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Nuclear Reactor Kinetics: 1934–1999 and Beyond

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Abstract

When one of the editors of this book, Professor Yousry Azmy, asked me to give a lecture on the development of reactor kinetics during the twentieth century and the future direction of research in this area in the twenty-first century, my reaction was, “Wow! Review the developments of a century of reactor kinetics. That’s a lot to cover.” But then, upon reflection on the fact that the discipline of reactor kinetics, and reactor physics in general, did not even exist until the 1930s, I realized that I did not have to review a whole century of development, but rather, a mere two thirds of the century! Still a somewhat daunting task!

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Notes

  1. 1.

    For a collection of articles on reactor kinetics, which included the kinetics of neutron pulses, see the following conference proceedings, which contains many articles that were representative of the state-of-the-art in the late 1960s: Hetrick, D. L. (Editor), Dynamics of Nuclear Systems. 1972, Tucson, AZ: University of Arizona Press.

  2. 2.

    For example see: Schiff, L. I., Quantum Mechanics, 3rd Edition. 1968, New York: McGraw-Hill; or Messiah, A., Quantum Mechanics, Volume I. 1958, Amsterdam, The Netherlands: North Holland; or Dirac, P.A.M., Principles of Quantum Mechanics, 4th Edition. 1958, Oxford: The Oxford University Press.

References

  1. Duderstadt JJ, Hamilton LJ (1976) Nuclear reactor analysis. Wiley, New York

    Google Scholar 

  2. Henry AF (1975) Nuclear-reactor analysis. MIT Press, Cambridge, MA

    Google Scholar 

  3. Glasstone S, Edlund MC (1952) The elements of nuclear reactor theory. Van Nostrand, New York

    Google Scholar 

  4. Murray RL (1957) Nuclear reactor physics. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  5. Meghreblian RV, Holmes DK (1960) Reactor analysis. McGraw-Hill, New York

    Google Scholar 

  6. Lamarsh JR (1966) Introduction to nuclear reactor theory. Addison-Wesley Series in Nuclear Engineering. Addison-Wesley, Reading, MA

    Google Scholar 

  7. Bell GI, Glasstone S (1970) Nuclear reactor theory. Van Nostrand Reinhold, New York

    Google Scholar 

  8. Weinberg AM, Wigner EP (1958) The physical theory of neutron chain reactors. The University of Chicago Press, Chicago, IL

    Google Scholar 

  9. Davison B (1958) Neutron transport theory. The International Series of Monographs on Physics. The Oxford University Press, London/New York

    Google Scholar 

  10. Case KM, Zweifel PF (1967) Linear transport theory. Addison-Wesley, Reading, MA

    MATH  Google Scholar 

  11. Duderstadt JJ, Martin WR (1979) Transport theory. Wiley, New York

    MATH  Google Scholar 

  12. Keepin GR (1965) Physics of nuclear kinetics. Addison-Wesley Series in Nuclear Science and Engineering. Addison-Wesley, Reading, MA

    Google Scholar 

  13. Hetrick DL (1971) Dynamics of nuclear reactors. The University of Chicago Press, Chicago, IL

    Google Scholar 

  14. Akcasu Z, Lellouche GS, Shotkin LM (1971) Mathematical methods in nuclear reactor dynamics. Academic, New York

    Google Scholar 

  15. Stacey WM (1969) Space-time nuclear reactor kinetics. Nuclear science and technology. Academic, New York

    Google Scholar 

  16. Segrè E (Chairman of the Editorial Board) (1962) Enrico Fermi – Collected Papers, vol I, Italy 1921–1938. The University of Chicago Press, Chicago, IL

    Google Scholar 

  17. Segrè E (Chairman of the Editorial Board) (1962) Enrico Fermi – Collected Papers, vol II, United States 1939–1954. The University of Chicago Press, Chicago, IL

    Google Scholar 

  18. Wightman AS (Ed) (1992) The collected works of Eugene Paul Wigner, Part A The Scientific Papers, vol V. In: Weinberg AM (ed) Nuclear energy. Springer, Berlin/New York

