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Auteur : Grafiati
Publié le 14 mars 2023

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1

Jarmouni-Idrissi, K., et L. Thevenot. « HOMOGENIZATION OF A NONLINEAR NEUTRON TRANSPORT PROBLEM ». Transport Theory and Statistical Physics 31, no 2 (21 mai 2002) : 93–123. http://dx.doi.org/10.1081/tt-120003969.

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2

Vosoughi, Naser, Akbar Salehi, Majid Shahriari et 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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3

TÜRECİ, R. Gökhan. « Machine Learning Applications to the One-speed Neutron Transport Problems ». Cumhuriyet Science Journal 43, no 4 (27 décembre 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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4

Tsyfra, Ivan, et 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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5

Sengupta, A. « Full range solution of half space neutron transport problem ». ZAMP Zeitschrift f�r angewandte Mathematik und Physik 46, no 1 (janvier 1995) : 40–60. http://dx.doi.org/10.1007/bf00952255.

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6

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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7

Bourhrara, Lahbib, et 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 (août 2006) : 137–56. http://dx.doi.org/10.1080/00411450600901748.

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8

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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9

Mancusi, Davide, et 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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10

Chen, Gen-Shun, et Anthony W. Leung. « Positive Solutions for Reactor Multigroup Neutron Transport Systems : Criticality Problem ». SIAM Journal on Applied Mathematics 49, no 3 (juin 1989) : 871–87. http://dx.doi.org/10.1137/0149051.

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11

Khromov, V., E. Kryuchkov, G. Tikhomirov, L. Goncharov et V. Kondakov. « Probabilistic Method of Discrete Ordinates in a Neutron Transport Problem ». Nuclear Science and Engineering 121, no 2 (octobre 1995) : 264–76. http://dx.doi.org/10.13182/nse95-a28563.

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12

Williams, M. M. R. « The flat flux problem in one-speed neutron transport theory ». Annals of Nuclear Energy 30, no 5 (mars 2003) : 513–47. http://dx.doi.org/10.1016/s0306-4549(02)00108-1.

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13

Saracco, P., N. Abrate, M. Burrone, S. Dulla et P. Ravetto. « STUDY OF THE EIGENVALUE SPECTRA OF THE NEUTRON TRANSPORT PROBLEM IN PN APPROXIMATION ». EPJ Web of Conferences 247 (2021) : 03018. http://dx.doi.org/10.1051/epjconf/202124703018.

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The study of the steady-state solutions of neutron transport equation requires the introduction of appropriate eigenvalues: this can be done in various different ways by changing each of the operators in the transport equation; such modifications can be physically viewed as a variation of the corresponding macroscopic cross sections only, so making the different (generalized) eigenvalue problems non-equivalent. In this paper the eigenvalue problem associated to the time-dependent problem (α eigenvalue), also in the presence of delayed emissions is evaluated. The properties of associated spectra can give different insight into the physics of the problem.
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14

Yíldíz, C. « Calculation of the higher order eigenvalues for a homogeneous sphere using the FN method ». Kerntechnik 66, no 1-2 (1 janvier 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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15

Wang, Xinyu, Bin Zhang, Yixue Chen et Jun Xiong. « Verification of the Discrete Ordinates Goal-Oriented Multi-Collision Source Algorithm with Neutron Streaming Problems ». Energies 15, no 22 (8 novembre 2022) : 8335. http://dx.doi.org/10.3390/en15228335.

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The shielding calculation of neutron streaming problems with ducts is characterized by the strong anisotropy of angular flux, which poses a challenge for the analysis of nuclear installations. The discrete ordinate method is one of the most commonly deterministic techniques to solve the neutron transport equation, in which the accuracy and efficiency neutron are crucial to ensure the reliability of the streaming shielding simulation. We implemented the goal-oriented multi-collision source algorithm in the 3D transport code ARES. This algorithm can determine the importance factor based on the adjoint transport calculation, obtain the response function to enable problem-dependent, goal-oriented spatial decomposition, and provide the error estimation as a driving force behind the dynamic quadrature to optimize the source iteration. This study focuses on verifying the goal-oriented multi-collision source algorithm under the neutron streaming problems, and the capabilities of the algorithm have been tested on IRI-TUB benchmark of SINBAD database. The numerical results show that the algorithm can effectively control the angular discretization error for the neutron streaming problems, which is more economical than the traditional discrete ordinate calculation.
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16

