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The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations
One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characte...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999889/ https://www.ncbi.nlm.nih.gov/pubmed/33800360 http://dx.doi.org/10.3390/e23030319 |
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author | Maren, Alianna J. |
author_facet | Maren, Alianna J. |
author_sort | Maren, Alianna J. |
collection | PubMed |
description | One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy ([Formula: see text]) and the interaction enthalpy ([Formula: see text]). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before [Formula: see text] approaches the known divergence as [Formula: see text] , (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where [Formula: see text] and [Formula: see text] , and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses. |
format | Online Article Text |
id | pubmed-7999889 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-79998892021-03-28 The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations Maren, Alianna J. Entropy (Basel) Article One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy ([Formula: see text]) and the interaction enthalpy ([Formula: see text]). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before [Formula: see text] approaches the known divergence as [Formula: see text] , (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where [Formula: see text] and [Formula: see text] , and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses. MDPI 2021-03-08 /pmc/articles/PMC7999889/ /pubmed/33800360 http://dx.doi.org/10.3390/e23030319 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ). |
spellingShingle | Article Maren, Alianna J. The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title | The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title_full | The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title_fullStr | The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title_full_unstemmed | The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title_short | The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations |
title_sort | 2-d cluster variation method: topography illustrations and their enthalpy parameter correlations |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7999889/ https://www.ncbi.nlm.nih.gov/pubmed/33800360 http://dx.doi.org/10.3390/e23030319 |
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