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:

  • Interfacial instabilities in smectic fields and growth driven by Gaussian curvature: Nonequilibrium motion of interfaces is quite often driven by reduction of the excess energy of the interface. In the classical case, the local excess energy is proportional to the local mean curvature, resulting in an extensively studied problem in a number of fields of Physics and Materials Science. The Gaussian curvature, a surface intrinsic quantity, is often not taken into account as its integral over a closed surface is constant, regardless of the shape of the surface (Gauss-Bonnet theorem). Hence, surface distortions (fluctuations) do not contribute to the energy unless there is a change in the topology of the surface. These researchers are studying the motion of a smectic-isotropic interface in a think film smectic for which the local kinetic motion of the interface does depend on the Gaussian curvature. The model equations for the smectic-isotropic phase have been developed and extended to include full hydridynamic coupling. The resulting equations are being solved numerically with a spectral method (that relies of FFTW and MPI).
    The custom developed code is completed, and is currently in production.
  • 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.

  • Morphology and singularities in nematic/isotropic boundaries: Two phase interfaces separating domains with non trivial broken symmetries lead to domain morphologies that need to accommodate topological constraints in addition to satisfying the usual rules of free energy minimization. These researchers have developed a computational model that is based on a mean field theory description of the nematic to describe tactoids in chromonic liquid crystals. In this system topological defect cores are very large (on the order of microns) and it is therefore possible to image their structure with optical imaging tools. Ongoing experiments are reveailng novel morphologies associated with a sensitive balance between phase elasticity (related to the broken symmetry), anisotropy, and topology. This model differs from the classical Landau-de Gennes tensor order parameter representation of a nematic/isoptropic phase. The researchers are currently examining negative tactoids (isotropic domains in an ordered matrix) to understand the formation of cusp singularities when the background matrix has non zero topological charge.

Project Investigators

Cody Schimming
Professor Jorge Vinals
Eduardo Vitral
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