Zhao, Zhengang, et Yunying Zheng. « Numerical Approximation for Fractional Neutron Transport Equation ». Journal of Mathematics 2021 (13 mars 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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17

Chiba, Go, et Kazuyuki Numata. « Neutron transport benchmark problem proposal for fast critical assembly without homogenizations ». Annals of Nuclear Energy 34, no 6 (juin 2007) : 443–48. http://dx.doi.org/10.1016/j.anucene.2007.02.018.

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18

Liemert, André, et Alwin Kienle. « The line source problem in anisotropic neutron transport with internal reflection ». Annals of Nuclear Energy 60 (octobre 2013) : 206–9. http://dx.doi.org/10.1016/j.anucene.2013.05.007.

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19

Prolo Filho, João Francisco, et Marco Paulsen Rodrigues. « A Closed Form Solution for a One-Dimensional Multi-Layered Neutron Transport Problem by Analytical Discrete Ordinates Method ». Defect and Diffusion Forum 372 (mars 2017) : 50–59. http://dx.doi.org/10.4028/www.scientific.net/ddf.372.50.

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In this work, the Analytical Discrete Ordinates Method (ADO method) is used to provide a closed form solution for a class of one-dimensional neutron transport problems in Cartesian geometry, considering heterogeneous media with linearly anisotropic scattering effects. In this context, the mathematical model will describe a steady-state phenomenon, with neutron sources located inside and on the boundaries of the domain of interest. In the process, the integro-differential transport equation is transformed into an ODE system by the SN angular discretization, which homogeneous solution is obtained with a quadratic eigenvalues problem with reduced order. A particular solution in terms of constants is used. To validate the code, the method and provide benchmark results, test problems will be treated and results will be discussed.
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20

Zheng, Weixiong, et Ryan G. McClarren. « Accurate least-squares P scaling based on problem optical thickness for solving neutron transport problems ». Progress in Nuclear Energy 101 (novembre 2017) : 394–400. http://dx.doi.org/10.1016/j.pnucene.2017.06.001.

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21

Rodriguez, Damian Martin, Shane J. Kennedy et Phillip M. Bentley. « Properties of elliptical guides for neutron beam transport and applications for new instrumentation concepts ». Journal of Applied Crystallography 44, no 4 (28 juin 2011) : 727–37. http://dx.doi.org/10.1107/s0021889811018590.

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The use of nonlinear tapered guides is becoming more common in advanced neutron scattering facilities around the world. Elliptical guides offer the promise of high performance not only as focusing devices but as an efficient way to transport neutrons over long distances. Here, the analytical expressions to determine their performance are derived and discussed. Under certain conditions, an increase in flux delivery is observed with increasing guide length, due to an increase in the angular spread of the neutrons reflected in the guide. The performance is only limited by the distance between the source and the guide entrance, the dimensions of the instrument placed after it, and the supermirror coating. As an example of the potential of elliptical geometry in instrumentation, a new small-angle neutron scattering (SANS) instrument concept is proposed, in which the neutron source is directly coupled to a half-ellipse, and the instrumental performance is evaluated by means of analytical expressions. The results show that such an instrument may provide a viable alternative to conventional pinhole SANS for high-resolution measurements and small samples, being substantially more compact and simpler to operate. The main limitation comes from the coma aberration which is inevitable on extended sources. The extent of the coma problem is also analysed.
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22

Kim, Inhyung, et Yonghee Kim. « INVESTIGATION ON DETERMINISTIC TRUNCATION TO CONTINUOUS ENERGY MONTE CARLO NEUTRON TRANSPORT CALCULATION ». EPJ Web of Conferences 247 (2021) : 04023. http://dx.doi.org/10.1051/epjconf/202124704023.

