Math Everywhere

pp 291-307

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

  • Luis BonillaAffiliated withGrupo de Modelización, Simulación Numérica y Matemática Industrial, Universidad Carlos III de Madrid
  • , Ana CarpioAffiliated withDepartamento de Matemática Aplicada, Universidad Complutense de Madrid
  • , John C. NeuAffiliated withDepartment of Mathematics, Universidad de California at Berkeley

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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.