8 papers
Using the Renormalized Energy from Ginzburg-Landau Theory to Compute Solution Landscapes in the Reduced Landau-de Gennes Theory
Yucen Han, Apala Majumdar
We study nematic liquid crystal phases confined to bounded, two-dimensional (2D) domains, in the reduced Landau-de Gennes (rLdG) theoretical framework. The rLdG framework is equiva…
The Asymptotic Theory of Ginzburg--Landau Critical Points on Domains with Corners
Yucen Han, Apala Majumdar
We study the critical points of the two-dimensional Ginzburg--Landau energy on domains with corners and imposed Dirichlet boundary condition which vanishes prec…
A Landau-de Gennes Type Theory for Cholesteric-Helical Smectic-Smectic C* Liquid Crystal Phase Transitions
Apala Majumdar, Baoming Shi, Dawei Wu +2
We present a rigorous mathematical analysis of a modified Landau-de Gennes (LdG) theory modeling temperature-driven phase transitions between cholesteric, helical smectic, and smec…
Dissipative solutions to a Beris-Edwards type model for compressible active nematic liquid crystals
Kuntal Bhandari, Apala Majumdar, Šárka Nečasová
We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary d…
Landau-de Gennes Modelling of Confinement Effects and Cybotactic Clusters in Bent-Core Nematic Liquid Crystals
Yucen Han, Prabakaran Rajamanickam, Bedour Alturki +1
We study bent-core nematic (BCN) systems in two-dimensional (2D) and three-dimensional (3D) settings, focusing on the role of cybotactic clusters, phase transitions, confinement ef…
Neural Network-Based Tensor Model for Nematic Liquid Crystals with Accurate Microscopic Information
Baoming Shi, Apala Majumdar, Lei Zhang
The phenomenological Landau-de Gennes (LdG) model is a powerful continuum theory to describe the macroscopic state of nematic liquid crystals. However, it is invariably less accura…
A Modified Landau-de Gennes Theory for Smectic Liquid Crystals: Phase Transitions and Structural Transitions
Baoming Shi, Yucen Han, Chengdi Ma +2
We mathematically model Smectic-A (SmA) phases with a modified Landau-de Gennes (mLdG) model. The orientational order of the SmA phase is described by a tensor-order parameter $\ma…
A diffuse-interface Landau-de Gennes model for free-boundary problems in the theory of nematic liquid crystals
Dawei Wu, Baoming Shi, Yucen Han +3
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, an…