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This paper presents the application and evaluation of a deterministic truncation of Monte Carlo (DTMC) solution method in a whole core reactor problem based on a continuous energy transport calculation. The DTMC method has been studied and developed as a systematic way to truncate the high-fidelity Monte Carlo (MC) solution to reduce the computational cost without compromising the essential reliability of the solution. Its fea-sibility and capability were preliminarily validated in several benchmark problems using a multi-group energy MC code. In this paper, further study has been conducted in the more practical application with the continuous-energy based MC calculation. The con-cept of the DTMC method is briefly described. Improvements to enhance the numerical stability and efficiency are specified in details. The DTMC method is applied to an SMR problem, in which reactor parameters are estimated to characterize the numerical per-formance and are compared to the standard MC method. Last, the computing time and corresponding figure-of-merit are evaluated.
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23

Seleznev, E., V. Bereznev, I. Chernova et A. Belov. « USING PARTIAL EQUATIONS FOR ANALYSIS OF THE FAST BREEDER REACTOR KINETICS ». PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES : NUCLEAR AND REACTOR CONSTANTS 2019, no 3 (26 septembre 2019) : 153–62. http://dx.doi.org/10.55176/2414-1038-2019-3-153-162.

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To analyze the possibilities of using the system of partial neutron transport equations in evaluating the kinetics of a fast breeder reactors compared to the classical system of equations, computational studies of test models of MET-1000 and MOX-1000 reactors developed in the framework of the Generation-IV. As transient processes, the displacements (dumping and lifting) of control rods were simulated, and the reactivity effects in the indicated reactors were evaluated through the solution of stationary problems, i.e. through the use of an asymptotic estimate of the reactivity obtained from the solution of the stationary eigenvalue problem and from the processing of the inverse solution kinetic equation method from solving the transient problem. Test calculations were carried out in 26 and 28 group approximations using the BNAB-93 and BNAB-RF libraries and eight groups of delayed neutrons. The article shows that the features of determining, both calculation and measurement, the effects of reactivity and efficiency of control rods in fast breeder reactors are related to the working region of the neutron spectrum.
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Guo, Yan, et Lei Wu. « Regularity of Milne problem with geometric correction in 3D ». Mathematical Models and Methods in Applied Sciences 27, no 03 (mars 2017) : 453–524. http://dx.doi.org/10.1142/s0218202517500075.

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Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish [Formula: see text]-regularity for its solutions. Combined with a uniform [Formula: see text]-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.
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Liu, Yang, Hangyu Shi, Liangzhi Cao, Qi Zheng et Xiaoping Ouyang. « A new method to solve the neutron transport problem of spherical structure ». Annals of Nuclear Energy 165 (janvier 2022) : 108749. http://dx.doi.org/10.1016/j.anucene.2021.108749.

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26

Anli, Fikret, Faruk Yaşa, Süleyman Güngör et Hakan Öztürk. « TN approximation to neutron transport equation and application to critical slab problem ». Journal of Quantitative Spectroscopy and Radiative Transfer 101, no 1 (septembre 2006) : 129–34. http://dx.doi.org/10.1016/j.jqsrt.2005.11.010.

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27

Zemskov, E., K. Melnikov et I. Tormyshev. « CALCULATION OF THE PARAMETERS OF STOCHASTIC NEUTRON KINETICS IN ZERO POWER NUCLEAR REACTORS ». PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES : NUCLEAR AND REACTOR CONSTANTS 2019, no 1 (26 mars 2019) : 250–62. http://dx.doi.org/10.55176/2414-1038-2019-1-250-262.

