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Journal articles on the topic 'Point kinetics equations'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Espinosa-Paredes, Gilberto, Marco-A. Polo-Labarrios, Erick-G. Espinosa-Martínez, and Edmundo del Valle-Gallegos. "Fractional neutron point kinetics equations for nuclear reactor dynamics." Annals of Nuclear Energy 38, no. 2-3 (February 2011): 307–30. http://dx.doi.org/10.1016/j.anucene.2010.10.012.

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12

Nahla, Abdallah A., and Mohammed F. Al-Ghamdi. "Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/282367.

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Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM) is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.

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13

Suescún-Díaz, D., and G. Espinosa-Paredes. "On the numerical solution of the point reactor kinetics equations." Nuclear Engineering and Technology 52, no. 6 (June 2020): 1340–46. http://dx.doi.org/10.1016/j.net.2019.11.034.

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14

Nahla, Abdallah A. "Taylor’s series method for solving the nonlinear point kinetics equations." Nuclear Engineering and Design 241, no. 5 (May 2011): 1592–95. http://dx.doi.org/10.1016/j.nucengdes.2011.02.016.

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15

Hamada, Yasser Mohamed. "Trigonometric Fourier-series solutions of the point reactor kinetics equations." Nuclear Engineering and Design 281 (January 2015): 142–53. http://dx.doi.org/10.1016/j.nucengdes.2014.11.017.

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16

Quintero-Leyva, Barbaro. "CORE: A numerical algorithm to solve the point kinetics equations." Annals of Nuclear Energy 35, no. 11 (November 2008): 2136–38. http://dx.doi.org/10.1016/j.anucene.2008.07.002.

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17

Wollmann da Silva, M., R. Vasques, B. E. J. Bodmann, and M. T. Vilhena. "A nonstiff solution for the stochastic neutron point kinetics equations." Annals of Nuclear Energy 97 (November 2016): 47–52. http://dx.doi.org/10.1016/j.anucene.2016.06.026.

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18

Aboanber, Ahmed E., and Abdallah A. Nahla. "A novel fractional technique for the modified point kinetics equations." Journal of the Egyptian Mathematical Society 24, no. 4 (October 2016): 666–71. http://dx.doi.org/10.1016/j.joems.2016.02.001.

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19

Espinosa-Paredes, G., M. A. Polo-Labarrios, L. Díaz-González, A. Vázquez-Rodríguez, and E. G. Espinosa-Martínez. "Sensitivity and uncertainty analysis of the fractional neutron point kinetics equations." Annals of Nuclear Energy 42 (April 2012): 169–74. http://dx.doi.org/10.1016/j.anucene.2011.11.023.

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20

Hamieh, S. D., and M. Saidinezhad. "Analytical solution of the point reactor kinetics equations with temperature feedback." Annals of Nuclear Energy 42 (April 2012): 148–52. http://dx.doi.org/10.1016/j.anucene.2011.12.021.

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21

Diniz, Rodrigo Costa, Alessandro da Cruz Gonçalves, and Felipe Siqueira de Souza da Rosa. "Adjusted mean generation time parameter in the neutron point kinetics equations." Annals of Nuclear Energy 133 (November 2019): 338–46. http://dx.doi.org/10.1016/j.anucene.2019.05.019.

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22

Sadeghi, H., and P. Darania. "On the approximate solutions of the fractional neutron point kinetics equations." Annals of Nuclear Energy 148 (December 2020): 107693. http://dx.doi.org/10.1016/j.anucene.2020.107693.

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23

Aboanber, A. E. "Analytical solution of the point kinetics equations by exponential mode analysis." Progress in Nuclear Energy 42, no. 2 (January 2003): 179–97. http://dx.doi.org/10.1016/s0149-1970(03)80008-2.

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24

Nahla, Abdallah A., and A. A. Hemeda. "Picard iteration and Padé approximations for stiff fractional point kinetics equations." Applied Mathematics and Computation 293 (January 2017): 72–80. http://dx.doi.org/10.1016/j.amc.2016.08.008.

