Abstract
Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects.
Highlights
Nematic liquid crystals’ combination of fluidity and orientational order both underlies nematics’ widespread technological applications and endows them with topological defects, localized breakdowns in the orientational order stabilized by the medium’s broken symmetries
In addition to writing efficient code to carry out the required lattice-based minimizations of the Q-tensor field in a domain, we advocate the use of the graphical user interface (GUI) we developed to rapidly prototype and explore the effects of particular boundaries, colloidal inclusions, and external fields that may be of experimental interest
As demonstrated in our sample study, openQmin utilizes MPI to enable Landau-de Gennes (LdG) modeling at typical size scales of experimental relevance, at the ∼ 10 μm range, with fast convergence enabled by the Fast Inertial Relaxation Engine (FIRE) algorithm
Summary
Nematic liquid crystals’ combination of fluidity and orientational order both underlies nematics’ widespread technological applications and endows them with topological defects, localized breakdowns in the orientational order stabilized by the medium’s broken symmetries. The broad usefulness of the LdG theory goes hand in hand with a significant limitation of scale: Resolving defects at a priori unknown locations requires the simulation lattice spacing to be comparable to or smaller than the size of the defect core, the region in which nematic order breaks down, which in thermotropic nematics is typically a few nanometers This is often thousands of times smaller than the individual micron-scale colloidal particles of interest. It offers a user-friendly GUI environment for rapid prototyping of topological defect configurations as a function of liquid crystal parameters, boundary geometry, and the presence of colloidal inclusions It targets large-scale systems using OpenMPI [68] to support parallelization across both CPU and GPU resources to scale up to the supra-micron length scales of experimental relevance.
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