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The majority of neutron-physical problems of nuclear power plants design can be solved on the basis of various approximations to the Boltzmann transport equation in terms of the averaged characteristics of the reactor: the effective multiplication factor, neutron flux, average neutron lifetime, etc. However, the neutron chain reaction itself is always stochastic. There are situations in which the stochastic nature of the chain reaction cannot be ignored. This is the so-called “blind” start-up problem with a weak external neutron source, the work of physical assemblies of “zero” power, the analysis of the reactivity noise of such assemblies, etc. Despite the well-developed theoretical basis for the stochastic description of the behavior of neutrons in a nuclear reactor, there are still not enough calculation algorithms and programs for stochastic kinetics analysis. The paper presents two computational algorithms for point reactor model, which are developed on the basis of the theory of Markov branching random processes. The first one is based on the balance equation for the probabilities of death and birth of prompt and delayed neutrons in a reactor, the second one is based on calculating the first and second moments of neutron number distributions and using the assumption that these distributions can be approximated by gamma distributions with sufficient accuracy. On the basis of these algorithms, programs have been created that allow one to calculate various scenarios for introducing reactivity and an external source into the system. The calculation of pulsed experiments on prompt and delayed neutrons to determine the waiting time of the threshold neutron pulse at the Godiva II installation showed a qualitative agreement of the results for both the two computational algorithms and the experimental data.
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Calloo, Ansar, Romain Le Tellier et David Couyras. « COMPARISON OF CHEBYSHEV AND ANDERSON ACCELERATIONS FOR THE NEUTRON TRANSPORT EQUATION ». EPJ Web of Conferences 247 (2021) : 03001. http://dx.doi.org/10.1051/epjconf/202124703001.

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This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.
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Merk, B. « An Analytical Approximation Solution for a Time-Dependent Neutron Transport Problem with External Source and Delayed Neutron Production ». Nuclear Science and Engineering 161, no 1 (janvier 2009) : 49–67. http://dx.doi.org/10.13182/nse161-49.

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Gupta, Anurag, et R. S. Modak. « Krylov sub-space methods for K-eigenvalue problem in 3-D neutron transport ». Annals of Nuclear Energy 31, no 18 (décembre 2004) : 2113–25. http://dx.doi.org/10.1016/j.anucene.2004.07.001.

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Willert, Jeffrey, H. Park et D. A. Knoll. « A comparison of acceleration methods for solving the neutron transport k -eigenvalue problem ». Journal of Computational Physics 274 (octobre 2014) : 681–94. http://dx.doi.org/10.1016/j.jcp.2014.06.044.

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32

Boffi, V. C., W. L. Dunn et G. Spiga. « A Rigorous Solution to the Classical Space-Dependent Neutron Slowing Down Transport Problem ». Nuclear Science and Engineering 99, no 3 (juillet 1988) : 197–207. http://dx.doi.org/10.13182/nse88-a28993.

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Żurkowski, Wojciech, Piotr Sawicki, Wojciech Kubiński et Piotr Darnowski. « Application of genetic algorithms in optimization of SFR nuclear reactor design ». Nukleonika 66, no 4 (25 novembre 2021) : 139–45. http://dx.doi.org/10.2478/nuka-2021-0021.

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Abstract This work presents a demonstrational application of genetic algorithms (GAs) to solve sample optimization problems in the generation IV nuclear reactor core design. The new software was developed implementing novel GAs, and it was applied to show their capabilities by presenting an example solution of two selected problems to check whether GAs can be used successfully in reactor engineering as an optimization tool. The 3600 MWth oxide core, which was based on the OECD/NEA sodium-cooled fast reactor (SFR) benchmark, was used a reference design [1]. The first problem was the optimization of the fuel isotopic inventory in terms of minimizing the volume share of long-lived actinides, while maximizing the effective neutron multiplication factor. The second task was the optimization of the boron shield distribution around the reactor core to minimize the sodium void reactivity effect (SVRE). Neutron transport and fuel depletion simulations were performed using Monte Carlo neutron transport code SERPENT2. The simulation resulted in an optimized fuel mixture composition for the selected parameters, which demonstrates the functionality of the algorithm. The results show the efficiency and universality of GAs in multidimensional optimization problems in nuclear engineering.
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Sobolev, Artem V., et Pavel A. Danilov. « Problems of radiation safety calculations related to spent nuclear fuel transport casks ». Nuclear Energy and Technology 6, no 1 (27 mars 2020) : 43–47. http://dx.doi.org/10.3897/nucet.6.51778.

