Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field
Abstract We introduce a novel computational methodology for indexing the Euler characteristics of $$\:N$$ -dimensional objects by overlaying ( $$\:N$$ +1)-dimensional chiral vector fields. Analogous to how the skyrmion number characterizes a two-dimensional magnetic skyrmion through the integration...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-04-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-95495-9 |
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| author | Tae Jung Moon Seong Min Park Han Gyu Yoon Gyunghun Yu Hee Young Kwon Changyeon Won |
| author_facet | Tae Jung Moon Seong Min Park Han Gyu Yoon Gyunghun Yu Hee Young Kwon Changyeon Won |
| author_sort | Tae Jung Moon |
| collection | DOAJ |
| description | Abstract We introduce a novel computational methodology for indexing the Euler characteristics of $$\:N$$ -dimensional objects by overlaying ( $$\:N$$ +1)-dimensional chiral vector fields. Analogous to how the skyrmion number characterizes a two-dimensional magnetic skyrmion through the integration of the solid angle of its spin field, we generalize this principle to arbitrary dimensions. By iteratively applying a simple numerical process, we generate ( $$\:N$$ +1)-dimensional chiral vector fields on $$\:N$$ -dimensional objects. The Euler characteristics of these objects are calculated by aggregating the local solid angles subtended by neighboring chiral vectors. In this study, we focus on verifying our method in two and three dimensions. For dimensions higher than three, we conduct preliminary experiments on simple objects to explore potential applicability. Although our method shows promising potential in higher dimensions, further investigation is required to fully understand its applicability beyond three dimensions. |
| format | Article |
| id | doaj-art-c19fbd2f024b4b1a8fb185d3ae517236 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c19fbd2f024b4b1a8fb185d3ae5172362025-08-20T03:27:09ZengNature PortfolioScientific Reports2045-23222025-04-011511910.1038/s41598-025-95495-9Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral fieldTae Jung Moon0Seong Min Park1Han Gyu Yoon2Gyunghun Yu3Hee Young Kwon4Changyeon Won5Department of Physics, Kyung Hee UniversityDepartment of Physics, Kyung Hee UniversityDepartment of Physics, Kyung Hee UniversityDepartment of Physics, Kyung Hee UniversityCenter for Spintronics, Korea Institute of Science and TechnologyDepartment of Physics, Kyung Hee UniversityAbstract We introduce a novel computational methodology for indexing the Euler characteristics of $$\:N$$ -dimensional objects by overlaying ( $$\:N$$ +1)-dimensional chiral vector fields. Analogous to how the skyrmion number characterizes a two-dimensional magnetic skyrmion through the integration of the solid angle of its spin field, we generalize this principle to arbitrary dimensions. By iteratively applying a simple numerical process, we generate ( $$\:N$$ +1)-dimensional chiral vector fields on $$\:N$$ -dimensional objects. The Euler characteristics of these objects are calculated by aggregating the local solid angles subtended by neighboring chiral vectors. In this study, we focus on verifying our method in two and three dimensions. For dimensions higher than three, we conduct preliminary experiments on simple objects to explore potential applicability. Although our method shows promising potential in higher dimensions, further investigation is required to fully understand its applicability beyond three dimensions.https://doi.org/10.1038/s41598-025-95495-9 |
| spellingShingle | Tae Jung Moon Seong Min Park Han Gyu Yoon Gyunghun Yu Hee Young Kwon Changyeon Won Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field Scientific Reports |
| title | Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field |
| title_full | Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field |
| title_fullStr | Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field |
| title_full_unstemmed | Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field |
| title_short | Computing Euler characteristic of $${N}$$ -dimensional objects via a Skyrmion-inspired overlaying ( $${N}$$ +1)-dimensional chiral field |
| title_sort | computing euler characteristic of n dimensional objects via a skyrmion inspired overlaying n 1 dimensional chiral field |
| url | https://doi.org/10.1038/s41598-025-95495-9 |
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