Relevant bibliographies by topics / Point kinetics equations

Academic literature on the topic 'Point kinetics equations'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Point kinetics equations"

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Singh, Sudhansu, and Mohapatra Dinakrushna. "Solution of the reactor point kinetics equations by MATLAB computing." Nuclear Technology and Radiation Protection 30, no. 1 (2015): 11–17. http://dx.doi.org/10.2298/ntrp1501011s.

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The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.
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Aboanber, Ahmed E. "Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics." International Journal of Nuclear Energy 2013 (August 13, 2013): 1–12. http://dx.doi.org/10.1155/2013/903904.

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The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Padé approximation (GPA) method shows high accuracy, high efficiency, and stable character of the solution.
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Espinosa-Paredes, G., and D. Suescún-Díaz. "Point reactor kinetics equations from P1 approximation of the transport equations." Annals of Nuclear Energy 144 (September 2020): 107592. http://dx.doi.org/10.1016/j.anucene.2020.107592.

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Nahla, Abdallah A., and Adel M. Edress. "Efficient stochastic model for the point kinetics equations." Stochastic Analysis and Applications 34, no. 4 (May 31, 2016): 598–609. http://dx.doi.org/10.1080/07362994.2016.1159519.

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Sathiyasheela, T. "Inhomogeneous point kinetics equations and the source contribution." Nuclear Engineering and Design 240, no. 12 (December 2010): 4083–90. http://dx.doi.org/10.1016/j.nucengdes.2010.09.036.

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Hayes, J. G., and E. J. Allen. "Stochastic point-kinetics equations in nuclear reactor dynamics." Annals of Nuclear Energy 32, no. 6 (April 2005): 572–87. http://dx.doi.org/10.1016/j.anucene.2004.11.009.

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Abramov, B. "CORRECTION OF INVERSE POINT KINETICS EQUATIONS FOR MEASUREMENT REACTIVITY IN THE PROMPT JUMP APPROXIMATION." PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS 2019, no. 2 (June 26, 2019): 151–59. http://dx.doi.org/10.55176/2414-1038-2019-2-151-159.

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We consider methods for calculating the reactivity of a nuclear reactor from the measured dependence of the neutron flux in the reactor on time, based on the use of the inverse point kinetics equations, which relate the values of reactivity and neutron flux in the reactor. The main attention is paid to the correction of the equations of inverse point kinetics in the prompt-jump approximation (or in the theory of singular perturbations for equations with a small parameter with the highest derivative). The nonequivalence of the corresponding problems for the direct and inverse point kinetics equations in the prompt-jump approximation is noted, which consists in the fact that, contrary to expectations, the reactivity values appearing in these problems do not generally coincide with each other. The reasons for this non-equivalence are investigated and ways to eliminate it are considered. New inverse point kinetics equations are proposed in the prompt-jump approximation, devoid of the indicated disadvantage of the traditional equations. These equations are tested by substituting in them analytical solutions of the corresponding (direct) Cauchy problems for point kinetics equations using the apparatus of the theory of systems of ordinary differential equations, adapted to the problem in question. It is shown that the use of the equations proposed in the work leads to the correct determination of reactivity immediately after the instantaneous introduction of a disturbance into the reactor, and not in asymptotics, as is usually the case when applying traditional equations.
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Nahla, Abdallah A., and Elsayed M. E. Zayed. "Solution of the nonlinear point nuclear reactor kinetics equations." Progress in Nuclear Energy 52, no. 8 (November 2010): 743–46. http://dx.doi.org/10.1016/j.pnucene.2010.06.001.

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Nahla, Abdallah A. "Analytical solution to solve the point reactor kinetics equations." Nuclear Engineering and Design 240, no. 6 (June 2010): 1622–29. http://dx.doi.org/10.1016/j.nucengdes.2010.03.003.

