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Physica D: Nonlinear Phenomena
Volume 222, Issues 1-2, October 2006, Pages 131-140
Coagulation-fragmentation Processes
 
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doi:10.1016/j.physd.2006.07.029    
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Copyright © 2006 Elsevier Ltd All rights reserved.

Kinetics of helium bubble formation in nuclear materials

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L.L. Bonillaa, Corresponding Author Contact Information, E-mail The Corresponding Author, A. Carpiob, E-mail The Corresponding Author, J.C. Neuc, E-mail The Corresponding Author and W.G. Wolferd, E-mail The Corresponding Author

aGrupo de Modelización, Simulación Numérica y Matemática Industrial, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain

bDepartamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain

cDepartment of Mathematics, Universidad de California at Berkeley, Berkeley, CA 94720, USA

dLawrence Livermore National Laboratory, Livermore, CA 94550, USA


Available online 22 September 2006.

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 Schaldach and Wolfer involving a truncated system of moment equations.

Keywords: Discrete kinetic equations; Helium bubbles; Boundary layers for discrete equations

Article Outline

1. Introduction
2. Nondimensionalization of the kinetic equations
3. Outer solution and relation to the continuum limit equations
3.1. Continuum limit and similarity solution
3.2. Outer solution for the discrete problem
4. Leading edge of the size distribution function
5. Moment closure
6. Conclusions
Acknowledgements
Appendix A. Approximating the sums View the MathML source
Appendix B. Derivation of the equation for the wave front profile using a book-keeping small parameter
Appendix C. Solution of the equation for the leading front
Appendix D. Moment equations following from a closure assumption preserving scaling symmetry
References







Corresponding Author Contact InformationCorresponding author. Tel.: +34 91 6249445; fax: +34 91 6249129.

Physica D: Nonlinear Phenomena
Volume 222, Issues 1-2, October 2006, Pages 131-140
Coagulation-fragmentation Processes
 
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