other among microbial siderophores known to date and its activity equals that of the most efficient synthetic commercial iron fertilizer-Fe EDDHA. Siderophores produced by several rhizosphere organisms including Rhizopus Pseudomonas were purified. Monoclonal antibodies were produced and used to develop a method for detection of the siderophores produced by plant-growth-promoting microorganisms in barley rhizosphere. The presence of an Fe-ferrichrome uptake in fluorescent Pseudomonas spp. was demonstrated, and its structural requirements were mapped in P. putida with the help of biomimetic ferrichrome analogs. Using competition experiments, it was shown that FOB, Cop B and FC share at least one common determinant in their uptake pathway. Since FC analogs did not affect FOB or Cop-mediated 55Fe uptake, it could be concluded that these siderophores make use of a different receptor(s) than FC. Therefore, recognition of Cop, FOB and FC proceeds through different receptors having different structural requirements. On the other hand, the phytosiderophores mugineic acid (MA and DMA), were utilized indirectly via ligand exchange by P. putida. Receptors from different biological systems seem to differ in their structural requirements for siderophore recognition and uptake. The design of genus- or species-specific drugs, probes or chemicals, along with an understanding of plant-microbe and microbe-microbe relationships as well as developing methods to detect siderophores using monoclonal antibodies are useful for manipulating the composition of the rhizosphere microbial population for better plant growth, Fe-nutrition and protection from diseases.