The present work concerns the calculation of the infinitesimal porosity by using theMenger’s Sponge model. This computation is based on the grossone theory consideringthe pore volume estimation for the Menger’s Sponge and afterwards the classical definitionof the porosity, given by the ratio between the volume of voids and the total volume (voidsplus solid phase). The aim is to investigate the different solutions given by the standardcharacterization of the porosity and the grossone theory without the direct estimation ofthe fractal dimension. Once the utility of this procedure had been clarified, the focus movesto possible practical applications in which infinitesimal parts can play a fundamental role.The discussion on this matter still remains open.

Usage of infinitesimals in the Menger's Sponge model of porosity

FALLICO, Carmine;VELTRI, Massimo
2012-01-01

Abstract

The present work concerns the calculation of the infinitesimal porosity by using theMenger’s Sponge model. This computation is based on the grossone theory consideringthe pore volume estimation for the Menger’s Sponge and afterwards the classical definitionof the porosity, given by the ratio between the volume of voids and the total volume (voidsplus solid phase). The aim is to investigate the different solutions given by the standardcharacterization of the porosity and the grossone theory without the direct estimation ofthe fractal dimension. Once the utility of this procedure had been clarified, the focus movesto possible practical applications in which infinitesimal parts can play a fundamental role.The discussion on this matter still remains open.
2012
Infinitesimals; Porosity; Fractals
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/143516
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