We consider a birth and growth model for crystallization processes in d space dimensions, where growth is driven by the gradient of the concentration. A nonlinear condition for the concentration is given on the boundary and a multi-front moving boundary problem arises.We propose a new formulation based on the Schwartz distributions by coupling the growth of the crystals and the diffusion of the concentration. We complete the deterministic growth model by considering stochastic nucleations in space and time. The coupling of the growth dynamics with the evolution of the underlying field of the concentration of matter finally causes the stochastic geometry of the crystals.
A Birth and Growth Model for Kinetic-Driven Crystallization Processes. Part 1, Modeling / D. Aquilano, V. Capasso, A. Micheletti, S. Patti, L. Pizzocchero, M. Rubbo. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 10:1(2009), pp. 71-92.
Titolo: | A Birth and Growth Model for Kinetic-Driven Crystallization Processes. Part 1, Modeling |
Autori: | CAPASSO, VINCENZO (Secondo) PIZZOCCHERO, LIVIO (Penultimo) |
Parole Chiave: | Birth and growth processes ; Crystal growth ; Diffusion ; Level set method |
Settore Scientifico Disciplinare: | Settore MAT/06 - Probabilita' e Statistica Matematica Settore MAT/07 - Fisica Matematica |
Data di pubblicazione: | 2009 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.nonrwa.2007.08.015 |
Appare nelle tipologie: | 01 - Articolo su periodico |