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Theler, Germán G., and Fabián J. Bonetto. "On the stability of the point reactor kinetics equations." Nuclear Engineering and Design 240, no. 6 (June 2010): 1443–49. http://dx.doi.org/10.1016/j.nucengdes.2010.03.007.

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Dissertations / Theses on the topic "Point kinetics equations"

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Gana, Inès. "Caractérisation physique et chimique des substances à activité thérapeutique : application aux études de profil de stabilité et de préformulation." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCB164/document.

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Le développement d’un médicament pour une cible thérapeutique donnée passe par plusieurs étapes qui se résument en une étape de criblage, une phase préclinique et plusieurs phases cliniques. Ces étapes permettent de sélectionner une substance active et de démontrer son efficacité thérapeutique et sa sécurité toxicologique. Ces deux critères définissent la qualité du médicament qui, une fois démontrée, doit être garantie pendant toute sa durée de validité. La qualité est évaluée au moyen d’études de stabilité qui sont réalisées d’abord sur la matière première de la substance active au cours de la phase de pré-développement du médicament, ensuite sur le produit fini. La stabilité intrinsèque de la substance active concerne à la fois ses propriétés chimiques et ses propriétés physiques qui sont liées à la nature de la substance. L’étude de stabilité repose d’abord sur la caractérisation de ces propriétés, et ensuite sur l’étude de la sensibilité de la substance à l’égard des facteurs environnementaux pouvant modifier les propriétés intrinsèques de la substance. L’approche adoptée dans ce travail repose d’une part sur l’évaluation de la stabilité chimique c’est à dire de la réactivité chimique des substances à usage pharmaceutique au travers des études de pureté chimique et des études de dégradation forcée de ces substances en solution, et d’autre part, sur l’évaluation de la stabilité physique. Dans ce cadre, l’étude du polymorphisme cristallin revêt une grande importance, tout comme l’aptitude à la formation d’hydrates ou de solvates. Cette étude, basée sur la thermodynamique, consiste pour l’essentiel à construire un diagramme de phases pression-température permettant de définir les domaines de stabilité relative des différentes formes cristallines. Cinq substances actives, existant à l’état solide et entrant dans la composition de médicaments administrés par voie orale, ont été étudiées dans le cadre de ce travail. L’analyse chimique du tienoxolol, présentant un effet anti-hypertenseur, a montré qu’il est très sensible à l’hydrolyse et à l’oxydation. Sept produits de dégradation ont été identifiés pour ce produit dont un schéma probable de fragmentation a été établi. Des diagrammes de phases pression-température ont été construits pour le bicalutamide et le finastéride, médicaments du cancer de prostate, en utilisant une approche topologique basée simplement sur les données disponibles dans la littérature. Cette étude a montré que la relation thermodynamique (énantiotropie ou monotropie) entre les formes cristallines sous conditions ordinaires peut être modifiée en fonction de la température et de la pression. Ce résultat est important pour la production des médicaments car il montre comment une telle information peut être obtenue par des mesures simples et accessibles aux laboratoires de recherche industrielle, sans que ces derniers soient contraints d’expérimenter sous pression. La méthode topologique de construction de diagramme de phases a été validée ensuite en la comparant à une méthode expérimentale consistant à suivre, par analyse thermique, des transitions de phases en fonction de la pression. La méthode expérimentale a été appliquée à deux composés, la benzocaine, anesthésique local, et le chlorhydrate de cystéamine, médicament utilisé pour les cystinoses. Les deux formes étudiées de benzocaine présentent une relation énantiotrope qui se transforme en relation monotrope à haute pression. Une nouvelle forme cristalline (forme III) du chlorhydrate de cystéamine a été découverte au cours de ce travail. La relation thermodynamique entre cette forme III et la forme I est énantiotrope dans tout le domaine de température et de pression. De plus, le chlorhydrate de cystéamine, classé hygroscopique, a fait l’objet d’une étude quantitative de sa sensibilité à l’eau, montrant qu’il devient déliquescent sans formation préalable d’hydrate (...)