    Google Scholar 

  19. Amaldi E, Fermi E (1936) Sull’Assorbimento dei Neutroni Lenti. – III. Ricerca Scientifica 7(1):56–59

    Google Scholar 

  20. FermiE, Amaldi E, Pontecorvo B, Rasetti F, Segrè E (1934) Influence of hydrogeneous substances on the radioactivity produced by neutrons – I. Ricerca Scientifica 5(2):282–283

    Google Scholar 

  21. Fermi E (1936) Sul Moto dei Neutroni nelle Sostanze Idrogenate. Ricerca Scientifica. 7(2):13–52

    Google Scholar 

  22. Wigner EP (1942) On Variations of the power output in a running pile, CP-351 (Chicago Project Report), November 11, Chicago University, Metallurgical Laboratory: Chicago, IL (see in [18] above)

    Google Scholar 

  23. Fermi E (1942) Problem of time dependence of the reaction rate: effect of delayed neutrons emission, CP-291 (Chicago Project Report), October 7, Chicago University, Metallurgical Laboratory: Chicago, IL (see [17] above)

    Google Scholar 

  24. Parks DE, Nelkin MS, Wikner NF, Beyster JR (1970) Slow Neutron Scattering and Thermalization, with Reactor Applications. WA Benjamin, New York

    Google Scholar 

  25. Beckurts KH, Wirtz K (1964) Neutron physics. Springer, New York

    MATH  Google Scholar 

  26. Williams MMR (1966) The slowing down and thermalization of neutrons. North-Holland, Amsterdam

    Google Scholar 

  27. Ussachoff LN (1955) Equation for the importance of neutrons, kinetics and the theory of perturbations. Proceedings international conference on peaceful uses of atomic energy, Geneva, 1955, P/656, 5: p. 503–510. Columbia University Press, New York

    Google Scholar 

  28. Henry AF (1955) Computation of parameters appearing in the reactor kinetics equations, WAPD-124, December 1955, Westinghouse Electric Corp. Bettis Plant, Pittsburgh, PA

    Google Scholar 

  29. Henry AF (1958) Application of reactor kinetics to the analysis of experiments. Nucl Sci Eng 3:52–70

    Google Scholar 

  30. Lewins J (1965) Importance, the adjoint function: the physical basis of variational and perturbation theory in transport and diffusion problems. Pergamon, Oxford/New York

    Google Scholar 

  31. Henry AF, Curlee NJ (1958) Verification of a method of treating neutron space-time problems. Nucl Sci Eng 4:727

    Google Scholar 

  32. Kaplan S (1961) The property of finality and the analysis of problems in reactor space-time kinetics by various modal expansions. Nucl Sci Eng 9:357

    Google Scholar 

  33. Henry AF (1964) The application of inhour modes to the description of nonseparable reactor transients. Nucl Sci Eng 20:338–351

    Google Scholar 

  34. Ott K, Meneley D (1969) Accuracy of the quasistatic treatment of spatial reactor kinetics. Nucl Sci Eng 36(3):402

    Google Scholar 

  35. Ott K, Madell JT (1966) Quasistatic treatment of spatial phenomena in reactor dynamics. Nucl Sci Eng 26(4):563

    Google Scholar 

  36. Stacey Jr, WM, Adams CH (1967) Time-integrated method: a quasistatic neutron space-time approximation. Trans Am Nucl Soc 10:251–252

    Google Scholar 

  37. Lewins J (1960) The approximate separation of kinetics problems into time and space functions by a variational principle. J Nucl Energy Part A 12:108

    Google Scholar 

  38. Gyftopoulos EP (1964) General reactor dynamics. In: Thompson TJ, Beckerly JG (eds) The technology of nuclear reactor safety, vol I. MIT Press, Cambridge, MA, pp 175–204

    Google Scholar 

  39. Becker M (1968) A generalized formulation of point nuclear reactor kinetics equations. Nucl Sci Eng 31(3):458–463

    Google Scholar 

  40. Dorning J, Spiga G (1978) Point kinetics as an asymptotic representation of space-dependent, energy-dependent, and angle-dependent reactor kinetics. Trans Am Nucl Soc 28(June):761–762

