119 citations · 773 across the 45 of their papers we have counts for
45 papers
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…
On the approximation of quasiperiodic functions with Diophantine frequencies by periodic functions
Kai Jiang, Shifeng Li, Pingwen Zhang
We present an analysis of the approximation error for a -dimensional quasiperiodic function with Diophantine frequencies, approximated by a periodic function with the fundam…
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…
Numerical Methods and Analysis of Computing Quasiperiodic Systems
Kai Jiang, ShiFeng Li, Pingwen Zhang
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is o…
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…
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,…
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…
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…
Detecting Suspected Epidemic Cases Using Trajectory Big Data
Chuansai Zhou, Wen Yuan, Jun Wang +5
Emerging infectious diseases are existential threats to human health and global stability. The recent outbreaks of the novel coronavirus COVID-19 have rapidly formed a global pande…
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…
A note to paper: Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
Hailiang Liu, Hui Zhang, Pingwen Zhang
This note serves to provide additional details for the proof of Lemma 3.6 in our paper [Liu, Zhang and Zhang, Comm. Math. Sci., 3(2005), pp.201-218]. Moreover, we will also present…
Construction of a pathway map on a complicated energy landscape
Jianyuan Yin, Yiwei Wang, Jeff Z. Y. Chen +2
How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce…
Nonlocal Diffusion Operators for Normal and Anomalous Dynamics
Weihua Deng, Xudong Wang, Pingwen Zhang
The Laplacian is the infinitesimal generator of isotropic Brownian motion, being the limit process of normal diffusion, while the fractional Laplacian serves as the i…
Onsager-theory-based dynamic model for nematic phases of bent-core molecules and star molecules
Jie Xu, Pingwen Zhang
We construct the molecular model and the tensor model for the dynamics of the nematic phases of bent-core molecules and star molecules in incompressible fluid. We start from the mo…
Boundary problems for the fractional and tempered fractional operators
Weihua Deng, Buyang Li, Wenyi Tian +1
For characterizing the Brownian motion in a bounded domain: , it is well-known that the boundary conditions of the classical diffusion equation just rely on the given informatio…
A Fast Algorithm for the Moments of Bingham Distribution
Yixiang Luo, Jie Xu, Pingwen Zhang
We propose a fast algorithm for evaluating the moments of Bingham distribution. The calculation is done by piecewise rational approximation, where interpolation and Gaussian integr…
Computing optimal interfacial structure of modulated phases
Jie Xu, Chu Wang, An-Chang Shi +1
We propose a general framework of computing interfacial structures between two modulated phases. Specifically we propose to use a computational box consisting of two half spaces, e…
Stability of half-degree point defect profiles for 2-D nematic liquid crystal
Zhiyuan Geng, Wei Wang, Pingwen Zhang +1
In this paper, we prove the stability of half-degree point defect profiles in for the nematic liquid crystal within Landau-de Gennes model.
Computing optimal interfacial structure of ordered phases
Jie Xu, Chu Wang, An-Chang Shi +1
We propose a general framework of computing interfacial structure. If an ordered phase is involved, the interfacial structure can be obtained by simply minimizing the free energy w…
Transition of defect patterns from 2D to 3D in liquid crystals
Yang Qu, Ying Wei, Pingwen Zhang
Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention. In this paper, we investig…
Application of Self-Consistent Field Theory to Self-Assembled Bilayer Membranes
Pingwen Zhang, An-Chang Shi
Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block copolymers are ubiquitous in biological and physiochemical systems. The shape and…