Usage of infinitesimals in the Menger鈥檚 Sponge model of porosity

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• 作者：Maria C. Vita ; ^{vita@dds.unical.it} ; ^{mcvita81@gmail.com} ; Samuele De Bartolo ^{samuele.debartolo@unical.it} ; Carmine Fallico ^{fallico@dds.unical.it} ; Massimo Veltri ^{veltrim@dds.unical.it}
• 关键词：Menger&rsquo ; s Sponge ; Infinite sets ; Porous media ; Porosity
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 April, 2012
• 卷：218
• 期：16
• 页码：8187-8195
• 文件大小：375 K

摘要

The present work concerns the calculation of the infinitesimal porosity by using the Menger鈥檚 Sponge model. This computation is based on the grossone theory considering the pore volume estimation for the Menger鈥檚 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.