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E L Starostin1, G H M van der Heijden1

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Summary

Thin elastic ribbons naturally form spherical shapes, offering new models for biopolymers and nanomaterials beyond traditional wormlike chain descriptions. This research identifies broader energy functionals with similar spherical tendencies.

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Area of Science:

  • Physics
  • Materials Science
  • Nanoscience

Background:

  • Classical wormlike chain models are insufficient for describing certain ribbonlike objects.
  • Developable elastic strips require specific energy minimization principles.

Purpose of the Study:

  • To investigate the geometric properties of thin rectangular ribbons.
  • To explore the tendency of these ribbons to form spherical shapes.
  • To identify a broader class of energy functionals exhibiting this property.

Main Methods:

  • Analysis of energy-minimizing configurations for the Sadowsky functional.
  • Mathematical modeling of narrow, developable elastic strips.
  • Characterization of forceless solutions.

Main Results:

  • Thin rectangular ribbons, as defined by the Sadowsky functional, exhibit a natural propensity to form spherical shapes.
  • Forceless solutions for these ribbons are found to lie on a sphere.
  • A wider range of energy functionals demonstrating this spherical tendency has been identified.

Conclusions:

  • The findings provide a new theoretical framework for understanding ribbonlike structures in biophysics and nanoscience.
  • The identified functionals offer alternative models for systems not amenable to classical descriptions.
  • This work advances the understanding of the geometry and mechanics of elastic ribbons.