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25

Fan, Gen, and Wen Bin Liu. "An Integral Method for Solving the Point Reactor Neutron Kinetics Equations with Newtonian Temperature Feedback." Advanced Materials Research 732-733 (August 2013): 83–89. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.83.

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A numerical integral method to efficiently solve the point kinetics equations with Newtonian temperature feedback is described and investigated, which employs the better basis function (BBF) for the approximation of the neutron density in integral of one time step. The numerical evaluation is performed by the developed BBF code. The code can solve the general non-linear kinetics problems with six groups of delayed neutron. For the application purposes, the developed code and the method are tested by using a variety of problems, including ramp reactivity input with or without temperature feedback. The results are shown that the BBF method is clearly an effective and accurate numerical method for solving the point kinetics equations with Newtonian temperature feedback, and it can be used in real time power reactor forecasting in order to prevent the reactivity accidents.

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26

Adebo, Oluwafemi Ayodeji, Ajibola Bamikole Oyedeji, Janet Adeyinka Adebiyi, Chiemela Enyinnaya Chinma, Samson Adeoye Oyeyinka, Oladipupo Odunayo Olatunde, Ezekiel Green, Patrick Berka Njobeh, and Kulsum Kondiah. "Kinetics of Phenolic Compounds Modification during Maize Flour Fermentation." Molecules 26, no. 21 (November 5, 2021): 6702. http://dx.doi.org/10.3390/molecules26216702.

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This study aimed to investigate the kinetics of phenolic compound modification during the fermentation of maize flour at different times. Maize was spontaneously fermented into sourdough at varying times (24, 48, 72, 96, and 120 h) and, at each point, the pH, titratable acidity (TTA), total soluble solids (TSS), phenolic compounds (flavonoids such as apigenin, kaempferol, luteolin, quercetin, and taxifolin) and phenolic acids (caffeic, gallic, ferulic, p-coumaric, sinapic, and vanillic acids) were investigated. Three kinetic models (zero-, first-, and second-order equations) were used to determine the kinetics of phenolic modification during the fermentation. Results obtained showed that fermentation significantly reduced pH, with a corresponding increase in TTA and TSS. All the investigated flavonoids were significantly reduced after fermentation, while phenolic acids gradually increased during fermentation. Among the kinetic models adopted, first-order (R2 = 0.45–0.96) and zero-order (R2 = 0.20–0.82) equations best described the time-dependent modifications of free and bound flavonoids, respectively. On the other hand, first-order (R2 = 0.46–0.69) and second-order (R2 = 0.005–0.28) equations were best suited to explain the degradation of bound and free phenolic acids, respectively. This study shows that the modification of phenolic compounds during fermentation is compound-specific and that their rates of change may be largely dependent on their forms of existence in the fermented products.

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27

Chen, Xiangyi, and Asok Ray. "On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant." Sci 2, no. 2 (April 26, 2020): 30. http://dx.doi.org/10.3390/sci2020030.

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This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

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28

Chen, Xiangyi, and Asok Ray. "On Singular Perturbation of Neutron Point Kinetics in the Dynamic Model of a PWR Nuclear Power Plant." Sci 2, no. 2 (May 27, 2020): 36. http://dx.doi.org/10.3390/sci2020036.

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This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

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29

Villar Goris, N. A., A. R. Selva Castañeda, E. E. Ramirez-Torres, J. Bory Reyes, L. Randez, L. E. Bergues Cabrales, and J. I. Montijano. "Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics." Revista Mexicana de Física 66, no. 5 Sept-Oct (September 1, 2020): 632. http://dx.doi.org/10.31349/revmexfis.66.632.

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The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.

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30

Kleene, K. C. "Equations describing the effects of the transient stability of subpopulations of nascent hnRNAs on the kinetics of turnover of hnRNA." Biochemical Journal 233, no. 3 (February 1, 1986): 905–8. http://dx.doi.org/10.1042/bj2330905.

