Computing with non-orientable defects: Nematics, smectics and natural patterns

Chiqun Zhang, Amit Acharya, Alan C. Newell, Shankar C. Venkataramani

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as ‘unphysical’ singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the ‘micro-physics’ to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.

Original languageEnglish (US)
Article number132828
JournalPhysica D: Nonlinear Phenomena
StatePublished - Mar 2021


  • Computation of defects
  • Defects in materials
  • Effective theories
  • Liquid crystals
  • Non-orientability
  • Pattern formation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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