    Google Scholar 

  41. Stakgold I (1967) Boundary value problems of mathematical physics, vol 1. Macmillan, New York/Collier-Macmillan Ltd, London

    MATH  Google Scholar 

  42. Dorning JJ (1980) Point kinetics with omega-mode shape functions via multiple-time-scale asymptotics. Trans Am Nucl Soc 34(June):281–283

    Google Scholar 

  43. Hille E, Phillips RS (1957) Functional Analysis and Semi-Groups, Rev. Ed., American Mathematical Society, Providence, RI

    Google Scholar 

  44. Lehner J, Wing GM (1955) On the spectrum of an unsymmetric operator arising in the transport theory of neutrons. Commun Pure Appl Math 8:217–234 (see also Wing GM (1962) An introduction to transport theory. Wiley, New York)

    MATH  MathSciNet  Google Scholar 

  45. Corngold N (1964) Some transient phenomena in thermalization. Part 1, Theory. Nucl Sci Eng 19:80

    Google Scholar 

  46. Bednarz R (1965) Spectrum of the Boltzmann operator with an isotropic thermalization kernel. In: Proceedings IAEA symposium on pulsed neutron research, vol I. IAEA, Vienna, p 259

    Google Scholar 

  47. Albertoni S, Montagnini B (1965) Some spectral properties of the transport equation and their relevance to pulsed neutron experiments. In: Proceedings IAEA symposium on pulsed neutron research, vol I. IAEA, Vienna, p 239

    Google Scholar 

  48. Dorning JJ, Thurber JK ( 1968) Unstable pulsed-neutron decay states in non-crystalline moderators. Trans Am Nucl Soc 11:290

    Google Scholar 

  49. Conn R, Corngold N (1969) A theory of pulsed neutron experiments in polycrystalline media. Nucl Sci Eng 37(1):85

    Google Scholar 

  50. Dorning JJ (1968) Time-dependent neutron thermalization in finite light water systems. Nucl Sci Eng 33(1):81–92

    Google Scholar 

  51. Nelkin M (1960) Scattering of slow neutrons by water. Phys Rev 119(2):741–746

    Google Scholar 

  52. Koppel JU, Young JA (1964) Neutron scattering by water taking into account the anisotropy of the molecular vibrations. Nucl Sci Eng 19:412

    Google Scholar 

  53. Küchle MF, Mitzel F, Wattecamps E, Werle H (1966) Proceedings international conference fast critical experiments and their analysis, ANL-7320. Argonne National Laboratory, Argonne, IL, p 506

    Google Scholar 

  54. Dorning J (1972) Fast and thermal prompt kinetics via models. In: Hetrick DL (ed) Dynamics of nuclear systems. The University of Arizona Press, Tucson, AZ

    Google Scholar 

  55. Dorning J, Nicolaenko B, Thurber JK (1969) Unstable decay states of far subcritical fast assemblies. Trans Am Nucl Soc 12(1):251 (see also Dorning J, Nicolaenko B, Thurber JK (1969) Some mathematical considerations on Cauchy integrals related to pulsed neutron dispersion relations. In: Neutron transport theory conference. ORO-3858–1, U.S. Atomic Energy Commission, Washington, DC, pp 76–121)

    Google Scholar 

  56. Dorning J, Nicolaenko B, Thurber JK (1969) Theory of pulse decay in subcritical fast systems with general cross sections. Trans Am Nucl Soc 12(2):656

    Google Scholar 

  57. Dorning J, Nicolaenko B, Thurber JK (1969) Time-behavior of pseudo-modes in subcritical fast systems described by exact elastic slowing down. Trans Am Nucl Soc 12(2):657

    Google Scholar 

  58. Mitzel F, Schroeter E (1969) Gepulste Experimente an der Schnellen Unterkritischen Anlage Karlsruhe (SUAK) und Vergleich der Ergebnisse mit Berechnungen. Nukleonik 12:110–117

