On the generation of periodic discrete structures with identical two-point correlation
M. Fernández, und F. Fritzen.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2242): 20200568 (2020)

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.

DOI: 10.1098/rspa.2020.0568
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@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 = {2021-01-18T18:00:45.000+0100},
  author = {Fernández, Mauricio and Fritzen, Felix},
  biburl = {https://puma.ub.uni-stuttgart.de/bibtex/22515bc88d2935f8b11d5564b28b20368/simtech},
  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 = {myown postPrint emma pn3 dae peerReviewed EXC2075 from:ffritzen},
  number = 2242,
  pages = 20200568,
  timestamp = {2021-01-18T18:00:45.000+0100},
  title = {On the generation of periodic discrete structures with identical two-point correlation},
  volume = 476,
  year = 2020
}

%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 myown postPrint emma pn3 dae peerReviewed EXC2075 from:ffritzen
%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.

PUMA

On the generation of periodic discrete structures with identical two-point correlation
M. Fernández, und F. Fritzen.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2242): 20200568 (2020)

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PUMA

On the generation of periodic discrete structures with identical two-point correlationM. Fernández, und F. Fritzen. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2242): 20200568 (2020)

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On the generation of periodic discrete structures with identical two-point correlation
M. Fernández, und F. Fritzen.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2242): 20200568 (2020)