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Kinetics of Nucleation and Growth: Classical Nucleation and Helium Bubbles in Nuclear Materials

In: Math Everywhere

Author

Listed:
  • Luis Bonilla

    (Universidad Carlos III de Madrid, Grupo de Modelización, Simulación Numérica y Matemática Industrial)

  • Ana Carpio

    (Universidad Complutense de Madrid, Departamento de Matemática Aplicada)

  • John C. Neu

    (Universidad de California at Berkeley, Department of Mathematics)

Abstract

Discrete kinetic equations describe homogeneous nucleation and many other processes such as the formation and growth of helium bubbles due to selfirradiation in plutonium. A key ingredient in the analysis of these equations is a wave front expansion which is the equivalent of boundary layer theory for discrete equations. This expansion solves approximately the nucleation problem, but it needs to be patched to an outer solution describing sizes not too close to the maximum size for the helium bubble problem. The composite theory yields an integrodifferential equation for the monomer concentration of single helium atoms which compares well with numerical solution of the full discrete model.

Suggested Citation

  • Luis Bonilla & Ana Carpio & John C. Neu, 2007. "Kinetics of Nucleation and Growth: Classical Nucleation and Helium Bubbles in Nuclear Materials," Springer Books, in: Giacomo Aletti & Alessandra Micheletti & Daniela Morale & Martin Burger (ed.), Math Everywhere, pages 291-307, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-44446-6_24
    DOI: 10.1007/978-3-540-44446-6_24
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