Bonilla , L.L. and Carpio Rodríguez, Ana María and Neu, J.C. and Wolfer, W.G.
(2006)
*Kinetics of helium bubble formation in nuclear materials.*
Physica D-nonlinear phenomena, 222
.
pp. 131-140.
ISSN PHYSICA D-NONLINEAR PHENOMENA

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Official URL: http://www.sciencedirect.com/science/journal/01672789

## Abstract

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by discrete kinetic equations for the number densities of bubbles having k atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to the previous approximation of Schalclach and Wolfer involving a truncated system of moment equations.

Item Type: | Article |
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Uncontrolled Keywords: | Discrete kinetic equations; Helium bubbles; Boundary layers for discrete equations |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Nuclear physics |

ID Code: | 14956 |

References: | [1] C.M. Schaldach, W.G. Wolfer, Kinetics of helium bubble formation in nuclear and structural materials, in: M.L. Grossbeck, T.R. Allen, R.G. Lott, A.S. Kumar (Eds.), Effects of Radiation on Materials: 21st Symposium, ASTM International, ASTM STP 1447, West Conshohocken, 2004. [2] A.J. Schwartz, M.A. Wall, T.G. Zocco, W.G. Wolfer, Characterization and modelling of helium bubbles in self-irradiated plutonium alloys, Phil. Mag. 85 (2005) 479–488. [3] A.G. McKendrick, Studies on the theory of continuous probabilities, with special reference to its bearing on natural phenomena of a progressive nature, Proc. London Math. Soc. 13 (1914) 401–416. [4] J.C. Neu, L.L. Bonilla, A. Carpio, Igniting homogeneous nucleation, Phys. Rev. E 71 (2005) 021601. 14 pages. [5] J.R. King, J.A.D. Wattis, Asymptotic solutions of the Becker–D¨oring equations with size-dependent rate constants, J. Phys. A 35 (2002) 1357–1380. |

Deposited On: | 24 Apr 2012 11:04 |

Last Modified: | 06 Feb 2014 10:13 |

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