The development of a drug for a given therapeutic target requires several steps, which can be summarized by drug screening, a preclinical phase and a number of clinical phases. These steps allow the selection of an active substance and a verification of its therapeutic efficacy and toxicological safety. The latter two criteria define the quality of the drug, which once demonstrated, must be guaranteed throughout its shelf life. Quality is assessed through stability studies that are carried out with the raw material of the active substance (preformulation phase) and with the final product. The intrinsic stability of the active substance depends on its chemical and physical properties and their characterization is the core of the stability studies, which in addition consists of sensitivity studies of the active pharmaceutical ingredient (API) for environmental factors that can modify the intrinsic properties of the substance. The approach presented in this work is based on the one hand on the assessment of the chemical stability, i.e. the reactivity of APIs through chemical purity studies and forced degradation in solution, and on the other hand on the assessment of the physical stability. For the latter, crystalline polymorphism is of great importance, as is the ability of the API to form hydrates or solvates. The study of crystalline polymorphism is based on the construction of pressure-temperature phase diagrams in accordance with thermodynamic requirements leading to the stability condition domains of the different crystalline forms. The stability behavior of five APIs used or meant for oral applications has been studied as part of this work. The chemical analysis of tienoxolol, an antihypertensive drug, has demonstrated its sensitivity for hydrolysis and oxidation. Seven degradation products were identified and patterns of fragmentation have been established. Pressure-temperature phase diagrams have been constructed for bicalutamide and finasteride, drugs against prostate cancer, using a topological approach based on data available in the literature. The study demonstrates that the thermodynamic relationship (enantiotropy or monotropy) between crystalline forms under ordinary conditions can change depending on the pressure. This is important for drug development as it demonstrates how stability information can be obtained by standard laboratory measurements accessible to industrial research laboratories without the necessity to carry out experiments under pressure. The topological approach for the construction of phase diagrams has subsequently been validated by measuring transition temperatures as a function of pressure. Experiments have been carried out with benzocaine, a local anesthetic, and with cysteamine hydrochloride, a drug used against cystinosis. Two crystalline forms were observed in the case of benzocaine. They exhibit an enantiotropic relationship that becomes monotropic at high pressure. For cysteamine hydrochloride, a new crystalline form (form III) was discovered. The thermodynamic relationship between the new form III and the known form I is enantiotropic for the entire temperature and pressure range. Cysteamine hydrochloride’s sensitivity to water has been studied, as it is hygroscopic. It has been demonstrated that it becomes deliquescent in the presence of water and no trace of a hydrate has been found. Finally, a study combining thermal and chromatographic methods showed that, under the effect of temperature, cysteamine hydrochloride turns into cystamine in the solid as well as in the liquid state, The latter is known to be an important impurity of cysteamine hydrochloride. In conclusion, the approach developed in this work allowed to characterize the stability properties of a number of APIs and to determine the factors that may change these properties and influence the intrinsic stability (...)
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Books on the topic "Point kinetics equations"

