The Becker–Döring Equations and the Lifshitz–Slyozov Theory of Coarsening |
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Authors: | J. J. L. Velázquez |
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Affiliation: | (1) Departamento de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense, Madrid, 28040, Spain |
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Abstract: | In this paper the relation between the kinetic set of Becker–Döring (BD) equations and the classical Lifshitz–Slyozov (LS) theory of coarsening is studied. A model that resembles the LS theory but keeps some of the nucleation effects is derived. For this model a solution is described that shows how the kinetic effects explain the particular solution selected in the LS theory. By means of a renormalization procedure, a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the LS theory. |
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Keywords: | Becker– Dö ring equations Lifshitz– Slyozov theory nucleation coarsening Fokker– Planck equations renormalization group asymptotics beyond all orders |
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