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Topology‐preserving phase‐field modeling of elastic bending energy.

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Title: Topology‐preserving phase‐field modeling of elastic bending energy.
Authors: Poudel, Sanjeeb1 (AUTHOR) spoudel@fsu.edu, Wang, Xiaoqiang1 (AUTHOR)
Source: Numerical Methods for Partial Differential Equations. Jan2025, Vol. 41 Issue 1, p1-19. 19p.
Subjects: Tangent function, Hyperbolic functions, Blood cells, Energy consumption, Topology
Abstract: In vesicle membranes, the minimum of the elastic bending energy determines the equilibrium shape. We can reformulate the energy using a phase‐field function and optimize it using the standard gradient flow approach. The method, in its typical formulation, allows topological changes in the membrane; however, in certain events, like in the simulation of blood cells, maintaining the initial topology of the membrane is crucial. In this study, we add a constraint on the phase‐field method to preserve the topology. We note that even if the phase‐field method is formulated using a hyperbolic tangent function, during a change in topology, the membrane's profile deviates from the tanh function. Owing to this idea, the constraint imposes an additional requirement on the profile to maintain the tanh shape, thus preserving the topology. We perform extensive experiments in two‐dimensional and three‐dimensional scenarios to demonstrate that our method preserves the topology during the simulation. [ABSTRACT FROM AUTHOR]
Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell 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: Topology‐preserving phase‐field modeling of elastic bending energy.
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  Data: <searchLink fieldCode="AR" term="%22Poudel%2C+Sanjeeb%22">Poudel, Sanjeeb</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> spoudel@fsu.edu</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiaoqiang%22">Wang, Xiaoqiang</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Numerical+Methods+for+Partial+Differential+Equations%22">Numerical Methods for Partial Differential Equations</searchLink>. Jan2025, Vol. 41 Issue 1, p1-19. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Tangent+function%22">Tangent function</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperbolic+functions%22">Hyperbolic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Blood+cells%22">Blood cells</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+consumption%22">Energy consumption</searchLink><br /><searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink>
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  Data: In vesicle membranes, the minimum of the elastic bending energy determines the equilibrium shape. We can reformulate the energy using a phase‐field function and optimize it using the standard gradient flow approach. The method, in its typical formulation, allows topological changes in the membrane; however, in certain events, like in the simulation of blood cells, maintaining the initial topology of the membrane is crucial. In this study, we add a constraint on the phase‐field method to preserve the topology. We note that even if the phase‐field method is formulated using a hyperbolic tangent function, during a change in topology, the membrane's profile deviates from the tanh function. Owing to this idea, the constraint imposes an additional requirement on the profile to maintain the tanh shape, thus preserving the topology. We perform extensive experiments in two‐dimensional and three‐dimensional scenarios to demonstrate that our method preserves the topology during the simulation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell 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: 10.1002/num.23152
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      – Code: eng
        Text: English
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        PageCount: 19
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      – SubjectFull: Tangent function
        Type: general
      – SubjectFull: Hyperbolic functions
        Type: general
      – SubjectFull: Blood cells
        Type: general
      – SubjectFull: Energy consumption
        Type: general
      – SubjectFull: Topology
        Type: general
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      – TitleFull: Topology‐preserving phase‐field modeling of elastic bending energy.
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            NameFull: Poudel, Sanjeeb
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            NameFull: Wang, Xiaoqiang
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              Text: Jan2025
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              Y: 2025
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              Value: 41
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            – TitleFull: Numerical Methods for Partial Differential Equations
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