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

TL;DR

This paper explores calculating porosity in the Menger's Sponge model using infinitesimals and grossone theory, comparing standard and novel approaches without relying on fractal dimension, with potential practical applications.

Contribution

It introduces a new method for porosity calculation using infinitesimals and grossone theory, bypassing traditional fractal dimension estimation.

Findings

Different solutions for porosity using standard and grossone methods

Clarification of the utility of infinitesimal-based porosity calculation

Discussion on potential practical applications of infinitesimal parts

Abstract

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