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Succi, Sauro. Why a Kinetic Theory of Fluids? Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0001.

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Fluid flows are a pervasive presence across most branches of human activity, including daily life. Although the basic equations governing the motion of fluid flows are known for two centuries (1822), since the work of Claude–Louis Navier (1785–1836) and Gabriel Stokes (1819–1903), these equations still set a formidable challenge to the quantitative, and sometimes even qualitative, understanding of the way fluid matter flows in space and time. Meteorological phenomena are among the most popular examples in point, but the challenge extends to many otherinstances of collective fluid motion, both in classical and quantum physics. This Chapter presents the Navier–Stokes equations of fluid mechanics and discuss the main motivations behind the kinetic approach to computational fluid dynamics.
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Sherwood, Dennis, and Paul Dalby. Chemical equilibrium and chemical kinetics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0014.

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Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.
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A Phase Rule Approach to Critical Point Phenomena in Chemically Reacting Systems: A Dissertation. Ann Arbor, USA: ProQuest Dissertations Publishing, 2017.

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Morawetz, Klaus. Simulations of Heavy-Ion Reactions with Nonlocal Collisions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0023.

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The scenario of heavy-ion reactions around the Fermi energy is explored. The quantum BUU equation is solved numerically with and without nonlocal corrections and the effect of nonlocal corrections on experimental values is calculated. A practical recipe is presented which allows reproducing the correct asymptotes of scattering by acting on the point of closest approach. The better description of dynamical correlations by the nonlocal kinetic equation is demonstrated by an enhancement of the high-energy part of the particle spectra and the enhancement of mid-rapidity charge distributions. The time-resolved solution shows the enhancement of neck formation. It is shown that the dissipated energy increases due to the nonlocal collision scenario which is responsible for the observed effects and not due to the enhancement of collisions. As final result, a method is presented how to incorporate the effective mass and quasiparticle renormalisation with the help of the nonlocal simulation scenario.
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Садовников, Василий. Теория гетерогенного катализа. Теория хемосорбции. Publishing House Triumph, 2021. http://dx.doi.org/10.32986/978-5-40-10-01-2001.

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This monograph is a continuation of the monograph by V.V. Sadovnikov. Lateral interaction. Moscow 2006. Publishing house "Anta-Eco", 2006. ISBN 5-9730-0017-6. In this work, the foundations of the theory of heterogeneous catalysis and the theory of chemisorption are more easily formulated. The book consists of two parts, closely related to each other. These are the theoretical foundations of heterogeneous catalysis and chemisorption. In the theory of heterogeneous catalysis, an experiment is described in detail, which must be carried out in order to isolate the stages of a catalytic reaction, to find the stoichiometry of each of the stages. This experiment is based on the need to obtain the exact value of the specific surface area of the catalyst, the number of centers at which the reaction proceeds, and the output curves of each of the reaction products. The procedures for obtaining this data are described in detail. Equations are proposed and solved that allow calculating the kinetic parameters of the nonequilibrium stage and the thermodynamic parameters of the equilibrium stage. The description of the quantitative theory of chemisorption is based on the description of the motion of an atom along a crystal face. The axioms on which this mathematics should be based are formulated, the mathematical apparatus of the theory is written and the most detailed instructions on how to use it are presented. The first axiom: an atom, moving along the surface, is present only in places with minima of potential energy. The second axiom: the face of an atom is divided into cells, and the position of the atom on the surface of the face is set by one parameter: the cell number. The third axiom: the atom interacts with the surrounding material bodies only at the points of minimum potential energy. The fourth axiom: the solution of the equations is a map of the arrangement of atoms on the surface. The fifth axiom: quantitative equations are based on the concept of a statistically independent particle. The formation energies of these particles and their concentration are calculated by the developed program. The program based on these axioms allows you to simulate and calculate the interaction energies of atoms on any crystal face. The monograph is intended for students, post-graduate students and researchers studying work and working in petrochemistry and oil refining.
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Book chapters on the topic "Point kinetics equations"

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Schramm, M., C. Z. Petersen, M. T. Vilhena, B. E. J. Bodmann, and A. C. M. Alvim. "On the Fractional Neutron Point Kinetics Equations." In Integral Methods in Science and Engineering, 229–43. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7828-7_17.

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Saha Ray, Santanu. "Numerical Simulation of Stochastic Point Kinetics Equation in the Dynamical System of Nuclear Reactor." In Nonlinear Differential Equations in Physics, 375–88. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1656-6_9.

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Silva, J. J. A., B. E. J. Bodmann, M. T. Vilhena, and A. C. M. Alvim. "On a Closed Form Solution of the Point Kinetics Equations with a Modified Temperature Feedback." In Integral Methods in Science and Engineering, 245–57. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7828-7_18.

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Razak, M. Mohideen Abdul. "Design of Coupled FIR Filters for Solving the Nuclear Reactor Point Kinetics Equations with Feedback." In Trends in Mathematics, 49–61. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68281-1_5.

