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Assembly and Characterization of Polyelectrolyte Complex Micelles
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Published on: March 2, 2020

Conformal smectics and their many metrics.

Gareth P Alexander1, Randall D Kamien, Ricardo A Mosna

  • 1Centre for Complexity Science and Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Equally spaced smectic configurations possess infinite conformal symmetry, linking them to null hypersurfaces in symmetric spacetimes. This symmetry can be extended to focal structures on curved substrates.

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Area of Science:

  • Theoretical physics
  • Condensed matter physics
  • Differential geometry

Background:

  • Smectic materials exhibit complex behaviors.
  • Conformal symmetry is a key concept in theoretical physics.
  • Understanding symmetries in curved spacetimes is crucial.

Purpose of the Study:

  • To explore the symmetries of equally spaced smectic configurations.
  • To establish a connection between smectic systems and null hypersurfaces.
  • To investigate the restoration of symmetries in focal structures.

Main Methods:

  • Mathematical analysis of smectic configurations.
  • Conformal mapping techniques.
  • Investigation of maximally symmetric spacetimes.

Main Results:

  • Equally spaced smectic configurations demonstrate infinite-dimensional conformal symmetry.
  • A natural map exists between smectic configurations and null hypersurfaces.
  • Additional symmetries can be restored for focal structures using conformal factors.

Conclusions:

  • Smectic systems exhibit profound underlying symmetries.
  • The established map provides new insights into both smectic physics and spacetime geometry.
  • This work opens avenues for studying smectics on curved substrates with enhanced symmetry properties.