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Numerically stable form factor of any polygon and polyhedron
Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes’s theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by us...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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International Union of Crystallography
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8056765/ https://www.ncbi.nlm.nih.gov/pubmed/33953657 http://dx.doi.org/10.1107/S1600576721001710 |
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author | Wuttke, Joachim |
author_facet | Wuttke, Joachim |
author_sort | Wuttke, Joachim |
collection | PubMed |
description | Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes’s theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals. |
format | Online Article Text |
id | pubmed-8056765 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | International Union of Crystallography |
record_format | MEDLINE/PubMed |
spelling | pubmed-80567652021-05-04 Numerically stable form factor of any polygon and polyhedron Wuttke, Joachim J Appl Crystallogr Research Papers Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes’s theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals. International Union of Crystallography 2021-03-25 /pmc/articles/PMC8056765/ /pubmed/33953657 http://dx.doi.org/10.1107/S1600576721001710 Text en © Joachim Wuttke 2021 https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited. |
spellingShingle | Research Papers Wuttke, Joachim Numerically stable form factor of any polygon and polyhedron |
title | Numerically stable form factor of any polygon and polyhedron |
title_full | Numerically stable form factor of any polygon and polyhedron |
title_fullStr | Numerically stable form factor of any polygon and polyhedron |
title_full_unstemmed | Numerically stable form factor of any polygon and polyhedron |
title_short | Numerically stable form factor of any polygon and polyhedron |
title_sort | numerically stable form factor of any polygon and polyhedron |
topic | Research Papers |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8056765/ https://www.ncbi.nlm.nih.gov/pubmed/33953657 http://dx.doi.org/10.1107/S1600576721001710 |
work_keys_str_mv | AT wuttkejoachim numericallystableformfactorofanypolygonandpolyhedron |