8 citations · 8 across the 13 of their papers we have counts for
13 papers
A Second-Order Method for Locating Critical Points of Prescribed Index on Energy Landscapes
Qiang Du, Baoming Shi
Exploring high dimensional energy landscape is a challenging problem in many applications where both ground states and transition states offer important information about the under…
From molecular model to tensor model of nematic liquid crystals through entropy decomposition
Baoming Shi, Dawei Wu, Lei Zhang +1
In the mathematical modeling of nematic liquid crystals, a practical and physically reliable -tensor model can be derived from Onsager's molecular model with the Bingha…
Convergence Analysis of the Discrete Constrained Saddle Dynamics and Their Momentum Variants
Qiang Du, Baoming Shi
We study the discrete constrained saddle dynamics and their momentum variants for locating saddle points on manifolds. Under the assumption of exact unstable eigenvectors, we estab…
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…
A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate
Qiang Du, Baoming Shi, Lei Zhang +1
We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of…
A Stochastic Algorithm for Searching Saddle Points with Convergence Guarantee
Baoming Shi, Lei Zhang, Qiang Du
Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global struc…
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…
Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions
Baoming Shi, Yucen Han, Apala Majumdar +1
We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau-de Gennes framework. There are…
A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms
Yucen Han, Baoming Shi, Lei Zhang +1
We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a…
Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids
Baoming Shi, Yucen Han, Jianyuan Yin +2
We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based a…
Nematic liquid crystals in a rectangular confinement: solution landscape and bifurcation
Baoming Shi, Yucen Han, Lei Zhang
We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of…