Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.Comment: 28 pages, 14 figure

Multiple testing with persistent homology

Multiple hypothesis testing requires a control procedure. Simply increasing simulations or permutations to meet a Bonferroni-style threshold is prohibitively expensive. In this paper we propose a null model based approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from these computational costs. We adapt an False Discovery Rate (FDR) control approach to the topological setting, and show it to be compatible both with our null model approach and with previous approaches to hypothesis testing in persistent homology. By extending a limit theorem for persistent homology on samples from point processes, we provide theoretical validation for our FWER and FDR control methods