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A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes.

Sanjay Dharmavaram1, Xinran Wan2, Luigi E Perotti3

  • 1Department of Mathematics, Bucknell University, 1 Dent Drive, Lewisburg, PA 17837, USA.

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|October 27, 2022
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Summary

This study introduces a new computational method for modeling particles on fluid membranes. The approach accurately captures particle-membrane interactions and deformations, advancing soft matter and biophysics research.

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Helfrich–Canham modelinteracting particleslipid membranesmodel for protein–membrane interactionsubdivision finite element

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Area of Science:

  • Soft matter physics
  • Biophysics
  • Computational mechanics

Background:

  • Modeling interacting particles on fluid membranes is crucial in soft matter and biophysics.
  • A key challenge is accurately simulating the coupling between substrate deformation and particle movement.

Purpose of the Study:

  • To develop a novel computational framework for simulating particle-membrane interactions.
  • To enable accurate modeling of coupled mechanics without artificial constraints.

Main Methods:

  • A thin-shell finite element formulation using subdivision surfaces was developed.
  • A variational Lagrangian framework was employed to couple particle and substrate mechanics.
  • Particles were parameterized on a reference configuration, allowing movement between mesh elements.

Main Results:

  • The finite element method was implemented and validated using the Helfrich-Canham energy model.
  • An efficient algorithm for locating particles on the reference mesh was presented.
  • Simulations reproduced symmetries from the Thomson problem, demonstrating the model's capability.

Conclusions:

  • The developed method effectively models the mechanics of particles interacting with deformable fluid shells.
  • This approach overcomes limitations of existing methods by allowing unconstrained particle movement.
  • The findings have implications for understanding complex systems in soft matter and biophysics.