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Pyeon, Cheol Ho. "Reactor Kinetics." In Accelerator-Driven System at Kyoto University Critical Assembly, 51–81. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0344-0_3.

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AbstractIn static and kinetic experimental analyses, the reactivity effect of introducing a neutron guide has been examined with various materials and adjustments of the beam window. With the objective of improving the KUCA core characteristics, the implementation of the neutron guide is predicted to increase the fast neutrons in directing the fuel region. With regard to the kinetic characteristics, the subcriticality and the prompt neutron decay constant are monitored for several core configurations and detector positions. The KUCA core is equipped to make locally a hard spectrum core region with the combined use of 235U fuel, a polyethylene moderator, and a Pb–Bi reflector for criticality. In this study, the first attempt is made to examine experimentally the characteristics of kinetics parameters in ADS comprised of 235U-fueled and Pb–Bi-zoned core, and spallation neutrons generated by an injection of 100 MeV protons onto the solid Pb–Bi target. Online monitoring of reactivity has been deduced in real time by the inverse kinetic method on the basis of the one-point kinetic equation with measured neutron signals in the core. Here, measurements by the one-point kinetic equation are validated through the subcriticality evaluation with the PNS histogram and the methodology by the inhour equation.
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Masterson, Robert E. "The Point Kinetics Approximation and the Inhour Equation." In Introduction to Nuclear Reactor Physics, 673–718. Boca Raton : Taylor & Francis, a CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa, plc, [2017]: CRC Press, 2017. http://dx.doi.org/10.1201/9781315118055-16.

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Schramm, M., A. C. M. Alvim, B. E. J. Bodmann, M. T. B. Vilhena, and C. Z. Petersen. "The Neutron Point Kinetics Equation: Suppression of Fractional Derivative Effects by Temperature Feedback." In Integral Methods in Science and Engineering, 551–62. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16727-5_46.

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da Silva, M. Wollmann, B. E. J. Bodmann, M. T. B. Vilhena, and R. Vasques. "Influence of Stochastic Moments on the Solution of the Neutron Point Kinetics Equation." In Integral Methods in Science and Engineering, 675–86. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16727-5_56.

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Espinosa, C. E., B. E. J. Bodmann, and M. T. Vilhena. "On the Neutron Point Kinetic Equation with Reactivity Decomposition Based on Two Time Scales." In Integral Methods in Science and Engineering, Volume 2, 65–75. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59387-6_7.

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Kim, Hag-Tae, Ganduulga, Dong Pyo Hong, and Kil To Chong. "A Numerical Approach to Solve Point Kinetic Equations Using Taylor-Lie Series and the Adomian Decomposition Method." In Lecture Notes in Electrical Engineering, 1031–38. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6738-6_127.

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Conference papers on the topic "Point kinetics equations"

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Liu, Dong, Xiuchun Luan, Tao Yu, Weining Zhao, and Lei Liu. "The Controllability of the Point Reactor Neutron Kinetics Equations." In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30494.

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In this paper, the conditions to ensure the controllability of the point reactor neutron kinetics equations are studied. In a nuclear reactor, due to the delayed neutron precursor concentration and the internal reactivity, the kinetics equations of the nuclear reactor are nonlinear. To solve the problem of the pole placement, the controllability of the point kinetics equations must be guaranteed. Then, a new method to analysis of the controllability conditions of the point kinetics equations of a reactor is carried out here. The method is based on the controllability matrix directly denoted by relevant symbols, and a formula used for controllability analysis is showed with symbols by calculating the determinant of the matrix. First, with using the linearization technique, the equations are linearized with respect to any possible equilibrium point. Subsequently, an analysis of the controllability of the general linear model that includes only one group delayed neutron precursor is performed, obtaining the interesting result that the controllability of the equations are controllable except when the effective precursor radioactive decay constant and the reciprocal of the fuel-to-coolant heat transfer mean time have the same value, which does not occur in practice. Thus, with the same method, the other analysis obtained the conditions to guarantee the controllability of the point kinetics equations with different groups delayed neutron precursor, which includes two-group, three-group and six-group models. Then, the results are compared with that of the numerical controllability matrix, obtaining the final conclusion that the results of the new analysis method give the closer results to the actual situation and list the restrictions that guarantee the controllability of the point reactor neutron kinetics equations.
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Vrban, Branislav, Miroslava Dobroňová, Jakub Lüley, Štefan Čerba, Filip Osuský, and Vladimír Nečas. "On the Taylor series solution of the reactor point kinetics equations." In APPLIED PHYSICS OF CONDENSED MATTER (APCOM 2021). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0066972.

