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Smectic pores and defect cores.

Elisabetta A Matsumoto1, Randall D Kamien, Christian D Santangelo

  • 1Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA ; Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA.

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Summary
This summary is machine-generated.

Riemann minimal surfaces describe bicontinuous systems. These surfaces are explicitly shown to be a nonlinear sum of two oppositely handed helicoids.

Keywords:
minimal surfacessmectic liquid crystalstopological defects

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Area of Science:

  • Differential Geometry
  • Materials Science
  • Nanotechnology

Background:

  • Riemann minimal surfaces are a known family of minimal surfaces.
  • They are used to model bicontinuous lamellar systems with pores connecting alternating layers.

Purpose of the Study:

  • To explicitly demonstrate the composition of Riemann minimal surfaces.
  • To analyze the structure of these surfaces in the context of materials science.

Main Methods:

  • Mathematical analysis of Riemann minimal surfaces.
  • Decomposition of the surfaces into fundamental components.

Main Results:

  • Riemann minimal surfaces are composed of a nonlinear sum of two helicoids.
  • The two helicoids have opposite handedness.

Conclusions:

  • The study provides a new understanding of the structure of Riemann minimal surfaces.
  • This finding has implications for the design and understanding of materials with bicontinuous structures.