A set-valued framework for birth-and-growth process

We propose a set-valued framework for the well-posedness of birth-and-growth process. Our birth-and-growth model is rigorously defined as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The...

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Bibliographic Details
Published inarXiv.org
Main Authors Aletti, Giacomo, Bongiorno, Enea G, Capasso, Vincenzo
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.05.2008
Subjects
Birth
Growth models
Mathematics - Probability
Mathematics - Statistics Theory
Nucleation
Statistics - Applications
Statistics - Theory
Well posed problems
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Summary:We propose a set-valued framework for the well-posedness of birth-and-growth process. Our birth-and-growth model is rigorously defined as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the used geometrical approach leads us to avoid problems arising by an analytical definition of the front growth such as boundary regularities. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, it is not local, i.e. for a fixed time instant, growth is the same at each space point.
ISSN:2331-8422
DOI:10.48550/arxiv.0805.3912