Strategies for the generation of periodic discrete structures with identical two-point correlation—called 2PC-equivalent—are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension through trivial embeddings, kernel-based extension and phase coalescence. Proofs are provided by means of discrete Fourier transform theory. A Python 3 implementation is offered for reproduction of examples and future applications.
Description
2PC correlation, equivalence, generation homogenization of periodic structures, two-point
%0 Journal Article
%1 fernandez2020c
%A Fernández, Mauricio
%A Fritzen, Felix
%D 2020
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%K EXC2075 dae emma from:ffritzen myown peerReviewed pn3 postPrint
%N 2242
%P 20200568
%R 10.1098/rspa.2020.0568
%T On the generation of periodic discrete structures with identical two-point correlation
%V 476
%X Strategies for the generation of periodic discrete structures with identical two-point correlation—called 2PC-equivalent—are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension through trivial embeddings, kernel-based extension and phase coalescence. Proofs are provided by means of discrete Fourier transform theory. A Python 3 implementation is offered for reproduction of examples and future applications.
@article{fernandez2020c,
abstract = {Strategies for the generation of periodic discrete structures with identical two-point correlation—called 2PC-equivalent—are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension through trivial embeddings, kernel-based extension and phase coalescence. Proofs are provided by means of discrete Fourier transform theory. A Python 3 implementation is offered for reproduction of examples and future applications. },
added-at = {2021-12-08T17:10:08.000+0100},
author = {Fernández, Mauricio and Fritzen, Felix},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/22515bc88d2935f8b11d5564b28b20368/katharinafuchs},
description = {2PC correlation, equivalence, generation homogenization of periodic structures, two-point},
doi = {10.1098/rspa.2020.0568},
interhash = {7b7d86094497dcda15b2bc25b0134764},
intrahash = {2515bc88d2935f8b11d5564b28b20368},
journal = {{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}},
keywords = {EXC2075 dae emma from:ffritzen myown peerReviewed pn3 postPrint},
number = 2242,
pages = 20200568,
timestamp = {2021-12-08T16:10:08.000+0100},
title = {On the generation of periodic discrete structures with identical two-point correlation},
volume = 476,
year = 2020
}