    Google Scholar 

  59. Gelbard EM (1973) Twenty years of reactor computation in retrospect. In: Proceedings conference numerical models and computational techniques for analysis of nuclear systems. NTIS, US Department of Commerce, Springfield, VA, p xxi–xxvi

    Google Scholar 

  60. Burns TJ, Dorning JJ (1973) A partial current balance method for space-, and energy-dependent reactor calculations.” In: Proceedings national topical meeting on mathematical models and computational techniques for analysis of nuclear systems, vol II. CONF-73044. American Nuclear Society, LaGrange Park, IL, p VII.162–VII.178 (see also Burns TJ, Dorning JJ (1975) Multidimensional applications of an integral balance technique for neutron diffusion computations. In: National topical meeting on computational methods in nuclear engineering, vol II. CONF-750413. US Energy Research and Development Agency, Washington, DC, pp V.57–V.68

    Google Scholar 

  61. Shober, RA, Henry AF (1976) Approximate analytical method for determining nodal fluxes. Trans Am Nucl Soc. 24(Nov 19):192–193

    Google Scholar 

  62. Birkhofer A, Werner W (1973) Efficiency of various methods for the analysis of space time kinetics. In: Proceedings national topical meeting on mathematical models and computational techniques for analysis of nuclear systems, vol II. CONF-730414. American Nuclear Society, LaGrange Park, IL, p IX–31

    Google Scholar 

  63. Lawrence RD, Dorning JJ (1978) Nodal Green-function method for multidimensional neutron diffusion calculations. Trans Am Nucl Soc 28(June):248–249

    Google Scholar 

  64. Lawrence RD, Dorning JJ (1980) A nodal Green-function method for multidimensional neutron diffusion calculations. Nucl Sci Eng 76(2):218–231

    Google Scholar 

  65. Greenman G, Smith KS, Henry AF (1979) Recent advances in an analytic nodal model for static and transient reactor analysis. In: Proceedings national topical meeting on computational methods in nuclear engineering, CONF-790402. American Nuclear Society, LaGrange Park, IL, p 3.49

    Google Scholar 

  66. Finnemann H (1975) A consistent nodal method for the analysis of space-time effects in large LWRs. In: Joint NEACRP/CSNI specialist’s meeting on new developments in three dimensional neutron kinetics and review of kinetics benchmark calculations. Laboratorium für Reaktorregelung und Anlagensicherung, Garching (Munich), Germany

    Google Scholar 

  67. Finnemann H, Bennewitz F, Wagner MR (1977) Interface current techniques for multidimensional reactor calculations. Atomkernenergie 30(2):123–128

    Google Scholar 

  68. Wagner MR (1979) A nodal discrete-ordinate method for the numerical solution of the multidimensional transport equation. In: Proceedings American nuclear society topical meeting on computational methods in nuclear engineering, vol 2. American Nuclear Society, LaGrange Park, IL, p IV–177

    Google Scholar 

  69. Dorning, JJ (1979) Modern coarse mesh methods, a development of the 70’s. In: Proceedings American nuclear society topical meeting on computational methods in nuclear engineering, vol 1. American Nuclear Society, LaGrange Park, IL, p III–1

    Google Scholar 

  70. Lawrence RD, Dorning JJ (1979) New course-mesh diffusion and transport methods for the efficient numerical calculation of multi-dimensional reactor power distributions. In: OECD/NEA-CRP specialists’ meeting on calculations of 3-dimensional rating distributions in operating reactors. OECD, Paris, p 383 (see also Lawrence RD, Dorning JJ (1980) A nodal integral transport theory method for multidimensional reactor physics and shielding calculations. In: Proceedings of the American nuclear society international topical meeting on 1980 advances in reactor physics and shielding. American Nuclear Society, LaGrange Park, IL, pp 240–251

    Google Scholar 

  71. Walters WF, Odell RD (1981) Nodal methods for discrete-ordinates transport problems in (X, Y) geometry. In: Proceedings American nuclear society topical meeting on advances in mathematical methods for the solution of nuclear engineering problems, vol 1. American Nuclear Society, Munich, Germany, p 115