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The paper discusses the stages of calculating the radiation safety of spent nuclear fuel (SNF) transport packages, in particular, transport casks and some related problems. The problem of describing the source of neutrons and gamma radiation of spent nuclear fuel is shown. For individual designs of fuel assemblies, data are given on isotopes that make the main contribution to the neutron source as well as on gamma rays in nuclear fuel material and structural materials. The authors emphasize the necessity of analyzing the influence of the initial spent fuel parameters on the formation of the radiation spectrum and, therefore, on the radiation situation around the transport casks. Consideration is given to the problem of assessing the attenuation of gamma radiation in calculating protection analytically and using software. Due to the ambiguity of the position of the zone with the highest effective dose value on the SNF transport cask surface, it is indicated that preliminary estimates are required to take into account all radiation sources and their nonuniformities. All the problems presented in the paper are currently being solved by means of rather complex and voluminous calculations that take a long time. In order to be able to conduct a preliminary assessment of the radiation situation around the transport casks, the authors propose to create a methodology that will determine the type of interrelations between the maximum effective dose and input parameters, such as fuel burnup, decay, fuel composition, protection material in the SNF transport cask, etc. This methodology will make it possible to improve the efficiency of the process of designing the SNF transport casks, avoid possible design errors and, in particular, when used as intended, resolve the issue of the SNF cask loading configuration.
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Nelson, Adam G., William Boyd et Paul K. Romano. « The Effect of the Flux Separability Approximation on Multigroup Neutron Transport ». Journal of Nuclear Engineering 2, no 1 (22 mars 2021) : 86–96. http://dx.doi.org/10.3390/jne2010009.

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The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.
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Bernal, Álvaro, Rafael Miró, Damián Ginestar et 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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Gonçalves, G. A., M. T. de Vilhena et B. E. J. Bodmann. « Heuristic geometric “eigenvalue universality” in a one-dimensional neutron transport problem with anisotropic scattering ». Kerntechnik 75, no 1-2 (mars 2010) : 50–52. http://dx.doi.org/10.3139/124.110051.

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Willert, Jeffrey, H. Park et William Taitano. « Applying Nonlinear Diffusion Acceleration to the Neutron Transport k-Eigenvalue Problem with Anisotropic Scattering ». Nuclear Science and Engineering 181, no 3 (novembre 2015) : 351–60. http://dx.doi.org/10.13182/nse14-131.

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Hongchun, Wu, Liu Pingping, Zhou Yongqiang et Cao Liangzhi. « Transmission probability method based on triangle meshes for solving unstructured geometry neutron transport problem ». Nuclear Engineering and Design 237, no 1 (janvier 2007) : 28–37. http://dx.doi.org/10.1016/j.nucengdes.2006.04.031.

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Nguyen, Tat Nghia, Yeon Sang Jung, Thomas Downar et Changho Lee. « Implementation of the transient fixed-source problem in the neutron transport code PROTEUS-MOC ». Annals of Nuclear Energy 129 (juillet 2019) : 199–206. http://dx.doi.org/10.1016/j.anucene.2019.01.005.

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Atalay, M. A. « The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory ». Annals of Nuclear Energy 23, no 3 (février 1996) : 183–93. http://dx.doi.org/10.1016/0306-4549(95)00024-7.

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Shulaia, D. A., et E. I. Gugushvili. « Inverse problem of spectral analysis of linear multigroup neutron transport theory in plane geometry ». Transport Theory and Statistical Physics 29, no 6 (octobre 2000) : 711–21. http://dx.doi.org/10.1080/00411450008214531.

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Sanchez, Richard, et Lahbib Bourhrara. « Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition ». Transport Theory and Statistical Physics 40, no 2 (septembre 2011) : 69–84. http://dx.doi.org/10.1080/00411450.2011.596607.

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Güleçyüz, M. Ç., et C. Tezcan. « The FN method for anisotropic scattering in neutron transport theory : The critical slab problem ». Journal of Quantitative Spectroscopy and Radiative Transfer 56, no 2 (août 1996) : 309–13. http://dx.doi.org/10.1016/0022-4073(96)00057-x.