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The equations that have been used previously to analyse the rate of decay of hnRNA implicitly assume that nascent hnRNAs are degraded stochastically. This assumption is inconsistent with electron-microscopic studies of transcription cited here, which show that nascent hnRNAs are not degraded during transcription, implying that hnRNA degradation occurs only after termination of transcription and release of the hnRNA from chromatin. Equations are derived describing the accumulation of radioactivity hnRNA during continuous labelling assuming that nascent hnRNAs are stable and that hnRNAs decay with first-order kinetics only after completion of transcription. The effects of the transient stability of nascent hnRNAs on the kinetics of hnRNA turnover can become important when the half-life of the hnRNA is shorter than the time to transcribe an hnRNA from the point of initiation to the point of termination. These equations should prove useful in studies of hnRNA turnover that require a precise description of the labelling kinetics of nascent and completed subpopulations of hnRNA.

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31

Aboanber, Ahmed E., Abdallah A. Nahla, and Ashraf M. El Mhlawy. "Mittag-Leffler and Padé approximations to stiff fractional two point kinetics equations." Progress in Nuclear Energy 104 (April 2018): 317–26. http://dx.doi.org/10.1016/j.pnucene.2017.12.002.

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32

Kinard, Matthew, and E. J. Allen. "Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics." Annals of Nuclear Energy 31, no. 9 (June 2004): 1039–51. http://dx.doi.org/10.1016/j.anucene.2003.12.008.

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33

Li, Haofeng, Wenzhen Chen, Lei Luo, and Qian Zhu. "A new integral method for solving the point reactor neutron kinetics equations." Annals of Nuclear Energy 36, no. 4 (May 2009): 427–32. http://dx.doi.org/10.1016/j.anucene.2008.11.033.

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34

Ganapol, B. D. "A highly accurate algorithm for the solution of the point kinetics equations." Annals of Nuclear Energy 62 (December 2013): 564–71. http://dx.doi.org/10.1016/j.anucene.2012.06.007.

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35

El_Tokhy, Mohamed S., and Imbaby I. Mahmoud. "Parameter analysis of the neutron point kinetics equations with feedback temperature effects." Annals of Nuclear Energy 68 (June 2014): 228–33. http://dx.doi.org/10.1016/j.anucene.2014.01.020.

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36

Nowak, Tomasz Karol, Kazimierz Duzinkiewicz, and Robert Piotrowski. "Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations." Annals of Nuclear Energy 73 (November 2014): 317–29. http://dx.doi.org/10.1016/j.anucene.2014.07.001.

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37

Cai, Yun, Xingjie Peng, Qing Li, and Kan Wang. "A numerical solution to the nonlinear point kinetics equations using Magnus expansion." Annals of Nuclear Energy 89 (March 2016): 84–89. http://dx.doi.org/10.1016/j.anucene.2015.11.021.

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38

Espinosa-Paredes, Gilberto. "Fractional-space neutron point kinetics (F-SNPK) equations for nuclear reactor dynamics." Annals of Nuclear Energy 107 (September 2017): 136–43. http://dx.doi.org/10.1016/j.anucene.2016.08.007.

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39

Espinosa-Paredes, Gilberto, and Carlos G. Aguilar-Madera. "Scaled neutron point kinetics (SUNPK) equations for nuclear reactor dynamics: 2D approximation." Annals of Nuclear Energy 115 (May 2018): 377–86. http://dx.doi.org/10.1016/j.anucene.2018.01.020.

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40

DEEPU, MUKUNDAN NAIR, and SADANAND SADASHIV GOKHALE. "MODELING OF SUPERSONIC COMBUSTION USING POINT IMPLICIT FINITE VOLUME METHOD." International Journal of Computational Methods 04, no. 02 (June 2007): 353–66. http://dx.doi.org/10.1142/s0219876207001060.