    Google Scholar 

  72. Badruzzaman A, Xie Z, Dorning JJ, Ullo JJ (1984) A discrete nodal transport method for three-dimensional reactor physics and shielding calculations. In: Proceedings American nuclear society topical meeting on reactor physics and shielding, vol 1. American Nuclear Society, LaGrange Park, IL, p 170

    Google Scholar 

  73. Dorning JJ (1985) Nodal transport methods after five years. In: Proceedings of the American nuclear society international topical meeting on advances in nuclear engineering computational methods. American Nuclear Society, LaGrange Park, IL, p 412

    Google Scholar 

  74. Smith KS (1986) Assembly homogenization techniques for light water-reactor analysis. Prog Nucl Energy 17(3):303–335

    Google Scholar 

  75. Lawrence RD (1986) Progress in nodal methods for the solution of the neutron diffusion and transport equations. Prog Nucl Energy 17(3):271–301

    MathSciNet  Google Scholar 

  76. Koebke K (1978) A new approach to homogenization and group condensation. In: IAEA technical committee meeting on homogenization methods in reactor physics. IAEA, Vienna

    Google Scholar 

  77. LarsenEW (1975) Neutron-transport and diffusion in inhomogeneous-media.1. J Math Phys 16(7):1421–1427

    Google Scholar 

  78. Larsen EW (1976) Neutron-transport and diffusion in inhomogeneous-media.2. Nucl Sci Eng 60(4):357–368

    Google Scholar 

  79. Chiang RT, Dorning JJ (1980) A homogenization theory for lattices with burnup and non-uniform loadings. In: Proceedings of the American nuclear society international topical meeting on 1980 advances in reactor physics and shielding. American Nuclear Society, LaGrange Park, IL, p 319–329

    Google Scholar 

  80. Zhang H, Rizwan-uddin, Dorning JJ (1997) Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods: Part II. Transport Theory Stat Phys 26(4):433–468

    MATH  MathSciNet  Google Scholar 

  81. Zhang H, Rizwan-uddin, Dorning JJ (1997) A multiple-scales systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies. Transport Theory Stat Phys 26(7):765–811

    MATH  MathSciNet  Google Scholar 

  82. Jackson CJ, Cacuci DG, Finnemann HB (1999) Dimensionally adaptive neutron kinetics for multidimensional reactor safety transients - I: new features of RELAP5/PANBOX. Nucl Sci Eng 131(2):143–163

    Google Scholar 

  83. Jackson CJ, Cacuci DG, Finnemann HB (1999) Dimensionally adaptive neutron kinetics for multidimensional reactor safety transients – II: dimensionally adaptive switching algorithms. Nucl Sci Eng 131(2):164–186

    Google Scholar 

  84. Wachspress EL (1966) Iterative solution of elliptical systems. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  85. Clark M, Hansen KF (1964) Numerical methods of reactor analysis. Academic, New York

    MATH  Google Scholar 

  86. Varga RS (1962) Matrix iterative analysis. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  87. Greenspan H, Kelber CN, Okrent D (1968) Computing methods in reactor physics. Gordon & Breach, New York

    MATH  Google Scholar 

  88. Cadwell WR, Henry AF, Vigilotti AJ (1964) WIGLE: A program for the solution of the two-group space-time diffusion equations in slab geometry, WAPD-TM-416. Pittsburgh, PA, Westinghouse Bettis Atomic Power Laboratory. See also: Henry AF, Vota AV (1965) WIGL2: A program for the solution of the one-dimensional, two-group, space-time diffusion equations accounting for temperature, xenon, and control feedback, WAPD-TM-532, Westinghouse Atomic Power Laboratory, Pittsburgh, PA

    Google Scholar 

  89. Yasinsky JB, Natelson M, Hageman LA (1968) TWIGL – a program to solve the two-dimensional, two-group, space-time neutron diffusion equations with temperature feedback, WAPD-TM-748, Westinghouse Bettis Atomic Power Laboratory, Pittsburgh, PA