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Douglass, Steven, et Nathan Gibson. « K-MEANS CLUSTERING OF NEUTRON SPECTRA FOR CROSS SECTION COLLAPSE ». EPJ Web of Conferences 247 (2021) : 03010. http://dx.doi.org/10.1051/epjconf/202124703010.

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The process of generating cross sections for whole-core analysis typically involves collapsing cross sections against an approximate spectrum generated by solving problems with reduced scope (e.g., 2D slices of a fuel assembly). Such spectra vary with the location of a material region and with other state parameters (e.g., burnup, temperature, soluble boron concentration), resulting in a burdensome and potentially time consuming process to store and load spectra. Commonly, this is resolved by manually determinining material regions for which the cross sections can be collapsed with a single weighting flux, requiring a combination of domain knowledge, engineering judgment, and trial and error. Exploring new reactor concepts and solving increasingly complicated problems with deterministic transport methods will therefore benefit greatly from an automated approach to grouping spectra independent of problem geometry or reactor type. This paper leverages a data analytics technique known as k-means clustering to group regions with similar weighting spectra into individual clusters, within each of which an average weighting flux is applied. Despite the clustering algorithm being agnostic to the physics of the problem, the approach results in a nearly 98% decrease in number of spectra regions with minimal impact to the accuracy.
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Logoteta, Domenico. « Hyperons in Neutron Stars ». Universe 7, no 11 (28 octobre 2021) : 408. http://dx.doi.org/10.3390/universe7110408.

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I review the issues related to the appearance of hyperons in neutron star matter, focusing in particular on the problem of the maximum mass supported by hyperonic equations of state. I discuss the general mechanism that leads to the formation of hyperons in the core of neutron stars and I review the main techniques and many-body methods used to construct an appropriate equation of state to describe the strongly interacting system of hadrons hosted in the core of neutron stars. I outline the consequences on the structure and internal composition of neutron stars and also discuss the possible signatures of the presence of hyperons in astrophysical dynamical systems like supernova explosions and binary neutron star mergers. Finally, I briefly report about the possible important role played by hyperons in the transport properties of neutron star matter and on the consequences of neutron star cooling and gravitational wave instabilities induced by the presence of hyperons.
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Johnson, Andrew, et Dan Kotlyar. « APPLICATION OF A CUSTOM DEPLETION FRAMEWORK TO THE PREDICTION OF NEUTRON FLUX DISTRIBUTION THROUGH DEPLETION ». EPJ Web of Conferences 247 (2021) : 02004. http://dx.doi.org/10.1051/epjconf/202124702004.

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Previous works by the authors have introduced the spatial flux variation method (SFV) for predicting the changes in neutron flux due to a change in material compositions. In order to remove a full transport solution at the end-of-step, this work presents a framework responsible for computing macroscopic cross sections after a depletion event. These end of-step cross sections are estimators of changes in neutron loss and production, and enable the prediction of neutron flux using only information obtained from a single beginning of-step transport solution. The framework reads in all relevant data needed to model the depletion system, including one-group cross sections and effective fission yields to reproduce the problem using an external solver. The framework also supports extrapolating microscopic cross sections in order to rebuild the end-of-step macroscopic cross sections needed for the flux prediction. Results indicate that the SFV method is not adversely effected by the external depletion solution, and can be implemented alongside an existing transport-depletion framework.
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Kadem, Abdelouahab, et Adem Kilicman. « Note on the Solution of Transport Equation by Tau Method and Walsh Functions ». Abstract and Applied Analysis 2010 (2010) : 1–13. http://dx.doi.org/10.1155/2010/704168.

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We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.
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Bülbül, A., et F. Anlı. « Chebyshev polynomial (TN) approximation to neutron transport theory and application to the critical slab problem ». Kerntechnik 73, no 4 (septembre 2008) : 163–66. http://dx.doi.org/10.3139/124.100559.

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Yildiz, C. « The spherical harmonics method for anisotropic scattering in neutron transport theory : the critical sphere problem ». Journal of Quantitative Spectroscopy and Radiative Transfer 71, no 1 (octobre 2001) : 25–37. http://dx.doi.org/10.1016/s0022-4073(01)00009-7.

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