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Numerical modeling of turbulent-reacting flow field in supersonic combustors is presented. When flow field and chemical kinetics with differing time scales need to be solved simultaneously, explicit treatment of all conservation terms with reaction chemistry results in stiff equations and has a tendency to degrade the performance of numerical method. A method of preconditioning, in which the conservation equations in conjunction with chemical source terms alone is treated implicitly. Such a method has the advantage of both explicit and implicit methods. A code was developed using above method and tested successfully for a supersonic combustor configuration.

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41

DHANOA, M. S., S. LÓPEZ, R. SANDERSON, and J. FRANCE. "Simplified estimation of forage degradability in the rumen assuming zero-order degradation kinetics." Journal of Agricultural Science 147, no. 3 (December 8, 2008): 225–40. http://dx.doi.org/10.1017/s0021859608008241.

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SUMMARYIn the present paper, a simplified procedure using few in situ data points is derived and then evaluated (using a large database) against reference values estimated with the standard nylon bag first-order kinetics model. The procedure proposed involved a two-stage mathematical process, with a statistical prediction of some degradation parameters (such as lag time) and then a kinetic model derived by assuming degradation follows zero-order kinetics to determine effective degradability in the rumen (E). In addition to the estimation of washout fraction and discrete lag, which is common to both procedures, the simplified procedure requires measurement of dry matter losses at one incubation time point only. Thus, interference of the animal rumen will be much reduced, which will lead to increased capacity for feed evaluation. Calibration of the zero-order model against the first-order model showed that suitable estimates of E can be obtained with disappearance at 24, 48 or 72 h as the single incubation end time point. The strength of the calibration is such that an end incubation time point as low as 24 h may be sufficient, which may reduce substantially the total incubation time required and thus the impact on the experimental animal. Relevant regression equations to predict reference values of parameters such as lag time or E are also developed and validated.

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42

Wannan, Rania, Muhammad Aslam, Muhammad Farman, Ali Akgül, Farhina Kouser, and Jihad Asad. "Fractional Order Techniques for Stiff Differential Equations Arising from Chemistry Kinetics." European Journal of Pure and Applied Mathematics 15, no. 3 (July 31, 2022): 1144–57. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4406.

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In this paper, we consider the stiff systems of ordinary differential equations arising from chemistry kinetics. We develop the fractional order model for chemistry kinetics problems by using the Caputo Fabrizio and Atangana-Baleanu derivatives in Caputo sense. We apply the Sumudu transform to obtain the solutions of the models. Uniqueness and stability analysis ofthe problem are also established by using the fixed point theory results. Numerical results are obtained by using the proposed schemes which supports theoretical results. These concepts are very important for using the real-life problems like Brine tank cascade, Recycled Brine tank cascade, pond pollution, home heating and biomass transfer problem. These results are crucial for solving the nonlinear model in chemistry kinetics.

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43

Schiassi, Enrico, Mario De Florio, Barry D. Ganapol, Paolo Picca, and Roberto Furfaro. "Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics." Annals of Nuclear Energy 167 (March 2022): 108833. http://dx.doi.org/10.1016/j.anucene.2021.108833.

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44

Ganapol, Barry. "A refined way of solving reactor point kinetics equations for imposed reactivity insertions." Nuclear Technology and Radiation Protection 24, no. 3 (2009): 157–66. http://dx.doi.org/10.2298/ntrp0903157g.

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We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs). The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg), is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.

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45

Suescún-Díaz, Daniel, Yohan M. Oviedo-Torres, and Luis E. Girón-Cruz. "Solution of the stochastic point kinetics equations using the implicit Euler-Maruyama method." Annals of Nuclear Energy 117 (July 2018): 45–52. http://dx.doi.org/10.1016/j.anucene.2018.03.013.

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46

Zhu Qian, Shang Xue-Li, and Chen Wen-Zhen. "Homotopy analysis solution of point reactor kinetics equations with six-group delayed neutrons." Acta Physica Sinica 61, no. 7 (2012): 070201. http://dx.doi.org/10.7498/aps.61.070201.

