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Evolution of Vortex Filaments and Reconnections in the Gross–Pitaevskii Equation and its Approximation by the Binormal Flow Equation.

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Title: Evolution of Vortex Filaments and Reconnections in the Gross–Pitaevskii Equation and its Approximation by the Binormal Flow Equation.
Authors: Arrayás, M.1 (AUTHOR) manuel.arrayas@urjc.es, Fontelos, M. A.2 (AUTHOR), González, M. D. M.3 (AUTHOR), Uriarte, C.1 (AUTHOR)
Source: Journal of Low Temperature Physics. Jul2025, Vol. 220 Issue 1, p61-74. 14p.
Subjects: Vortex motion, Superfluidity, Computer simulation, Fibers, Curvature
Abstract: The evolution of a vortex line following the binormal flow equation (i.e. with a velocity proportional to the local curvature in the direction of the binormal vector) has been postulated as an approximation for the evolution of vortex filaments in both the Euler system for inviscid incompressible fluids and the Gross–Pitaevskii equation in superfluids. We address the issue of whether this is a suitable approximation or not and its degree of validity by using rigorous mathematical methods and direct numerical simulations. More specifically, we show that as the vortex core thickness goes to zero, the vortex core moves (at leading order and for long periods of time) with a velocity proportional to its local curvature and the binormal vector to the curve. The main idea of our analysis lies in a reformulation of the Gross–Pitaevskii equation in terms of associated velocity and vorticity fields that resemble the Euler system written in terms of vorticity in its weak form. We also present full numerical simulations aimed to compare Gross–Pitaevskii and binormal flow in various physical situations of interest such as the periodic evolution of deformed vortex rings and the reconnection of vortex filaments. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Low Temperature Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Evolution of Vortex Filaments and Reconnections in the Gross–Pitaevskii Equation and its Approximation by the Binormal Flow Equation.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Low+Temperature+Physics%22">Journal of Low Temperature Physics</searchLink>. Jul2025, Vol. 220 Issue 1, p61-74. 14p.
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  Data: The evolution of a vortex line following the binormal flow equation (i.e. with a velocity proportional to the local curvature in the direction of the binormal vector) has been postulated as an approximation for the evolution of vortex filaments in both the Euler system for inviscid incompressible fluids and the Gross–Pitaevskii equation in superfluids. We address the issue of whether this is a suitable approximation or not and its degree of validity by using rigorous mathematical methods and direct numerical simulations. More specifically, we show that as the vortex core thickness goes to zero, the vortex core moves (at leading order and for long periods of time) with a velocity proportional to its local curvature and the binormal vector to the curve. The main idea of our analysis lies in a reformulation of the Gross–Pitaevskii equation in terms of associated velocity and vorticity fields that resemble the Euler system written in terms of vorticity in its weak form. We also present full numerical simulations aimed to compare Gross–Pitaevskii and binormal flow in various physical situations of interest such as the periodic evolution of deformed vortex rings and the reconnection of vortex filaments. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Low Temperature Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10909-025-03267-6
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      – Code: eng
        Text: English
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        PageCount: 14
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      – SubjectFull: Vortex motion
        Type: general
      – SubjectFull: Superfluidity
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Fibers
        Type: general
      – SubjectFull: Curvature
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      – TitleFull: Evolution of Vortex Filaments and Reconnections in the Gross–Pitaevskii Equation and its Approximation by the Binormal Flow Equation.
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              M: 07
              Text: Jul2025
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              Y: 2025
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