98 citations · 325 across the 26 of their papers we have counts for
26 papers
Computing stable configurations of confined smectic liquid crystals with a deep variational framework
Yuchen Xie, Baoming Shi, Yucen Han +1
Smectic liquid crystals are layered liquid-crystalline phases characterized by orientational order and periodic density modulation. Although their structures can be modeled using c…
Subspace curvature-scaling high-index saddle dynamics for accelerating ill-conditioned saddle point searches
Jianyuan Yin, Lei Zhang, Zhiyi Zhang
We propose a subspace curvature-scaling high-index saddle dynamics (SCS-HiSD) method to accelerate high-index saddle dynamics (HiSD) for locating ill-conditioned saddle points. The…
Exploring transition pathways in the Landau-Brazovskii model
Zhiyi Zhang, Gang Cui, Kai Jiang +4
The Landau-Brazovskii model provides a theoretical framework for describing various phases arising from competing short- and long-range interactions in many physical systems. In th…
Nucleation and phase transition of decagonal quasicrystals
Tiejun Zhou, Lei Zhang, Pingwen Zhang +2
In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-pres…
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…
Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and…
Revealing Excited States of Rotational Bose-Einstein Condensates
Jianyuan Yin, Zhen Huang, Yongyong Cai +2
Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the rotational Bose-Einstein condens…
A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the force in the standard saddle dyna…
Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We present a mathematical and numerical investigation to the shrinkingdimer saddle dynamics for finding any-index saddle points in the solution landscape. Due to the dimer approxim…
Discretization and index-robust error analysis for constrained high-index saddle dynamics on high-dimensional sphere
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensio…
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…
Error estimates for Euler discretization of high-index saddle dynamics
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
High-index saddle dynamics provides an effective means to compute the any-index saddle points and construct the solution landscape. In this paper we prove error estimates for Euler…
Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm
Bing Yu, Lei Zhang, Pingwen Zhang +1
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper,…
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…
Solution Landscapes of the Simplified Ericksen--Leslie Model and its Comparison with the Reduced Landau--de Gennes Model
Yucen Han, Jianyuan Yin, Yucheng Hu +2
We investigate the solution landscapes of a simplified Ericksen--Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent bou…
Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model
Yucen Han, Joseph Harris, Lei Zhang +1
We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a paramete…
Modeling and Computation of Liquid Crystals
Wei Wang, Lei Zhang, Pingwen Zhang
Liquid crystal is a typical kind of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over…
Solution landscape of the Onsager model identifies non-axisymmetric critical points
Jianyuan Yin, Lei Zhang, Pingwen Zhang
We investigate critical points of the Onsager free-energy model on a sphere with different potential kernels, including the dipolar potential, the Maier-Saupe potential, the couple…
Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement
Zhen Xu, Yucen Han, Jianyuan Yin +3
We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki model. The projected saddle…
Transition pathways connecting crystals and quasicrystals
Jianyuan Yin, Kai Jiang, An-Chang Shi +2
Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals…
Solution landscape of a reduced Landau-de Gennes model on a hexagon
Yucen Han, Jianyuan Yin, Pingwen Zhang +2
We investigate the solution landscape of a reduced Landau--de Gennes model for nematic liquid crystals on a two-dimensional hexagon at a fixed temperature, as a function of ---t…
Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach
Yucen Han, Zirui Xu, An-Chang Shi +1
A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extensi…
A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons
Yucen Han, Apala Majumdar, Lei Zhang
We study reduced nematic equilibria on regular two-dimensional polygons with Dirichlet tangent boundary conditions, in a reduced two-dimensional Landau-de Gennes framework, discuss…