A birth-and-growth model is rigorously defined as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the proposed geometrical approach let us avoid problems arising from 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, is not local, i.e. for a fixed time instant, growth is the same at each point space. The proposed setting allows us to investigate nucleation and growth processes also from a statistical point of view. Different consistent set-valued estimators for growth processes and for the nucleation hitting function are derived.

A Stochastic Geometric Framework for Dynamical Birth-and-Growth Processes: Related Statistical Analysis / G. Aletti, E.G. Bongiorno, V. Capasso (MATHEMATICS IN INDUSTRY). - In: Progress in Industrial Mathematics at ECMI 2012 / [a cura di] M. Fontes, M. Günther, N. Marheineke. - [s.l] : Springer, 2014. - ISBN 9783319053646. - pp. 371-377 (( Intervento presentato al 17. convegno European Conference on Mathematics for Industry tenutosi a Lund nel 2012 [10.1007/978-3-319-05365-3_51].

A Stochastic Geometric Framework for Dynamical Birth-and-Growth Processes: Related Statistical Analysis

G. Aletti
Primo
;
E.G. Bongiorno;V. Capasso
2014

Abstract

A birth-and-growth model is rigorously defined as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the proposed geometrical approach let us avoid problems arising from 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, is not local, i.e. for a fixed time instant, growth is the same at each point space. The proposed setting allows us to investigate nucleation and growth processes also from a statistical point of view. Different consistent set-valued estimators for growth processes and for the nucleation hitting function are derived.
Nucleation Process; Observation Window; Finite Measure Space Filter; Probability Space Discrete; Time Formulation
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/01 - Statistica
Centro di Ricerca Interdisciplinare su Modellistica Matematica, Analisi Statistica e Simulazione Computazionale per la Innovazione Scientifica e Tecnologica ADAMSS
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/687416
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