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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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Autor principal: Wuttke, Joachim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: International Union of Crystallography 2021
Materias:
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
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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.
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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
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