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Schaun, Natália, Fernanda Tumelero, and Claudio Zen Petersen. "Solution of the Neutron Point Kinetics equations by applying the Rosenbrock method." In 18th Brazilian Congress of Thermal Sciences and Engineering. ABCM, 2020. http://dx.doi.org/10.26678/abcm.encit2020.cit20-0765.

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Kim, Hagtae, Dong Pyo Hong, and Kil To Chong. "A numerical solution of point kinetics equations using the Adomian Decomposition Method." In 2012 International Conference on Systems and Informatics (ICSAI). IEEE, 2012. http://dx.doi.org/10.1109/icsai.2012.6223630.

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Luan, Xiuchun, Jie Zhou, and Yu Zhai. "Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations." In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30562.

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A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.
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Zhang, Yining, Haochun Zhang, Yang Su, and Guangbo Zhao. "A Comparative Study of 10 Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67275.

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Point reactor neutron kinetics equations describe the time dependent neutron density variation in a nuclear reactor core. These equations are widely applied to nuclear system numerical simulation and nuclear power plant operational control. This paper analyses the characteristics of 10 different basic or normal methods to solve the point reactor neutron kinetics equations. These methods are: explicit and implicit Euler method, explicit and implicit four order Runge-Kutta method, Taylor polynomial method, power series method, decoupling method, end point floating method, Hermite method, Gear method. Three different types of step reactivity values are introduced respectively at initial time when point reactor neutron kinetics equations are calculated using different methods, which are positive reactivity, negative reactivity and higher positive reactivity. The calculation results show that (i) minor relative error can be gain after three types of step reactivity are introduced, when explicit or implicit four order Runge-Kutta method, Taylor polynomial method, power series method, end point floating method or Hermite method is taken. These methods which are mentioned above are appropriate for solving point reactor neutron kinetics equations. (ii) the relative error of decoupling method is large, under the calculation condition of this paper. When a higher reactivity is introduced, the calculation of decoupling method cannot be convergence. (iii) after three types of step reactivity are introduced respectively, the relative error of implicit Euler method is higher than any other method except decoupling method. The third highest is Gear method. (iv) when the higher reactivity is introduced, the relative error of explicit and implicit Euler method are almost coincident, and higher than any other methods obviously. (v) 4 methods are suitable for solution on these given conditions, which are implicit Runge-Kutta method, Taylor polynomial method, power series method and end point floating method, considering both the accuracy and stiffness.
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Zhang, Zhizhu, and Yun Cai. "A Numerical Solution to the Point Kinetic Equations Using Diagonally Implicit Runge Kutta Method." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60011.

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It would take a long time to solve the point kinetics equations by using full implicit Runge-Kutta (FIRK) for the strong stiffness. Diagonally implicit Runge-Kutta (DIRK) is a useful tool like FIRK to solve the stiff differential equations, while it could greatly reduce the computation compared to FIRK. By embedded low-order Runge-Kutta, DIRK is implemented with the time step adaptation technique, which improves the computation efficiency of DIRK. Through four typical cases with step, ramp sinusoidal and zig-zag reactivity insertions, it shows that the results obtained by DIRK are in perfect agreement with other available results and DIRK with adaptive time step technique has more efficiency than DIRK with the fixed time step.
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Cai, Yun, Xingjie Peng, Qing Li, Zhizhu Zhang, Zhumin Jiang, and Guo Rui. "Parallel Computation of the Point Neutron Kinetic Equations Using Parallel Revisionist Integral Deferred Correction." In 2018 26th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icone26-81205.

