Temporal evolution of the domain structure in a Poisson-Voronoi nucleation and growth transformation. Results for one and three dimensions
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Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
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hdl:2117/2172
Tipus de documentArticle
Data publicació2008
Condicions d'accésAccés obert
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Abstract
The distribution of spatial domain structures originated during one and three dimensional
Poisson-Voronoi transformations are computed analytically extending the recently obtained re-
sults for the two dimensional case. The presented method gives a full description of the developed
microstructure and is valid for tessellations of any dimensionality. The temporal and spatial depen-
dences of the domain structure are completely discriminated and separated, showing the existence of
geometric configurations independent of time. A single computation of the probability distribution
of these geometric configurations allows us to calculate the total free-boundary and size probabil-
ity distributions at any desired time. The obtained results show full agreement with stochastic
simulations and reproduce completely the previously existing partial results. A discussion about
the potential applications of the method to the calculation of other geometrical properties and the
characteristics of the final static structure leading to a gamma distribution of sizes is also presented.
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