    Google Scholar 

  90. Courant R, Hilbert D (1953) Methods of mathematical physics. Interscience Publishers, New York

    Google Scholar 

  91. Kantorovich LV, Krylov VI (1964) Approximate methods of higher analysis. Interscience Publishers, New York

    Google Scholar 

  92. Kahan T, Rideau G (1952) Sur la Déduction de Divers Principes Variationnelles de la Théorie des Collisions à Partir d’un Principe Unique. Journal de Physique et Radiation 13:326–332

    MATH  MathSciNet  Google Scholar 

  93. Roussopoulos P (1953) Méthodes Variationnelles en Théorie des Collisions. Comptes Rendus Académie Science 236:1858–1856

    MATH  Google Scholar 

  94. Selengut DS (1959) Variational analysis of a multi-dimensional system. In: Hanford Works Quarterly Physics Report HW-59126. Hanford, WA, p 89–124

    Google Scholar 

  95. Stacey WM (1967) Variational functionals for space-time neutronics. Nucl Sci Eng 30(3):448

    MathSciNet  Google Scholar 

  96. Michael EPE, Dorning JJ (2001) Studies on nodal methods for the time-dependent convection diffusion equation. In: Proceedings of the American nuclear society international meeting on mathematical methods for nuclear applications. American Nuclear Society, LaGrange Park, IL

    Google Scholar 

  97. Michael EPE, Dorning JJ (2001) A primitive-variable nodal method for the time-dependent Navier–Stokes equations. In: Proceedings of the American nuclear society international meeting on mathematical methods for nuclear applications. American Nuclear Society, LaGrange Park, IL

    Google Scholar 

  98. Mays BE, Dorning JJ (2001) A nodal integral method for the dissipative shallow-water equations with Coriolis force. In: Proceedings of the American nuclear society international meeting on mathematical methods for nuclear applications. American Nuclear Society, LaGrange Park, IL

    Google Scholar 

  99. Azmy YY, Dorning JJ (1983). A nodal integral approach to the numerical solution of partial differential equations. In: Proceedings American Nuclear Society International Topical Meeting on Advances in Reactor Computations, vol II. American Nuclear Society, LaGrange Park, IL, pp 893–909

    Google Scholar 

  100. Ougouag AM, Dorning JJ (1980) A hybrid nodal Green’s function method for multigroup multidimensional neutron diffusion calculations. In: Proceedings American nuclear society international topical meeting on 1980 advances in reactor physics and shielding. American Nuclear Society, LaGrange Park, IL, pp 228–239

    Google Scholar 

  101. Ougouag AM, Rajic HL (1988) Illico-HO: a self-consistent higher-order coarse-mesh nodal method. Nucl Sci Eng 100(3):332–341

    Google Scholar 

  102. Azmy YY (1988) The weighted diamond-difference form of nodal transport methods. Nucl Sci Eng 98(1):29–40

    Google Scholar 

  103. Koebke K (1981) Advances in homogenization and dehomogenization. In: Proceedings international topical meeting on advances in mathematical methods for the solution of nuclear engineering problems, vol 2. American Nuclear Society, Munich, Germany, p 59

    Google Scholar 

  104. Smith KS, Henry AF, Lorentz R (1980) Nucl Sci Eng 17:303–335

    Google Scholar 

  105. Grad H (1958) Principles of the kinetic theory of gasses. In: Flügge S (ed) Handbuch Der Physik, Band XII. Springer, Berlin

    Google Scholar 

  106. Zhang H, Rizwan-uddin, Dorning JJ (1995) Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods – 1: diffusion equation-based theory. Nucl Sci Eng 121(2):226–244

    Google Scholar 

  107. Dorning J (2003) Homogenized multigroup and energy-dependent diffusion equations as asymptotic approximations to the Boltzmann equation. Trans Am Nucl Soc 89:313–316

    Google Scholar 

  108. Larsen EW (1977) A homogenized multigroup diffusion theory for the neutron transport equation. In: Glowinski R, Leon JL (eds) Third international symposium on computing methods in applied sciences and engineering. Lecture Noted in Mathematics, vol 704, 1979. Springer, Berlin, p 357

