Particle-based and continuum models for confined nematics in two dimensions

Humberto Híjar, Apala Majumdar

Research output: Contribution to journalArticlepeer-review


We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.
Original languageEnglish
Pages (from-to)3755-3770
Number of pages16
JournalSoft Matter
Issue number18
Early online date3 Apr 2024
Publication statusPublished - May 2024


  • stochastic multi-particle collision dynamics (N-MPCD) algorithm
  • nematic liquid crystals
  • relaxation dynamics
  • non-equilibrium dynamics
  • nematic defect dynamics


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