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The point kinetics is very important to the safety of the reactor operation. However, these equations are stiff and usually solved with very small time step. These equations are solved by Revisionist integral deferred correction (RIDC), which is a parallel time integration method. RIDC is a highly accurate method, and it reduces the error by iteration. Based on C++ and MPI, a four-core fourth-order RIDC is implemented and tested by several cases, such as step, ramp, and sinusoidal reactivity insertion. Compared with other methods, the time step of RIDC in the step reactivity insertion case is smaller, but it’s larger in the case of the sinusoidal reactivity insertion. RIDC can keep high accuracy while the time step is appropriately large. The numerical results also show that the speed-up ratio can achieve 2 when 4 processors are used.
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Wang, Xin, Kathryn D. Huff, Manuele Aufiero, Per F. Peterson, and Massimiliano Fratoni. "Coupled Reactor Kinetics and Heat Transfer Model for Fluoride Salt-Cooled High-Temperature Reactor Transient Analysis." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60728.

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Coupled reactor kinetics and heat transfer models have been developed at the University of California, Berkeley (UCB) to study Pebble-Bed, Fluoride-salt-cooled, High-temperature Reactors (PB-FHRs) transient behaviors. This paper discusses a coupled point kinetics model and a two-dimensional diffusion model. The former is based on the point kinetics equations with six groups of delayed neutrons and the lumped capacitance heat transfer equations. To account for the reflector effect on neutron lifetime, additional (fictional) groups of delayed neutrons are added in the point kinetics equations to represent the thermalized neutrons coming back from the reflectors. The latter is based on coupled multi-group neutron diffusion and finite element heat transfer model. Multi-group cross sections and diffusion coefficients are generated using the Monte Carlo code Serpent and defined as input in COMSOL 5.0.
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Fernanda Tumelero and Claudio Zen Petersen. "Perturbative Analysis of the Neutron Point Kinetics Equations with and without Temperature Feedback Effects by Polynomial Approach Method." In 23rd ABCM International Congress of Mechanical Engineering. Rio de Janeiro, Brazil: ABCM Brazilian Society of Mechanical Sciences and Engineering, 2015. http://dx.doi.org/10.20906/cps/cob-2015-0498.

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Reports on the topic "Point kinetics equations"

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Lahav, Ori, Albert Heber, and David Broday. Elimination of emissions of ammonia and hydrogen sulfide from confined animal and feeding operations (CAFO) using an adsorption/liquid-redox process with biological regeneration. United States Department of Agriculture, March 2008. http://dx.doi.org/10.32747/2008.7695589.bard.

