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This study analyzes membrane inclusion interactions using multipolar expansion. For five circular inclusions, interaction scales with distance, differing from other configurations and showing repulsive forces.

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Area of Science:

  • Membrane biophysics
  • Soft matter physics
  • Computational physics

Background:

  • Membrane inclusions induce curvature, affecting membrane properties.
  • Understanding multi-body interactions is crucial for biological and material systems.

Purpose of the Study:

  • To analytically and numerically investigate interactions between multiple identical membrane inclusions.
  • To determine how inclusion shape and arrangement influence interaction forces.

Main Methods:

  • Analytical multipolar expansion for tensionless membranes.
  • Numerical computation of multi-body interaction contributions.
  • Analysis of inclusions with arbitrary cross-sections and regular polygonal arrangements.

Main Results:

  • Analytical expressions for total asymptotic interaction up to N=6 circular inclusions.
  • Multi-body contributions are comparable to pairwise interactions.
  • For N=5, interaction scales as d^-6; for N!=5, it scales as d^-4.
  • Non-circular inclusions exhibit attractive (d^-2) or repulsive (d^-4) interactions depending on lobe number and amplitude.

Conclusions:

  • Analytical and numerical results show good agreement, confirming repulsive interactions for circular inclusions.
  • Inclusion shape and arrangement significantly alter interaction behavior, including attraction at large distances for specific non-circular shapes.
  • Interaction dependence on in-plane rotation angles is characterized.