    Google Scholar 

  109. Dorning JJ, Chiang RT (1980) A simultaneous development of point kinetics and lattice homogenization theory. In: Proceedings American Nuclear Society International Topical Meeting on 1980 Advances in Reactor Physics and Shielding. American Nuclear Society, LaGrange Park, IL, pp 309–318

    Google Scholar 

  110. Chernick J (1960) The dynamics of a xenon-controlled reactor. Nucl Sci Eng 8:233–243

    Google Scholar 

  111. Chernick J, Lellouche G, Wollman W (1961) The effect of temperature on xenon instability. Nucl Sci Eng 10:120–131

    Google Scholar 

  112. Canosa J, Brooks H (1966) Xenon-induced oscillations. Nucl Sci Eng 26:237

    Google Scholar 

  113. Christoffersen AP, Levine MM, Michael PA, Price GA (1973) Jack Chernick 1911–1971– Selected Papers. Brookhaven National Laboratory, Upton, New York

    Google Scholar 

  114. Ledinegg M (1938) In stability of flow during natural and forced convection. Die Wärme 61(2):8

    Google Scholar 

  115. Chernick J (1962) A review of nonlinear reactor dynamics problems, BNL 774 (T-291). Physics: Reactor Technology – TID-4500, 18th edn. Brookhaven National Laboratory, Upton, New York

    Google Scholar 

  116. Lahey Jr, RT, Moody FJ (1977) The thermal-hydraulics of a boiling water nuclear reactor. The American Nuclear Society, LaGrange Park, IL

    Google Scholar 

  117. Strogatz SH (1994) Nonlinear dynamics and chaos. Perseus Books (Westview Press), Cambridge, MA

    Google Scholar 

  118. Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New York

    MATH  Google Scholar 

  119. Achard J-L, Drew DA, Lahey Jr RT (1985) The analysis of nonlinear density – wave oscillations in boiling channels. J Fluid Mech 98:616

    MathSciNet  Google Scholar 

  120. Rizwan-uddin, Dorning JJ (1986) Some nonlinear dynamics of a heated channel. Nucl Eng Design 93:1–14

    Google Scholar 

  121. Karve AA, Dorning JJ, Rizwan-uddin (1997) Out-of-phase power oscillations in boiling water reactors. In: Proceedings of the joint international conference on mathematical methods and supercomputing for nuclear applications, vol 2. American Nuclear Society, LaGrange Park, IL, pp 1633–1647

    Google Scholar 

  122. Rizwan-uddin, Dorning JJ (1992) Stability of advanced boiling water reactors. In: American Nuclear Society Proceedings of the 1992 National Heat Transfer Conference, HTC vol 6. American Nuclear Society, LaGrange Park, IL, pp 161–170

    Google Scholar 

  123. Decker WJ, Dorning J (1996) Bifurcations and unfoldings in natural convection. Trans Am Nucl Soc 74:163–165

    Google Scholar 

  124. Decker WJ, Dorning J (1996) Transitions to chaos in natural convection. Trans Am Nucl Soc 74:165–166

    Google Scholar 

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Acknowledgments

I am very grateful to Ms. Alice Rice of Oak Ridge National Laboratory for her expert preparation of this manuscript.

The writing was done at Le Carlina Lodge in Biarritz, France, and I should like to thank Mlle. Juliette Bégué for arranging our stay there, and I especially want to thank M. Jean Bernes, whose kind and gentle heart, and quiet efficiency, kept everything running so smoothly at Le Carlina during the writing. And I enthusiastically add my gratitude to Mike and Paula Dudley for providing just the right amount of distraction at Le Carlina. Les vagues were also great!

Last, but not least, I thank Helen, my wife of 45 years, for her understanding and encouragement, not only during the writing of this chapter, but throughout our life together.

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    Present address: University of Virginia, Charlottesville, VA, USA

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Dorning, J. (2010). Nuclear Reactor Kinetics: 1934–1999 and Beyond. In: Nuclear Computational Science. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3411-3_8

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