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The project was originally aimed at investigating and developing new efficient methods for cost effective removal of ammonia (NH₃) and hydrogen sulfide (H₂S) from Concentrated Animal Feeding Operations (CAFO), in particular broiler and laying houses (NH₃) and hog houses (H₂S). In both cases, the principal idea was to design and operate a dedicated air collection system that would be used for the treatment of the gases, and that would work independently from the general ventilation system. The advantages envisaged: (1) if collected at a point close to the source of generation, pollutants would arrive at the treatment system at higher concentrations; (2) the air in the vicinity of the animals would be cleaner, a fact that would promote animal growth rates; and (3) collection efficiency would be improved and adverse environmental impact reduced. For practical reasons, the project was divided in two: one effort concentrated on NH₃₍g₎ removal from chicken houses and another on H₂S₍g₎ removal from hog houses. NH₃₍g₎ removal: a novel approach was developed to reduce ammonia emissions from CAFOs in general, and poultry houses in particular. Air sucked by the dedicated air capturing system from close to the litter was shown to have NH₃₍g₎ concentrations an order of magnitude higher than at the vents of the ventilation system. The NH₃₍g₎ rich waste air was conveyed to an acidic (0<pH<~5) bubble column reactor where NH₃ was converted to NH₄⁺. The reactor operated in batch mode, starting at pH 0 and was switched to a new acidic absorption solution just before NH₃₍g₎ breakthrough occurred, at pH ~5. Experiments with a wide range of NH₃₍g₎ concentrations showed that the absorption efficiency was practically 100% throughout the process as long as the face velocity was below 4 cm/s. The potential advantages of the method include high absorption efficiency, lower NH₃₍g₎ concentrations in the vicinity of the birds, generation of a valuable product and the separation between the ventilation and ammonia treatment systems. A small scale pilot operation conducted for 5 weeks in a broiler house showed the approach to be technically feasible. H₂S₍g₎ removal: The main goal of this part was to develop a specific treatment process for minimizing H₂S₍g₎ emissions from hog houses. The proposed process consists of three units: In the 1ˢᵗ H₂S₍g₎ is absorbed into an acidic (pH<2) ferric iron solution and oxidized by Fe(III) to S⁰ in a bubble column reactor. In parallel, Fe(III) is reduced to Fe(II). In the 2ⁿᵈ unit Fe(II) is bio-oxidized back to Fe(III) by Acidithiobacillus ferrooxidans (AF).In the 3ʳᵈ unit S⁰ is separated from solution in a gravity settler. The work focused on three sub-processes: the kinetics of H₂S absorption into a ferric solution at low pH, the kinetics of Fe²⁺ oxidation by AF and the factors that affect ferric iron precipitation (a main obstacle for a continuous operation of the process) under the operational conditions. H₂S removal efficiency was found higher at a higher Fe(III) concentration and also higher for higher H₂S₍g₎ concentrations and lower flow rates of the treated air. The rate limiting step of the H₂S reactive absorption was found to be the chemical reaction rather than the transition from gas to liquid phase. H₂S₍g₎ removal efficiency of >95% was recorded with Fe(III) concentration of 9 g/L using typical AFO air compositions. The 2ⁿᵈ part of the work focused on kinetics of Fe(II) oxidation by AF. A new lab technique was developed for determining the kinetic equation and kinetic parameters (KS, Kₚ and mₘₐₓ) for the bacteria. The 3ʳᵈ part focused on iron oxide precipitation under the operational conditions. It was found that at lower pH (1.5) jarosite accumulation is slower and that the performance of the AF at this pH was sufficient for successive operation of the proposed process at the H₂S fluxes predicted from AFOs. A laboratory-scale test was carried out at Purdue University on the use of the integrated system for simultaneous hydrogen sulfide removal from a H₂S bubble column filled with ferric sulfate solution and biological regeneration of ferric ions in a packed column immobilized with enriched AFbacteria. Results demonstrated the technical feasibility of the integrated system for H₂S removal and simultaneous biological regeneration of Fe(III) for potential continuous treatment of H₂S released from CAFO. NH₃ and H₂S gradient measurements at egg layer and swine barns were conducted in winter and summer at Purdue. Results showed high potential to concentrate NH₃ and H₂S in hog buildings, and NH₃ in layer houses. H₂S emissions from layer houses were too low for a significant gradient. An NH₃ capturing system was designed and tested in a 100-chicken broiler room. Five bell-type collecting devices were installed over the litter to collect NH₃ emissions. While the air extraction system moved only 10% of the total room ventilation airflow rate, the fraction of total ammonia removed was 18%, because of the higher concentration air taken from near the litter. The system demonstrated the potential to reduce emissions from broiler facilities and to concentrate the NH₃ effluent for use in an emission control system. In summary, the project laid a solid foundation for the implementation of both processes, and also resulted in a significant scientific contribution related to AF kinetic studies and ferrous analytical measurements.
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