CSENG Physics & Astronomy
College of Science & Engineering
Twin Cities
Project Title: 
Pattern Formation Outside of Thermodynamic Equilibrium

These researchers are using MSI for three projects:

  • Topological defect motion and crystal plasticity at the mesoscale: Plastic deformation in crystals arises mainly due to the motion of dislocations under the action of externally applied stresses. The mutual interaction of dislocations under applied loads leads to the development of intricate dislocation patterns such as dislocation cells and labyrinths, often with dipolar dislocation walls, and mosaics. It is a fundamental challenge of theories and models of plasticity to predict such microstructure, with the attendant, often large, deformation and internal stress fields. Different approaches have been used in the literature to model the development of dislocation microstructures. The researchers use mesoscale field dislocation mechanics (MFDM) theory to understand the statistical properties of an ensemble of dynamical dislocation pattern forming simulations in a full 3D setting in a rate dependent FCC single crystal.
  • Self consistent field theory of nematic liquid crystals: The nematic phase of a liquid crystal is an equilibrium phase characterized by long ranged molecular orientational order. Liquid crystal molecules typically have uniaxial symmetry (head-tail symmetry) and therefore allow defects of half integer degree. The degree of order and the structure of the defect core have been typically beyond experimental resolution, and therefore often modeled as effective or point singularities of the (continuous) order parameter field. Recent experiments in lyotropic chromonic liquid crystals have revealed defect core sizes on a scale of a few microns, and have determined their spatial structure in some detail. Neither of the two current theories in use for the description of nematic phases can address the core structure observed. In one, the Oseen-Frank theory, defects are point singularities of the so called director field, and removed with appropriate cut-off approaches. In the second, the Landau-de Gennes theory, the order parameter at the core is phenomenological, and largely isotropic (in disagreement with experiments). This group has developed a self consistent field theory of the nematic, which needs to be solved numerically. As in the Landau-de Gennes theory, this approach is based on a tensor order parameter description of the nematic phase. Unlike the latter, the researchers can guarantee that the eigenvalues of the order parameter remain in the physically admissible range throughout the defect, as well as allow different energies for splay and bend distortions while retaining boundedness of the energy. This is also a central feature of the molecular interactions in this lyotropic liquid crystal.

  • Hydrodynamic extension to a self-consistent field theory of nematic liquid crystals: A number of results have been obtained on this topic (see previous paragraph), which match well with experiments. A new class of nematic phases concerns both active and biological matter in which new phenomena are being uncovered in phases that, like nematics, break rotational symmetry. Important for this applications are hydrodynamics flows, and the researchers intend to extend the description based on a self consistent field theory to encompass transport modes.

Project Investigators

Lucas Myers
Cody Schimming
Carter Swift
Professor Jorge Vinals
Eduardo Vitral
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