6 papers
Uniform asymptotics and entropy structure of the Bingham distribution in arbitrary dimensions
Dawei Wu, Lei Zhang, Pingwen Zhang
The Bingham distribution is widely used to model directional data with antipodal symmetry, and its normalizing constant and moments play a central role in statistical inference…
Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials
Thialita M. Nascimento, Lei Zhang
In this work, we study local minimizers of elliptic functionals with strong absorption terms and unbounded, sign-changing sources. These problems naturally interpolate between two…
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…
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…
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…