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47

KOBAYASHI, Keisuke. "Rigorous Derivation of Multi-Point Reactor Kinetics Equations with Explicit Dependence on Perturbation." Journal of Nuclear Science and Technology 29, no. 2 (February 1992): 110–20. http://dx.doi.org/10.1080/18811248.1992.9731503.

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48

Depner, T. A., and J. T. Daugirdas. "Equations for normalized protein catabolic rate based on two-point modeling of hemodialysis urea kinetics." Journal of the American Society of Nephrology 7, no. 5 (May 1996): 780–85. http://dx.doi.org/10.1681/asn.v75780.

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The normalized protein catabolic rate (PCRn) can be calculated from predialysis and postdialysis BUN measurements in patients receiving intermittent dialysis. This measure of net protein catabolism, adjusted for body size, is a useful clinical measure of nutrition that correlates with patient outcome and, in patients who are in nitrogen balance, is a reasonable estimate of dietary protein intake. Whereas simplified formulae that estimate the per-treatment dose of hemodialysis, expressed as Kt/Vurea (Kt/V), are in common use, simplified methods for determining PCRn have only recently appeared. In the study presented here, equations were derived for calculating PCRn from the predialysis BUN and Kt/V. The equations were of the general form: PCRn = C0/(a + bKt/V + c/(Kt/NLL)) + 0.168, where Co is the predialysis BUN in mg/dL. Three sets of coefficients were developed for patients dialyzed thrice weekly: one for patients dialyzed after the long interval at the beginning of the week, one for patients dialyzed at midweek, and the third for patients dialyzed at the end of the week. Two similar sets of coefficients were developed for patients dialyzed twice weekly. For patients with remaining function in the native kidney remnant, equations were developed and refined for upgrading PCRn by adjusting C0 upward. The equations were validated by comparing the calculated PCRn with PCRn determined by a formal iterative model of urea kinetics in a series of 119 dialyses in 51 patients dialyzed thrice weekly (r = 0.9952; mean absolute error, 1.97 +/- 1.39%) and in a series of 71 dialyses in 25 patients dialyzed twice weekly (r = 0.9956; mean absolute error, 2.17 +/- 1.56%). These simple yet accurate equations should be useful in epidemiologic studies or in clinical laboratories where limited data are available for each patient or when iterative computer techniques cannot be applied.

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Kale, Vivek, Rakesh Kumar, K. Obaidurrahman, and Avinash Gaikwad. "Linear stability analysis of a nuclear reactor using the lumped model." Nuclear Technology and Radiation Protection 31, no. 3 (2016): 218–27. http://dx.doi.org/10.2298/ntrp1603218k.

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The stability analysis of a nuclear reactor is an important aspect in the design and operation of the reactor. A stable neutronic response to perturbations is essential from the safety point of view. In this paper, a general methodology has been developed for the linear stability analysis of nuclear reactors using the lumped reactor model. The reactor kinetics has been modelled using the point kinetics equations and the reactivity feedbacks from fuel, coolant and xenon have been modelled through the appropriate time dependent equations. These governing equations are linearized considering small perturbations in the reactor state around a steady operating point. The characteristic equation of the system is used to establish the stability zone of the reactor considering the reactivity coefficients as parameters. This methodology has been used to identify the stability region of a typical pressurized heavy water reactor. It is shown that the positive reactivity feedback from xenon narrows down the stability region. Further, it is observed that the neutron kinetics parameters (such as the number of delayed neutron precursor groups considered, the neutron generation time, the delayed neutron fractions, etc.) do not have a significant influence on the location of the stability boundary. The stability boundary is largely influenced by the parameters governing the evolution of the fuel and coolant temperature and xenon concentration.

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50

Nowak, Tomasz Karol, Kazimierz Duzinkiewicz, and Robert Piotrowski. "Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor." Archives of Control Sciences 24, no. 2 (June 1, 2014): 129–54. http://dx.doi.org/10.2478/acsc-2014-0009.

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Abstract This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.

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