"hopfion" meaning in English

See hopfion in All languages combined, or Wiktionary

Noun

Forms: hopfions [plural]
Etymology: Blend of Hopfian + soliton Etymology templates: {{blend|en|Hopfian|soliton}} Blend of Hopfian + soliton Head templates: {{en-noun}} hopfion (plural hopfions)
  1. (mathematics) A knot in a three-dimensional continuous unit vector field that cannot be unknotted without cutting Categories (topical): Mathematics

Inflected forms

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      "args": {
        "1": "en",
        "2": "Hopfian",
        "3": "soliton"
      },
      "expansion": "Blend of Hopfian + soliton",
      "name": "blend"
    }
  ],
  "etymology_text": "Blend of Hopfian + soliton",
  "forms": [
    {
      "form": "hopfions",
      "tags": [
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    }
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  "head_templates": [
    {
      "args": {},
      "expansion": "hopfion (plural hopfions)",
      "name": "en-noun"
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  "senses": [
    {
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        },
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          "langcode": "en",
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          "orig": "en:Mathematics",
          "parents": [
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            "Sciences",
            "All topics",
            "Fundamental"
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        }
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      "examples": [
        {
          "ref": "2015, R.N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-Gonzalez, D.J. Frantzeskakis, L.A. Collins, P.G. Kevrekidis, “Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates”, in arXiv:",
          "text": "Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A knot in a three-dimensional continuous unit vector field that cannot be unknotted without cutting"
      ],
      "id": "en-hopfion-en-noun-XWm4OPsF",
      "links": [
        [
          "mathematics",
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        ],
        [
          "knot",
          "knot"
        ],
        [
          "three-dimensional",
          "three-dimensional"
        ],
        [
          "continuous",
          "continuous"
        ],
        [
          "unit vector",
          "unit vector"
        ],
        [
          "field",
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        ]
      ],
      "raw_glosses": [
        "(mathematics) A knot in a three-dimensional continuous unit vector field that cannot be unknotted without cutting"
      ],
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        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hopfion"
}
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    }
  ],
  "etymology_text": "Blend of Hopfian + soliton",
  "forms": [
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      "form": "hopfions",
      "tags": [
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          "ref": "2015, R.N. Bisset, Wenlong Wang, C. Ticknor, R. Carretero-Gonzalez, D.J. Frantzeskakis, L.A. Collins, P.G. Kevrekidis, “Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates”, in arXiv:",
          "text": "Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A knot in a three-dimensional continuous unit vector field that cannot be unknotted without cutting"
      ],
      "links": [
        [
          "mathematics",
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        ],
        [
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        "(mathematics) A knot in a three-dimensional continuous unit vector field that cannot be unknotted without cutting"
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    }
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}

Download raw JSONL data for hopfion meaning in English (1.5kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-02-08 from the enwiktionary dump dated 2025-02-02 using wiktextract (f90d964 and 9dbd323). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.